| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Department of Earth Sciences
University of Southern
California
Los Angeles, California, 90089-0740
(E.H.F.)
Southern California Earthquake Center
University of Southern
California
Los Angeles, California, 90089-0740
(SCEC)
 |
Abstract |
|---|
 Top Abstract IntroductionDefinition of Site EffectPrevious Research and Important...SCEC Phase III StudiesDiscussionAcknowledgmentsReferences |
|---|
Given the somewhat arbitrary nature of the site-effect distinction, it must be carefully defined in any given context. With respect to PSHA, we define the site effect as the response, relative to an attenuation relationship, averaged over all damaging earthquakes in the region. A diligent effort has been made to identify any attributes that predispose a site to greater or lower levels of shaking. The most detailed maps of Quaternary geology are not found to be helpful; either they are overly detailed in terms of distinguishing different amplification factors or present southern California strong-motion observations are inadequate to reveal their superiority. A map based on the average shear-wave velocity in the upper 30 m, however, is found to delineate significantly different amplification factors. A correlation of amplification with basin depth is also found to be significant, implying up to a factor of two difference between the shallowest and deepest parts of the Los Angeles basin. In fact, for peak acceleration the basin-depth correction is more influential than the 30-m shear-wave velocity. Questions remain, however, as to whether basin depth is a proxy for some other site attribute.
In spite of these significant and important site effects, the standard deviation of an attenuation relationship (the prediction error) is not significantly reduced by making such corrections. That is, given the influence of basin-edge-induced waves, subsurface focusing, and scattering in general, any model that attempts to predict ground motion with only a few parameters will have a substantial intrinsic variability. Our best hope for reducing such uncertainties is via waveform modeling based on first principals of physics.
Finally, questions remain with respect to the overall reliability of attenuation relationships at large magnitudes and short distances. Current discrepancies between viable models produce up to a factor of 3 difference among predicted 10% in 50-yr exceedance levels, part of which results from the uncertain influence of sediment nonlinearity.
|
Introduction |
|---|
|
TopAbstractIntroductionDefinition of Site EffectPrevious Research and Important...SCEC Phase III StudiesDiscussionAcknowledgmentsReferences |
|---|
Because both waveform modeling and dynamic analyses are in a relatively early stage of development, their application is generally reserved for critical facilities. Although PSHA is more deeply rooted in engineering practice, a fact reflected in current building codes (e.g., BSSC, 1995, 1998), important questions remain with respect to representing both earthquake sources (e.g., Field et al., 1999; Petersen et al., 2000) and wave-propagation effects (e.g., Senior Seismic Hazard Analysis Committee [SSHAC], 1997). Finally, it should be noted that PSHA and waveform modeling are not completely independent, as waveform modeling has been used to develop attenuation relationships for low-seismicity regions (e.g., Toro et al., 1997), and synthetic seismograms are often rescaled in practice to be consistent with empirical attenuation relationships (N. Abrahamson, written comm., 1999). Nevertheless, the distinction provides a useful conceptual framework as we seek a more complete representation of seismic hazard.
With funding primarily from the National Science Foundation and the United States Geological Survey (USGS), a consortium of academic, industry, and governmental organizations formed the Southern California Earthquake Center (SCEC) in 1991. The rationale for establishing SCEC was to facilitate an interdisciplinary, system level approach to earthquake hazard analysis. As stated in the original proposal, the specific goal was to do the following:
integrate research findings from various disciplines in earthquake-related science to develop a prototype probabilistic seismic hazard model (master model) for southern California. In essence,... the solid earth dynamics equivalent of global atmospheric and ocean circulation models....
The first milestone toward achieving this goal was the Phase II report (Working Group on California Earthquake Probabilities [WGCEP] 1995), which represented a large-scale effort to integrate seismic, geologic, and geodetic information into a single model of earthquake occurrence for southern California. As is often the case with scientific endeavors of this scale, the report seemed to raise more questions than it answered, particularly in terms of a discrepancy between observed and predicted seismicity rates (see Field et al. (1999) for the most recent overview). This problem was inherited by the subsequent generation of official seismic-hazard maps for California (Petersen et al., 1996; Petersen et al., 2000), which remain in use today. A recent working group has already revised earthquake probabilities for northern California (WGCEP, 1999), and a separate effort has been initiated by SCEC and the USGS to improve seismic hazard source models in southern California (http://www.scec.org/research/RELM).
The other element needed for PSHA is the ground-motion model. All of the studies mentioned thus far examined hazard for rock-site conditions only. In fact, as discussed subsequently, today's building codes are based on rock-site hazard maps and apply a site correction at a later stage. A more sophisticated and presumably reliable approach would be to apply site corrections within the hazard calculations directly. However, it has not been entirely clear how this should be done, as reflected by the fact that the most comprehensive treatment of PSHA to date (SSHAC, 1997), left the issue to future studies.
To fill this gap, SCEC initiated the Phase III effort in 1994. The goal has been to determine how, and to what extent, site effects can be accounted for in PSHA. The findings of the Phase III working group are presented in the various articles that compose this special issue of the BSSA, with this article providing an overview. The project has evolved dramatically since its inception, with significant contributions being made by several participants not part of the original Phase III working group (Joyner, 2000; Magistrale et al., 2000, Wald and Mori, 2000; Wills et al., 2000).
While we have concentrated on incorporating site effects in PSHA, many of our findings should be useful for waveform modeling as well. In fact, several of the Phase III papers use synthetic seismograms to address PSHA-related questions (Olsen, 2000; Anderson, 2000; Ni et al., 2000). Furthermore, while the SCEC master-model goal was originally articulated in terms of PSHA, considerable resources have been devoted to waveform modeling as well (e.g., Aki et al., 1995). Finally, it should be noted that SCEC does not make official hazard estimates. Rather, it applies an interdisciplinary approach to developing and testing the ingredients for seismic hazard analysis, and then distributes these results to users and government organizations in charge of hazard estimation.
This article is not intended to provide a comprehensive discourse on the physics of site response, nor does it represent a thorough review of the literature. Rather, the level of discussion has been economized with respect to accounting for site effects in PSHA of southern California. Readers interested in less provincial and/or more general reviews are referred to Aki (1988), Aki and Irikura (1991), Bard (1994), and to the proceedings of the Second International Symposium on the Effects of Surface Geology on Seismic Motion (Yokohama, Japan, 2–3 December 1998). Additional discussion and references can also be found in the individual articles that make up this issue.
Although our focus is on southern California, many of our findings should point to potentially useful lines of inquiry in other regions as well. However, there are some important conditions that have not been addressed in this collection of papers, such as the behavior of very soft sediments like San Francisco bay mud, which are much less pervasive in southern California. We have also ignored vertical-component ground motion.
Finally, history has shown that while scientific theories may be fleeting, the longest-lasting legacies of projects of this scope are often the data sets they generate. Therefore, a web page has been established to facilitate data distribution (http://www.scec.org/research/phase3). This site also contains several web-based applications that allow users to evaluate and test various attenuation relationships with different input values.
|
Definition of Site Effect |
|---|
|
TopAbstractIntroductionDefinition of Site EffectPrevious Research and Important...SCEC Phase III StudiesDiscussionAcknowledgmentsReferences |
|---|
The convulsion was greater along the Mississippi, as well as along the Ohio, than in the uplands. The strata in both valleys are loose. The more tenacious layers of clay and loam spread over the adjoining hills... suffered but little derangement. (Drake, 1815, p. 82).
Site effects were also recognized in the great Japan earthquake of 1891 (Milne, 1898), the 1906 San Francisco earthquake (e.g., Wood, 1908), and the Long Beach earthquake of 1933 (Wood, 1933). The first quantitative study of sediment amplification in southern California was by Gutenberg (1957). Despite these early observations, the incorporation of site effects in hazard estimation remains somewhat crude. Part of the problem is the ambiguous meaning of site response.
Many studies divide the factors influencing earthquake ground motion into source, path, and site effects, a distinction that has proven useful for understanding and predicting seismic motion (e.g., Aki, 1988). It is important to keep in mind, however, that this distinction is ultimately artificial. For example, one might logically define a site as the extent of a sedimentary deposit; but this leads to problems when such deposits are several kilometers deep and bounded by earthquake-generating faults. For example, how should one distinguish between path and site effects for a fault that ruptures along the edge of the Los Angeles basin? Such ambiguities inevitably lead to arbitrary distinctions, such as the 30-m-depth cutoff used to characterize site conditions in current building codes (e.g., Dobry et al., 2000). The practical importance of understanding site effects has fueled a great deal of research; the lack of a clear, absolute definition has led to a somewhat disparate body of literature on the topic. Nevertheless, the concept of site response is still useful provided the definition is clearly understood in any particular context.
Recall that the goal of PSHA is to consider all damaging earthquakes in a region. In this context, therefore, the site effect should be defined as the average behavior, relative to other sites, given all potentially damaging earthquakes. That is, because we don't know which earthquake will rupture next, we must average the site response over the variety of possible earthquake source locations. This will inevitably produce an intrinsic variability in the site response by virtue of different incidence angles, azimuths, and wave types. To warrant application of this average effect for microzonation purposes, the difference between sites must, to some extent, exceed the intrinsic variability at each site (Hudson, 1972; Aki, 1988).
It is also important that attributes used to define the site be readily available (e.g., in map form) or realistically obtainable, and that site factors be defined relative to the reference motion appropriate to whatever source-path model is being applied. For example, it would not be appropriate to apply a sediment-to-bedrock Fourier spectral ratio as a correction to a rock-site peak-acceleration attenuation relationship. In other words, given the ultimate ambiguity between path and site effects, the specification of one must be made in the context of the other.
|
Previous Research and Important Issues |
|---|
|
TopAbstractIntroductionDefinition of Site EffectPrevious Research and Important...SCEC Phase III StudiesDiscussionAcknowledgmentsReferences |
|---|
Empirical Site Response Estimates
From Nuclear Explosions. In one of the 1985 USGS articles, Rogers
et al. (1985)
presented empirical site-response estimates by applying the
sediment-to-bedrock spectral-ratio technique pioneered by Borcherdt
(1970). Because direct
earthquake observations were limited to those of the 1971 San Fernando
earthquake, most of their recordings were of underground nuclear explosions
from the Nevada test site (Rogers et
al., 1979; Rogers et
al., 1984). After averaging results over three frequency
bands, they applied statistical clustering techniques to determine which of
several geotechnical parameters were most influential on site-response
estimates. At frequencies above 2 Hz, they found near-surface void ratio (a
proxy for shear wave velocity) to be most influential, with Holocene thickness
and/or depth to basement influential as well. Below 2 Hz they found Quaternary
thickness and/or depth to basement rock to be the controlling factors. They
noted, however, that some of the factors are "highly
interdependent" (Rogers et
al., 1985, p. 235), making it difficult to separate near
surface effects from deeper basin effects. As discussed below, this problem
continues to plague us today. Comparing nuclear-explosion data to recordings
of the 1971 San Fernando earthquake, they also concluded that nonlinear site
effects are negligible (also discussed later).
From Coda Waves. In a different approach, Su and Aki (1995) generated empirical site-amplification maps for southern California using the S-wave coda methodology developed by Aki and Chouet (1975), Tsujiura (1978), and Phillips and Aki (1986). One of the original motives for using coda waves was to take advantage of the relatively abundant vertical-component network data for which the corresponding direct S-wave arrivals are generally clipped. However, for PSHA, this approach is perhaps most appealing in that the coda is thought to be composed of scattered energy coming in from a variety of directions (Aki and Chouet, 1975), so the site-response estimates might naturally reflect an average over various source locations. Unfortunately, there is some disagreement on whether coda site-response estimates are consistent with the direct S-wave response; while some have found agreement between the two (e.g., Tsujiura, 1978; Kato et al., 1995), others have not (e.g., Margheriti et al., 1994; Seekins et al., 1995; Bonilla et al., 1997; Field 1996). Another concern is that the Su and Aki (1995) amplification factors are based on vertical-component network data and may not be applicable to horizontal-component motion.
From Ambient Noise. The use of ambient seismic noise (microseisms and/or microtremors) was also proposed to make up for the dearth of direct earthquake data. For example, Kagami et al. (1982) examined microtremor spectral ratios in the Los Angeles basin and found the amplitudes to correlate with depth to basement rock, nuclear explosions spectral ratio amplitudes of Rogers et al. (1979), and ratios obtained for the 1971 San Fernando earthquake. Kagami et al. (1986) found similar results from a more extensive set of observations carried out in the San Fernando Valley, and a two-dimensional, theoretical model was constructed by Navaro et al. (1990) which "shows a remarkable coincidence with the microtremor experimental data." In spite of these and other encouraging results (e.g., Yamanaka et al., 1993), questions still prevail with respect to the applicability of ambient noise measurements (see Bard, 1998, for a review). As such, no microtremor-based amplification map has been forthcoming for the region. Regardless of whether such a map can be generated, array analyses of ambient noise data may still prove useful in determining subsurface structure (e.g., Aki, 1957; Okada, 1987; Yamanaka et al., 1994).
From Recent Earthquake Data. The 1994 Northridge earthquake sequence finally provided the volume of digital data needed to make direct and widespread empirical estimates of earthquake site response in southern California. For example, Hartzell et al. (1996) inverted over 1,300 shear-wave recordings for site effects at 90 sites. Bonilla et al. (1997) did a similar analysis, but examined other site-response estimates as well, including horizontal to vertical ratios and coda amplification factors. In terms of S-wave amplification factors, both studies obtained spectral-ratio estimates effectively similar to those introduced by Borcherdt (1970), but by applying the generalized-inverse formulation of Andrews (1986). One reason for the latter approach is that many sediment sites in the region lack the nearby bedrock site needed to compute traditional spectral ratios. In the generalized-inverse approach, a simple patheffect correction is made, and the source and site effects are subsequently solved for simultaneously. The potential problem with such site effect estimates is that any difference between the true and assumed path effect will be mapped into the site response. Because all Northridge aftershocks emanate from the same main-shock region, this means that any regional focusing effects will contaminate the site-response estimates. Alternatively, we could include these regional effects in our definition of "site response", but then acknowledge that there will be some intrinsic variability among earthquakes throughout the region. Either way, the question remains as to whether such site-response estimates obtained from one earthquake (or aftershock sequence) will apply to those of another.
Harmsen (1997) performed a similar inversion for site response at 281 locations in the Los Angeles region using strong-motion records from the 1971 San Fernando, 1987 Whittier Narrows, 1991 Sierra Madre, and 1994 Northridge main shocks. In using these four earthquakes, Harmsen to some extent averaged over biases associated with each, at least at those sites where more than one earthquake was recorded.
Hartzell et al. (1998) combined the Northridge after-shock results of Hartzell et al. (1996) with the four main-shock results of Harmsen (1997) to produce a series of "First-Generation Site-Response Maps for the Los Angeles Region." These were obtained by contouring between all available sediment-site spectral-amplification values. As such, they represent the most comprehensive, empirically based site-amplification maps available for the Los Angeles region. Their 1–3 Hz map is reproduced here (Fig. 1). Note that it identifies several isolated locations with relatively high amplification values. The relevant question for PSHA is whether these will remain high for earthquakes other than those represented in the inversions, especially since no formal uncertainty estimates are provided. Nevertheless, the map does provide a model that can be tested against future data. In fact, one of the Phase III articles discussed below (Wald and Mori, 2000) compares the Hartzell et al. (1998) amplification factors with theoretical predictions based on borehole data.
|
Near-Surface Effects
As discussed by Joyner and Fumal
(1985), seismological theory
implies that ground motion should depend on near-surface conditions. For
example, if losses due to reflection, scattering, and anelastic attenuation
are negligible, then the energy along a tube of rays is conserved, and the
amplitude is proportional to:
 |
is density and ß is shear-wave velocity (e.g.,
Bullen, 1965;
Aki and Richards, 1980). Because determination of density and seismic velocities requires costly geotechnical studies, one naturally looks to geology for a proxy. Most traditional geological maps were produced with mineral-resource development in mind, emphasizing differences in bedrock units while lumping sediments together. Recognizing this shortcoming for earthquake ground-motion estimation, Tinsley and Fumal (1985) developed detailed geological maps for the Los Angeles region. Most notably, they divided Quaternary alluvium into eight subunits on the basis of age ("young" Holocene versus "old" Pleistocene) and grain size (fine, medium, coarse, and very coarse). A version of the Tinsley and Fumal (1985) map, compiled and modified slightly by Park and Elrick (1998), is shown in Figure 2. This map remains one of the most detailed forms of Quaternary geological data available for the region. It therefore makes sense to relate relevant seismic parameters to each subunit.
|
Because density is relatively constant with depth, shear-wave velocity is the logical choice for representing site conditions. The question is how to reduce the depth-dependent velocity to a single, representative value. Joyner et al. (1981) proposed averaging the velocity over a depth range corresponding to one-quarter the wavelength of the period of interest. This generally produces frequency-dependent velocity values because longer wavelengths extend to, or sample, greater depths. By relating 1-Hz quarter-wavelength velocities inferred from 33 borehole sites to the detailed geology units of Tinsley and Fumal (1985), Fumal and Tinsley (1985) developed 1-Hz shear-wave velocity maps for the Los Angeles region.
The quarter-wavelength velocity is elegant in terms of having a physically
based extent of depth averaging. However, most previous boreholes were limited
to a depth of 
30 m, which corresponds to the extent of penetration
achievable by a drill rig in a single day of operation, with a step-function
increase in cost thereafter. This depth limitation generally precludes
computation of the quarter-wavelength velocity over at least some frequencies
of engineering interest. In fact, Fumal and Tinsley
(1985) had to extrapolate
borehole data in order to get the 33 values they applied.
An alternative is to compute the average velocity to a standard depth. For example, Tinsley and Fumal (1985) averaged velocities down to 30 m. This increased the number of average borehole velocities from 33 (under the quarter-wavelength definition) to 84. Using these values, they grouped like geological units together and thereby produced 30-m shear-wave velocity maps for the region.
Interestingly, the practical advantage of using average 30-m shear-wave velocity (referred to hereafter as V30) has prevailed over the theoretical superiority of the quarter-wavelength measure. Specifically, based on empirical studies (e.g., Borcherdt and Glassmoyer, 1992) and the recommendation of Borcherdt (1993, 1994), V30 was adopted as a means of classifying sites in the 1994 NEHRP building code provisions (BSSC, 1995). V30 has also been used to parameterize site effects in the attenuation relationships of Boore et al. (1993, 1997).
One might naturally question the validity of using V30
(or the quarter-wavelength velocity for that matter) when strong impedance
contrasts exist. Such discontinuities will cause reflections from and/or
reverberations within layers, thereby violating the conservation of energy
arguments mentioned previously. However, assuming no anelastic attenuation,
Day (1996) demonstrated
theoretically that even if strong resonances exist, the response averaged over
some finite-frequency bandwidth is still inversely proportional to
averaged to some depth; the
greater the depth, the greater the frequency resolution. Taken to the limit,
this means that the response averaged over all frequencies (zero resolution)
depends only on the velocity and density at zero depth. Considering this issue
further, Anderson et al.
(1996) found additional
support for the use of V30, but added that attenuation
effects should be accounted for as well, especially at deeper sediment
sites.
Basin Effects
Basin-Edge-Induced Waves. Examining displacement records from the
1971 San Fernando earthquake, Hanks
(1975) noted that surface
waves were prevalent in the Los Angeles basin. From an array analysis, Liu and
Heaton (1984) demonstrated
that these surface waves were converted from body waves along the basin edge.
Vidale and Helmberger (1988)
successfully modeled the behavior using two-dimensional finite-difference
approach. A particularly good example of basin-edge induced waves
(Fig. 3) was obtained in the
Coachella Valley during the 1992 Landers earthquake after-shock sequence
(Field, 1996). Although the
initial S waves are amplified relative to bedrock, the largest
amplitudes come from a wave that propagates across the valley from the
northeastern edge (see caption for details). Interestingly, this area of the
Coachella Valley had the largest level of shaking (outside the epicentral
region) during the 2000 Hector Mine earthquake
(Scientists from the USGS, SCEC, and
CDMG, 2000), presumably due to basin-edge-induced waves. This
should not be surprising given the close juxta-position of the Landers and
Hector Mine ruptures. The relevant question with respect to PSHA is whether
this part of the Coachella Valley will constitute a bright spot when the
earthquake is in an entirely different location.
|
Subsurface Focusing. Another important basin effect is focusing caused by subsurface structure. Perhaps the most dramatic example of this was observed in Santa Monica during the Northridge earthquake sequence (Gao et al., 1996). Aftershock recordings just 650 m apart exhibited peak-motion differences of up to a factor of 5 (Fig. 4). These differences generally correlate with the damage distribution of the main shock (Gao et al., 1996). Such observations are at least 100 years old.
|
It is an easy matter to select two stations within 1,000 feet of each other where the average range of horizontal motion at the one station shall be five times, and even ten times, greater than it is at the other (Milne, 1898).
However, modern studies are providing the physical explanation for this variability. A debate remains over whether the damage in Santa Monica resulted from the deeper (Gao et al., 1996) or shallower (Alex and Olsen, 1998; Graves et al., 1998) wedge structure depicted in Figure 4. Both explanations involve constructive interference, or focusing, of waves traveling different paths. As such, they both imply that the exact pattern of shaking will be sensitive to source location, a fact born out by the aftershock observations (Gao et al., 1996). With respect to PSHA, this raises the question of whether the amplification pattern from the Northridge earthquake, or any site-effect map that is dominated by this earthquake (e.g., Fig. 1), is applicable to other events as well. It also raises the question of how much effort is warranted in determining the exact subsurface structure when the final result will be sensitive to the unknown locations, and perhaps even slip distributions, of future earthquakes.
Another case of subsurface focusing was documented by Hartzell et al. (1997) in Sherman Oaks, California. In fact, they concluded that "... sedimentary structures in the upper 1 to 2 km and topography on the sediment-basement interface... can be the dominant factor in the modification of local ground motion" (p. 1377). This also suggests that the amplification pattern will be somewhat, perhaps even largely, dependent on earthquake location.
Intrinsic Variability. The presence of basin-edge-induced surface waves and focusing effects does not bode well for predicting site effects in PSHA; it suggests that site response will have a large intrinsic variability with respect to source location. This would help explain several studies, in southern California alone, that identify large differences in earthquake shaking over hundred-meter distances (e.g., Steidl, 1993; Field and Hough, 1996; Hartzell et al., 1996, 1997; Meremonte et al., 1996), and that find ground motion to be sensitive to source location (e.g., Frankel, 1994; Hough et al., 1995; Meremonte et al., 1996; Scrivner and Helmberger, 1999). In fact, from 3D finite-difference simulations for a simplified San Andreas fault rupture, Frankel (1993) showed that the amplification pattern in the San Bernardino Valley is sensitive to the distribution of source asperities as well. Thus, not only is the separation of path and site effects somewhat vague and arbitrary, but so is the separation of source effects.
Average Behavior. Although an intrinsic variability of basin response with respect to rupture location seems inevitable, there may be some systematic behavior on average. Recall, for example, that Rogers et al. (1985) identified a correlation between spectral-ratio amplitudes and basin depth. In fact, this had been noted even earlier (e.g., Trifunac and Lee, 1978; Rogers et al., 1979), and has been noted since (e.g., Campbell, 1987; Hartzell et al., 1996; Hartzell et al., 1998). For this reason, and as discussed below, considerable effort has gone into understanding a possible basin-depth effect in the Phase III collection of articles.
Nonlinear Site Effects
In the complications described previously, we have so far ignored the issue
of sediment nonlinearity. To the extent that sediments yield at high levels of
strain—a violation of Hooke's law resulting in a nonlinear
response—amplification factors can be dependent on the ground-motion
level (Reid, 1910). Because
the vast body of literature on this topic has been reviewed elsewhere (e.g.,
Beresnev and Wen, 1996;
Field et al., 1998a;
Yoshida and Iai, 1998), only
a very brief overview in the context of southern California is given here.
The engineering community has long believed that sediment nonlinearity is significant (e.g., Schnabel et al., 1972). Their perspective is based largely on laboratory studies, where observed stress-strain loops imply a reduced effective shear modulus and an increased damping (lower Q) at higher levels of strain. On the basis of theoretical modeling, especially at the highest levels of shaking, the net effect is believed to be a reduction of amplification factors with increasing ground motion (e.g., Borcherdt, 1994). As discussed below, this perspective is reflected in the current generation of building codes (e.g., Dobry et al., 2000).
Given a dearth of direct observations and a concern that laboratory studies may be misleading, seismologists traditionally have been skeptical of the significance of sediment nonlinearity. Their approach has been to adopt the simpler, linear model until data demand otherwise. For example, based in part on the work of Rogers et al. (e.g., 1995) discussed earlier, Aki's 1988 review article concluded that: "... except for the obvious case of liquefaction,... the amplification factor obtained using weak-motion data can be used to predict... strong ground motion..." (Aki, 1988, p. 115). Interestingly, Aki later became one of the earliest seismological converts, stating that: "Non-linear amplification at sediment sites appears to be more pervasive than seismologists used to think" (Aki, 1993). However, agreement among seismologists was not unanimous (e.g., Wennerberg, 1996; Chin and Aki, 1996), and skeptics maintained that documented cases were isolated and/or associated with liquefaction. This left the question open, especially for sediment conditions that typify southern California.
New data with which to test the nonlinearity issue were provided by the 1994 Northridge earthquake. For example, comparing weak- and strong-motion amplification factors, Field et al. (1997) concluded that nonlinear effects were statistically significant between approximately 1.0 and 5.0 Hz. Their results, reproduced in Figure 5, generally have been corroborated by other studies (e.g., Su et al., 1998; Hartzell, 1998; and Beresnev et al., 1998; Field et al., 1998b). Thus, from a seismological perspective, sediments seemed to behave more nonlinearly during the Northridge earthquake than had been expected. From the engineering perspective, however, the Northridge data implied less nonlinearity than had been expected (e.g., Chang and Bray, 1997; Borcherdt, 1996).
|
Although results like those in Figure 5 allowed us to reject the null hypothesis that the response was linear, the averaging required to do so generally precludes a detailed understanding of the physics. In fact, according to a recent textbook on the topic, "... there is no nonlinear model of any kind established on a sound physical basis" (Ishihara, 1996, p. 28). This, coupled with a general lack of empirical data, suggests that we should expect some surprises. For example, one of the most widely used approaches for modeling sediment nonlinearity is the equivalent-linear formulation (Idriss Seed, 1968; Schnabel et al., 1972), which generally predicts that as ground motion increases, the reduction in amplification will be greater at higher frequencies. However, Yu et al. (1993) applied a more explicit nonlinear model and found that high-frequency amplification factors can actually be increased (in direct contrast to an equivalent-linear prediction). Another surprising manifestation of nonlinearity is the presence of high-frequency spikes in some acceleration records (Zeghal and Elgamal, 1994; Archuleta, 1998; Bonilla et al., 1998). These findings suggest that an open mind is needed as we sift through existing data and explore various theoretical models.
It also should be noted that purely linear models can explain some observations that previously have been attributed to nonlinearity. For example, O'Connell (1999) argues that the discrepancy shown in Figure 5 can be explained by scattering alone. He suggests that waves from different parts of an extended fault sample different volumes of crust and therefore arrive less coherently than energy from small events. If the effect is more pronounced at sediment sites than at rock sites, we might expect the discrepancy seen in Figure 5. Two lines of reasoning are presented to support this contention. First, he shows that the inclusion of empirical scattering functions in synthetic seismograms reduces amplitudes by a factor of 1.82 on average (his Table 1). However, these simulations are for sediment sites only. To explain the discrepancy in Figure 5, it remains to be shown that the scattering effect is negligible at rock sites. Second, a series of 3D finite-difference proxy experiments were carried out from which the author concluded that he could reproduce the 3-Hz empirical observations of Field et al. (1997). However, the comparison is not completely applicable in that his simulations were for peak acceleration, which is presumably more influenced by scattering than the Fourier-spectral observations of Field et al. (obtained from 20-sec windows). Nevertheless, he does point out a previously overlooked phenomenon that may be important, especially for peak-motion based attenuation relationships. More is said regarding nonlinear site response in the context of the Phase III articles below.
|
Site Amplification in Current Building Codes
The development and current use of site coefficients in building codes has
been reviewed by Dobry et al.
(2000). The 1994 and 1997
NEHRP provisions (BSSC, 1995,
1998), the 1997 Uniform
Building Code (UBC), and the 2000 International Building Code (IBC) apply the
classification scheme listed in Table
1, and the amplification factors listed in Tables
2 and
3. This overall approach was
developed by consensus, based on empirical amplification factors at lower
levels of shaking (rock PGA less than 0.1g) and on numerical
modeling of laboratory results at higher groundmotion levels (see
Borcherdt, 1994, or
Dobry et al., 2000,
for details). As discussed previously, the sites are classified according to
the average 30-m shear-wave velocity (V30). Separate
amplification factors are given for short-period response near 0.2 sec
(Fa in Table
2), and for longer-period response above 1.0 sec
(Fv in Table
3).
|
|
In current building codes the amplification factors listed in Tables 2 and 3 are applied to the ground motion given in rock-site hazard maps. Strictly speaking, this approach is not valid if several different scenarios, with different implied ground-motion levels, contribute to the rock-site hazard (e.g., to the 2% in 50 years exceedance level). In such cases, a separate site correction should be applied to each event before computing the composite hazard. For practical purposes, however, applying a single, representative amplification factor to all events may be adequate, or all that is warranted, given our present understanding of nonlinearity.
|
SCEC Phase III Studies |
|---|
|
TopAbstractIntroductionDefinition of Site EffectPrevious Research and Important...SCEC Phase III StudiesDiscussionAcknowledgmentsReferences |
|---|
Because the distinction between path and site effects (and even source effects) is ultimately artificial, any site corrections must be made in the context of the entire model. With respect to PSHA, this means the site effect should be defined relative to whatever attenuation relationship is being applied. For this reason, most of the studies in this volume are focused on the development and/or evaluation of attenuation relationships. The Phase III articles in this issue can be categorized as follows:
The above categorization is not generally used in the discussion of each article below. Rather, a more thematic narrative is followed.
Empirical Amplification Versus Theoretical Borehole Predictions
The article by Wald and Mori
(2000) compares the
site-specific empirical amplification factors of Hartzell et al.
(1998,
Fig. 1) with theoretical
predictions based on borehole data. A total of 33 sites were available for the
comparison, having both an observed value (not an interpolated value as in
Figure 1), and borehole data
within 290 m of the site. Three types of borehole-based predictions are
examined: average 30-m shear-wave velocity (V30); a
quarter-wavelength amplification factor, which is proportional to the
quarter-wavelength velocity discussed previously
(Joyner et al.,
1981); and the complete vertically incident plane S-wave
response predicted by the 1D, linear propagator-matrix method of Haskell
(1960). The comparison is made
for three frequency ranges (1–3 Hz, 3–5 Hz, and 5–7 Hz).
Their result for 1–3 Hz, which generally shows the greatest correlation,
is reproduced in Figure 6.
Interestingly, V30 is better correlated with observed
values than the quarter-wavelength or propagator-matrix amplification factors.
This implies that V30 is a better predictive parameter,
even though the other two are generally thought to be more accurate estimates.
It would appear that the more elaborate approaches are not elaborate enough to
be superior.
|
Although V30 at 1–3 Hz exhibits the highest correlation, a great deal of scatter remains. This could reflect uncertainties in the observed amplification factors, inadequacies in the predictions (e.g., the 1D and/or linear response assumption), a lack of exact colocation, or some combination of these. For example, applying a nonlinear model might increase the correlation by shifting the strong-motion predictions (open triangles) to lower values. Alternatively, there may be a large intrinsic variability in the response at each site, and there is not yet enough data to capture the average behavior (which in turn may or may not equal the borehole-based predictions in Figure 6). More analyses, and probably more data, are needed to resolve this issue. For now one should be prudent when applying the site-specific, empirical amplification factors of Hartzell et al. (1998), especially where interpolated via contouring in Figure 1. Similarly, one should recognize the potential inadequacies of any theoretical site-response prediction, especially in the context of the source-and path-effect model.
3D Finite-Difference Modeling of Basin Response
To make reliable predictions of basin response, one must have an accurate
model of the subsurface structure. Version 2 of the SCEC 3D seismic velocity
model of southern California is described in the article by Magistrale et
al. (2000). The model
consists of detailed, rule-based representations of the major southern
California basins (Los Angeles basin, Ventura basin, San Gabriel Valley, San
Fernando Valley, Chino basin, San Bernardino Valley, and the Salton Trough)
embedded in a 3D crust over a variable depth Moho. Outside the basins the
model is based on regional tomographic results, and Moho depths are determined
from receiver-function analyses. Shallow basin sediment velocities are
constrained by borehole data and the Wills et al.
(2000) map of
V30 (described in more detail later). The model is
implemented in a computer code that generates any specified 3D mesh of seismic
velocity and density values. A fence diagram of Magistrale et al.
(2000) S-wave
velocities is shown in Figure
7.
|
Recall that an important question is the intrinsic variability of basin response with respect to different earthquake source locations. Due to a present dearth of observations, this question must be addressed theoretically. The article by Olsen (2000) presents long-period (0–0.5 Hz) 3D finite-difference basin-response simulations for nine different scenario earthquakes. An earlier version of the Magistrale et al. (2000) structural model was used because the latter was not yet available (version 1 rather than version 2; see the individual articles for an exact description of the difference). The basin depth defined by the 2.5 km/sec shear-wave velocity isosurface for this model is shown in Figure 8, and the simulation results are shown in Figure 9. As a validation exercise, one of the simulations was for the 1994 Northridge earthquake. Figure 9 includes a comparison between predicted and observed peak velocities for this event (upper right). The agreement is generally within a factor of two.
|
|
The color maps in Figure 9 represent peak velocities for each simulated event, normalized by those from the same event in the background bedrock model. Each has also been normalized with respect to a 1D vertically propagating S-wave amplification factor. Thus, Figure 9 represents a reasonable attempt to isolate 3D basin effects for each event. Note that the amplification pattern varies greatly among the nine scenarios, implying a large intrinsic variability. In particular, the amplification pattern for the San Andreas fault differs depending on whether the rupture originates at the northwest or southeast end of the fault (bottom row in Figure 9). This sensitivity to the details of rupture is similar to what Frankel (1993) noted for the San Bernardino valley, and as previously mentioned, is an example of how the distinction between not only path and site effects, but also source effects, is ultimately artificial. The variability of amplification with respect to source location, let alone rupture, exacerbates the development of a generic amplification map. It again exemplifies how empirical estimates based on limited data (e.g., Fig. 1) may produce misleading results.
Given the large intrinsic variability in Figure 9, is there any systematic behavior that can be taken into account? As discussed previously, several studies have noted a correlation between the degree of amplification and basin depth. In fact, careful scrutiny of Figures 8 and 9 suggests such an effect. Figure 10 shows the average amplification versus depth (to the 2.5 km/sec shear-wave velocity isosurface) for each of the Olsen (2000) scenarios. Again, a large variability among events is observed, but a trend with basin depth is clear. The response averaged over all the earthquakes implies an amplification factor of about two at the deepest basin sites.
|
Wald and Graves (1998) have demonstrated that uncertainties in the basin model can have a significant effect on 3D ground-motion predictions. Therefore, one should be cautioned against overinterpreting the details of any simulation. However, the large intrinsic variability, and increase in average amplification with basin depth, are presumably robust inferences. Although the former is somewhat disappointing in terms of predicting ground motion, the latter lends support to the notion that basin depth may be a useful parameter in earthquake hazard estimation.
Evaluation and Development of Attenuation Relationships and Their Implications with Respect to PSHA
We now focus on accounting for site effects in PSHA. Again, in the context
of the source and path effect model, the question is how to appropriately
modify an attenuation-relationship prediction. Therefore the remainder of the
Phase III articles have concentrated on compiling new and relevant data,
evaluating existing attenuation relationships, developing new attenuation
relationships for southern California, and evaluating the implications of all
relationships with respect to PSHA. Following Field and Petersen
(2000), differences in ground
motion that exceed 10% are referred to here as "important" because
this is the threshold that typically influences engineering design. Similarly,
"significant" is reserved for statistical statements at the
one-sigma level (68% confidence), which is also customary in earthquake
engineering.
PSHA Basics. The goal of PSHA is to calculate the rate or probability of exceeding various levels of ground motion over a specified period of time, given all possible earthquakes in the region (Cornell 1968; Reiter, 1990). The two main components needed for the calculation are the source model and the attenuation relationship(s). Stated most simply, the source model specifies the magnitude, location, and probability of occurrence for all possible earthquakes in the region. The attenuation relationship gives an estimate of the ground motion at a site for a given earthquake. Specifically, it gives the mean and standard deviation for a ground-motion parameter (e.g., that natural log of PGA or response spectrum ordinate at a particular period), as a function of magnitude, distance, site type, faulting style, and sometimes, other parameters. The standard deviation, often referred to as sigma, reflects the inevitable imprecision or uncertainty associated with any model that strives to predict complex earthquake ground motion with so few parameters. This uncertainty is "aleatory" (dependent on chance) in that it reflects the intrinsic variability that cannot be reduced without changing the model (e.g., adding more parameters). An important question addressed below is whether this intrinsic variability can be significantly reduced with a more elaborate treatment of site effects.
For a given set of independent variables (i.e., magnitude, distance, site type, etc.), there is presumably a "true" mean and standard deviation of the ground-motion parameter for the entire population of events. The true values are, of course, unknown a priori. Rather, they are estimated from empirical or quasi-empirical data, usually by regression analysisassuming some analytical form. Many such attenuation relationships have been developed, several of which are documented in a special issue of Seismological Research Letters (1997, Volume 68, Number 1; see Abrahamson and Shedlock, 1997, for an overview). Attenuation relationships can differ in the following ways: (1) the assumed functional form; (2) the number and definition of independent variables; (3) the data selection/rejection criteria; and (4) the statistical treatment of sparse or unbalanced data. Given these choices, it is not surprising that different attenuation relationships often predict different levels of ground motion under equivalent conditions. Such disparities are referred to as "epistemic" uncertainties (related to a lack of knowledge) because additional studies and/or observations will eventually reveal the true mean and standard deviation for a given set of parameters.
Previously Published Attenuation Relationships. The article by Lee et al. (2000) evaluates five previously published attenuation relationships, each of which, being developed for shallow crustal earthquakes in active tectonic regions, should be applicable to southern California. These five relationships are listed in Table 4. To compare the predictions from the various relationships, one must adopt a consistent classification scheme. Lee et al. (2000) chose a Q/T/M categorization, based on Quaternary, Tertiary, and Mesozoic surface geology, because such information is readily available in map form (e.g., Park and Elrick, 1998) and can therefore be used for microzonation purposes. Table 4 shows how Lee et al. (2000) set the site parameters in each relationship to represent Q, T, and M. It should be noted that their designation may or may not agree with that of the original authors (reflecting a degree of judgement that is inevitable when applying someone else's relationship).
|
Figure 11, which shows the peak acceleration predicted by two of the attenuation relationships (Abrahamson and Silva, 1997; Boore et al., 1997), exemplifies several important issues. Most dramatic is the relative difference between rock (M) and soil (Q) ground motion. The Boore et al. (1997) model has a sediment amplification that is constant with respect to magnitude and/or distance. The Abrahamson and Silva (1997) relationship, on the other hand, has a nonlinear amplification factor that varies with magnitude and distance, resulting in sediment deamplification at higher ground-motion levels. Other, more subtle differences between the two relationships include (1) the definition of distance from the fault (Rjb vs Rrup; see Abrahamson and Shedlock, 1997, for an overview of the various distance measures); (2) that the decay of ground motion with distance at rock sites is constant with respect to magnitude for Boore et al. (1997), but is magnitude-dependent in the Abrahamson and Silva (1997) model; and (3) that each not only has a different standard deviation (uncertainty), but that for Abrahamson and Silva (1997) depends on magnitude, whereas that for Boore et al. (1997) does not.
|
As discussed below, existing data provide limited resolution of the influence of sediment nonlinearity on attenuation relationships. Therefore, the Phase III study by Ni et al. (2000) has approached the issue theoretically. Specifically, they investigated the response of two hypothetical soil profiles to several hundred synthetic seismograms. The nonlinear constitutive properties of the soil were based on a standard geotechnical model (derived from laboratory studies), and the nonlinear response was computed using an explicit (as opposed to equivalent-linear) formulation. They found that peak-acceleration amplification factors are indeed decreased with increasing input ground-motion levels, with deamplification occurring above 0.2–0.4g. A similar result was found for 0.3–sec response spectra, with less of an effect (and no deamplification) observed at longer periods. The prediction is consistent with the behavior of the Abrahamson and Silva attenuation relationship (Fig. 11). However, it assumes that the laboratory-based constitutive model is applicable to in situ conditions. In addition, other physical mechanisms, such as the scattering hypothesis of O'Connell (1999), might explain the same behavior.
Similarly, Anderson (2000) has addressed theoretically the question of whether the decay of amplitude with distance depends on earthquake magnitude. Using three different synthetic-seismogram simulation techniques, he finds that ground motion decays less rapidly with distance for larger magnitude earthquakes. Intuitively, this result suggests that at larger distances, and for larger earthquakes, there is more opportunity for constructive interference of scattered arrivals from various subevents on the fault. Again, this prediction is consistent with the behavior of the Abrahamson and Silva (1997) attenuation relationship, but is also dependent on various assumptions made in computing the synthetic seismograms.
The differences just discussed regarding the two attenuation relationships shown in Figure 11 are just a few of several that exist among the five attenuation relationships listed in Table 4. However, it is beyond the scope of this overview article to discuss all such differences in detail. In fact, such a discussion would likely be more confusing than enlightening. Instead, we focus on the differences that significantly influence seismic hazard (i.e., the probability of exceeding various ground-motion levels), as quantified in the article by Field and Petersen (2000).
There is an overwhelming number of factors that influence a seismic-hazard estimate, including the source model, ground-motion parameter, site location, site type, and attenuation relationship(s) chosen. To keep the volume of results manageable, Field and Petersen (2000) narrowed these degrees of freedom considerably. For example, only a single regional source model, developed by CDMG and the USGS (Petersen et al., 1996; Frankel et al., 1996), was applied, which having been used to generate their national hazard maps, represents the closest thing to a standard model for southern California. In keeping with other Phase III studies, the analysis was carried out for four ground-motion parameters: peak horizontal acceleration (PGA), and 0.3-, 1.0-, and 3.0-sec response spectral acceleration (SA) with 5% damping. Hazard curves, which give the rate of exceeding various ground-motion levels, were reduced to a single value by selecting the ground motion that is exceeded every 475 years on average (corresponding to the level that has a 10% chance of being exceeded in 50 years, referred to hereafter as the 10%-in-50 yr exceedance level). However, Field and Petersen (2000) show that conclusions regarding the influence of site effects should be applicable to 2%-in-50 yr and 40%-in-50 yr exceedance levels as well. Finally, they restricted their analysis to 43 representative sites extending along a profile from Palos Verdes, across the Los Angeles basin, over the San Gabriel Mountains, and into the Mojave Desert (Fig. 12). Even with these restrictions, more than 10,000 exceedance values were generated in testing the various attenuation relationships and associated site-effect parameterizations. To maintain brevity, only representative examples from the Field and Petersen (2000) analysis are presented here.
|
Figure 13 shows the PGA
10%-in-50 yr exceedance values along the profile for the two attenuation
relationships shown in Figure
11 (the Boore et al.,
1997, and Abrahamson and Silva,
1997, relationships). Separate lines are shown assuming Q, T, and
M site conditions along the entire profile (rather than assigning the actual
site category). The three prominent peaks in
Figure 13 at 7 km, 60 km, and
90 km along the profile correspond to events on the Palos Verdes (6.5 
M 7.1), Sierra Madre (6.5 M 7.0), and San
Andreas faults (M 7.8), respectively.
|
Note in Figure 13 that the Q exceedance values are always greater than those for M in the Boore et al. (1997) relationship, but that the M values generally exceed the Q values for the Abrahamson and Silva (1997) relationship. This discrepancy reflects the differing assumptions noted earlier regarding the influence of sediment nonlinearity. While the amplification factors of Boore et al. (1997) are constant (linear), those of Abrahamson and Silva (1997) depend on the PGA predicted for rock-site conditions (which in turn depends on magnitude and distance).
Recall that the 10%-in-50 yr ground-motion level depends, to some degree,
on all events represented in the source model. However, it is often the case
that only one or a few of the scenarios dominate the hazard, such as near the
peaks in Figure 13. Understanding which earthquakes are influential is key to assessing why
different attenuation relationships predict different hazard levels. The
process of identifying the magnitude(s) and distance(s) associated with the
dominant earthquake(s) is known as disaggregation
(McGuire and Shedlock, 1981;
McGuire, 1995;
Cramer and Petersen, 1996; Bazzurro and Cornell, 1999).
The values obtained depend not only on the site location, ground-motion
parameter, source model, and attenuation relationship applied, but also on how
the dominating values are measured (e.g., the median, mode, or mean of the
distribution of events). For the sake of brevity, we simply state here that
the 10%-in-50 yr exceedance levels across the profile of sites in
Figure 12 are generally
dominated by M 
6.75 events within 20 km of the site. There
are, of course, some exceptions, but the statement is accurate enough for
present purposes (see Field and Petersen,
2000, for details).
Clearly the reliability of a hazard estimate depends on the reliability of
the attenuation-relationship prediction at the dominant magnitudes and
distances (M 6.75 within 20 km here). For example, the
Abrahamson and Silva (1997)
attenuation relationship predicts sediment deamplification for PGA under these
conditions, whereas the Boore et al.
(1997) relationship predicts
amplification (Figs. 11 and
13). This discrepancy reflects
a problem that presently permeates hazard estimation: the conditions that
dominate hazard (e.g., shaking in close proximity to large earthquakes)
correspond to those where attenuation relationships are least constrained by
data.
Figure 14 shows the 10%-in-50 yr PGA hazard values across the profile of sites for all five attenuation relationships listed in Table 4, along with the mean and standard deviation (computed from natural-logarithmic values). Note that the site category (Q, T, or M) specific to each site has been applied in this figure. There is up to a factor of 3 difference among the 10%-in-50 yr exceedance levels implied by the five relationships in Figure 14, and up to a factor of two difference relative to the mean. The differences exhibited in Figure 14 are therefore important (>10%). They reflect epistemic uncertainties in that a true 10%-in-50 yr exceedance level presumably exists, and each of the predictions in Figure 14 constitutes an estimate. The customary practice is to average results obtained with various attenuation relationships (e.g., SSHAC, 1997). Interestingly, averaging the PGA exceedance levels for the five attenuation relationships in Table 4 removes any significant difference between Q and M (because of differing opinions on whether Q is amplified or deamplified relative to M). However, for 1.0- and 3.0-sec SA the differences between Q and M are significant (see Figure 3 of Field and Petersen, 2000).
|
The practice of averaging over the different hazard levels predicted by various attenuation relationships will not reveal the true hazard if all relationships are similarly biased to begin with (for example, by relying on a similar limited observational database). It should again be noted that the results in Figure 14 relate to the particular Q/T/M implementation outlined in Table 4, which may or may not agree with how others (including the original authors) would have applied each relationship.
Southern California Strong-Motion Database. The ultimate test for any attenuation relationship is how well it predicts empirical observations. Steidl and Lee (2000) have compiled a southern California strong-motion database for the purposes evaluating and developing attenuation relationships. The distribution of magnitudes and distances represented in this database is shown in Figure 15. As with any database, its use for evaluation and developmental purposes implicitly assumes that it is representative of long-term, average behavior. All of the attenuation relationships listed in Table 4 were developed using less regionally restrictive sets of observations. The hope here is that by focusing on the southern California database exclusively, we will learn something unique about the region and not be led astray by data limitations. The southern California focus is also necessary to evaluate the predictive capability of attributes associated with, for example, the 3D regional velocity model of Magistrale et al. (2000). Furthermore, even with its geographical limitation, the database of Steidl and Lee (2000) contains more observations than were used in developing some of the previous relationships (e.g., Boore et al., 1997).
|
Lee et al. (2000) QTM Corrections to Previous Relationships. The study by Lee et al. (2000) includes an evaluation of the five attenuation relationships listed in Table 4 with respect to the southern California strong-motion database (Steidl and Lee, 2000). Specifically, they computed a Q, T, and M bias for each relationship, which can be used as a southern California correction factor. They also computed an alternative magnitude-dependent sigma estimate (prediction error or standard deviation) for each relationship using the southern California data. Applying both of these as a correction to the five previously published relationships, Field and Petersen (2000) obtained the PSHA results shown in Figure 16 (which is analogous to Figure 14, but with the corrections applied). The differences between results in Figures 14 and 16 are due not only to the bias corrections, but also to differences in sigma as well.
|
Depending on the ground-motion parameter, typical values of sigma are
0.4 to 0.8 (for the natural log of ground motion). As discussed by
Field and Petersen (2000), and
shown in their Appendix Figure
6, changing sigma by more than about ±0.1 causes a 10%
change in the 10%-in-50 yr exceedance level. Thus, a useful rule of thumb in
this study (but not necessarily applicable elsewhere) is that changing sigma
by more than ±0.1 will produce an important difference in terms of
influencing engineering design. Increasing sigma increases the hazard (all
other things being equal), because higher ground motions become more probable.
Most of the Lee et al.
(2000) sigma values are
greater than those originally published, indicating that southern California
observations are more variable than those used in the original studies (see
Table 5 of Field and Petersen,
2000).
Applying both the southern California bias and sigma corrections of Lee
et al. (2000)
produced a more than 10% change in the 10%-in-50 yr exceedance level (under at
least some conditions) for all five relationships in
Table 4
(Field and Petersen, 2000).
Because all are based on the same data, one might expect the corrections to
bring the probabilistic ground-motion levels predicted by the five
relationships into better agreement. This is indeed sometimes true, as the
variability among Q-sites is lower in
Figure 16 than it is in
Figure 14 (compare dotted
lines). However, there are cases where the corrections increase the
variability among the 10%-in-50 yr exceedance levels (e.g., M-site results
between Figures 14 and
16). This can be explained as
follows. The Lee et al.
(2000) corrections are based
on the southern California strong-motion database, for which the average
magnitude and distance are 6.4 and 40 km, respectively
(Figure 15). Making the
corrections will presumably cause the attenuation relationships to agree more
at this magnitude and distance. However, because these are not the exact same
magnitudes and distances that are dominating the hazard (M 6.75
within 20 km), there is no guarantee that the corrections will make the
10%-in-50 yr exceedance levels agree more.
The question then becomes whether forcing agreement at the average magnitude and distance represented in the database will make the predictions more reliable at the conditions dominating the hazard. Stated differently, a bias at one magnitude and/or distance does not necessarily mean the attenuation relationship is biased at another magnitude and/or distance. Furthermore, there is no guarantee that the present southern California strong-motion database is representative of the average, long-term behavior. Because answers to these questions are presently unknown, it is difficult to argue for the superiority of the corrected relationships. As attenuation relationships are almost constantly undergoing revision, the results of Lee et al. (2000) would probably serve better as a guide to authors as they update their models.
Steidl
(2000)
Attenuation Relationship. Steidl
(2000) developed an
attenuation relationship for southern California by computing empirical
amplification factors (and new sigma estimates) relative to the Sadigh (1997)
rock-attenuation relationship. The amplification factors at each period depend
on the predicted rock-site PGA in order to allow nonlinear site effects. These
were obtained by averaging residuals between observed and predicted values for
Q, T, and M sites separately, and over different predicted rock PGA bins (PGA
0.05g; 0.05 < PGA 0.1; 0.1 < PGA 0.2; and 0.2
< PGA). The PGA results for Q and M are shown in
Figure 17. The average
residuals (or log-amplificationfactors) decrease with increasing predicted
rock PGA. This would suggest nonlinear amplification if the trend existed only
for Q sites. However, there is also a trend for M sites, suggesting a possible
problem with the Sadigh (1997) relationship (in the magnitude and/or distance
dependence). To demonstrate nonlinearity, therefore, it is necessary to divide
the Q amplification factors by the M amplifications factors (to remove the
magnitude and/or distance biases). Doing so produces equivocal results, mostly
because a limited number of high ground-motion rock-site observations give
rise to very large uncertainties. In fact, Steidl
(2000) attempted to
explicitly test the NEHRP amplification factors listed in Tables
2 and
3, but there were only two
M-site observations (needed to normalize the Q-site results) in the three
highest bins combined.
|
In spite of the potential problems with the Sadigh (1997) relationship and
ambiguities regarding the significance of nonlinearity, the Steidl
(2000) attenuation
relationship remains viable. As can be seen from
Figure 16, the 10%-in-50 yr
PGA exceedance levels predicted by this relationship are generally consistent
with the others. However, it is interesting to note that because relatively
large (M 6.75) magnitude events at short distances (<
20km) dominate the hazard, only the amplification factors for the highest
ground-motion bin (rock PGA > 0.2g) are effectively applied
(Field and Petersen, 2000).
Thus, we again face the issue that the hazard calculations are most dependent
on conditions least represented in the data.
Finally, it should be noted that Steidl also examined the following: (1) a subclassification of Q based on the detailed geology map of Tinsley and Fumal (1985); (2) a trend in residuals with respect to shear-wave velocity (V30) obtained within 1 km of the observation site; and (3) a trend in residuals with respect basin depth. These results are generally consistent with those of Lee and Anderson (2000) and Field (2000) discussed subsequently.
Lee and Anderson (2000) Attenuation Relationship. Lee and Anderson (2000) customized the Abrahamson and Silva (1997) attenuation relationship by evaluating prediction residuals relative to southern California observations. Their approach differs from that of Steidl (2000) in that residuals for sediment sites are computed relative to the deep-soil (rather than rock) prediction. Thus, the sediment site residuals already have a first-order, nonlinear site-effect correction. They examined whether residuals are significantly correlated with the following site attributes: amplification predicted from weak-motion aftershock studies; low-frequency amplification predicted from 3D finite-difference simulations (Olsen, 2000); kappa from weak-motion studies (Anderson and Hough, 1984); basin depth (Magistrale et al., 2000); and the detailed geological classifications of Tinsley and Fumal (1985), as modified by Park and Elrick (1998).
Figure 18 shows their average detailed geology residuals for PGA and 1.0-sec SA. Two of the Q subcategories (Qym and Qom) are both significant (at 68% confidence) and important (amplification greater than 10%) for PGA. However, neither is significantly different from the other Q subclassification residuals. None of the 1.0-sec SA results are significantly different from zero at the 68% level of confidence. Furthermore, there is no consistent trend with respect to the subunit age or grain size. For these reasons Lee and Anderson (2000) do not recommend application of their detailed geology corrections.
|
Of all the site attributes examined, basin depth produced the most unique
and statistically significant trends (with depth, again, being defined
relative to the 2.5 km/second shear-wave velocity isosurface in
Figure 8). The amplification
factors implied by their basin-depth corrections are shown in
Figure 19 for the profile
sites where depth is known (traversing near the deepest part of the Los
Angeles basin). Relative to zero-depth, which exhibits some deamplification,
the deepest basin sites are amplified by factors of 1.5 for PGA and
1.8 for 1.0-sec SA.
|
Lee and Anderson (2000) found that making the basin-depth and detailed geology corrections does not significantly reduce sigma (the prediction error, or standard deviation). In fact, they recommend using the sigma values published originally by Abrahamson and Silva (1997). For this reason, the effect of applying their basin-depth correction is to multiply the Abrahamson and Silva 10%-in-50 yr exceedance estimates by the amplification factors in Figure 19 (obviating the need to redo the PSHA calculations). Doing so has a statistically significant and important influence on hazard levels for all four ground-motion parameters (PGA, and 0.3-, 1.0-, and 3.0-sec SA).
Wills et al. (2000) V30 Map. As discussed previously, both Steidl (2000) and Lee and Anderson (2000) found that use of the detailed geology map of Tinsley and Fumal (1985) is not warranted for microzonation purposes. Following completion of those studies, a new detailed site-classification map was made available by Wills et al. (2000). This map, reproduced in Figure 20, uses the 1994 NEHRP classification scheme adopted in the 1997 UBC and 2000 IBC, with site types A, B, C, D, and E based on the average shear-wave velocity in the upper 30 m (Table 1). The map was compiled from 1:250,000 scale geology maps by combining similar units, and correlating these with in situ shear-wave velocity measurements where available (they did not use the map of Tinsley and Fumal, 1985). Because many geological units had shear-wave velocities that fell near the boundaries of the NEHRP categories, Wills et al. (2000) included intermediate categories as well (BC, CD, and DE). In addition to being directly tied to the building codes, the map has the advantage of covering the entire state of California, whereas the Tinsley and Fumal (1985) map, although more detailed, covers only a relatively small subregion of southern California.
|
It should be noted that the map provides only an estimate of the actual
site category. Site-specific values could differ from mapped categories as a
result of any one of the following: (1) errors in the original geological
maps; (2) inherent variability of V30 that falls outside
the defined boundaries; or (3) that the geological unit is less than 30 m in
thickness (the "thin alluvium" problem). According to their own
statistics, a location on the map has a 25% chance of being
misclassified. Obviously the implications of such errors should be considered
carefully in any application.
Field (2000) Attenuation Relationship. In a study closely akin to those of Steidl (2000) and Lee and Anderson (2000), Field (2000) tested whether use of the Wills et al. (2000) map is supported by southern California strong-motion data. Because the Boore et al. (1997) attenuation relationship is the only one that parameterizes site effects in terms of VS, it is the natural choice for use with the Wills et al. (2000) classification scheme. After determining the Wills et al. (2000) site type at each instrument location (Steidl and Lee, 2000), the observations were compared to those predicted by the Boore et al. (1997) relationship. Finding some discrepancies, especially for PGA, Field (2000) revised the Boore et al. relationship by solving for new parameter coefficients using the southern California data. Coefficients for 3.0-sec SA, which were not provided by Boore et al. (1997), were obtained as well.
As shown in Figure 21, Field (2000) found that the five site categories represented in the database (B, BC, C, CD, and D) generally exhibit distinct amplification factors. This is contrary to the conclusions of Steidl (2000) and Lee and Anderson (2000) with respect to the Tinsley and Fumal (1985) map. The one exception is for PGA, where differences do not justify a division into more than two site types (however, one is not led astray by doing so either). The resultant 10%-in-50 yr exceedance values for PGA and 1.0-sec SA are shown in Figure 22 (results for categories A, DE, and E are not shown because they are not represented in the southern California data). The 10%-in-50 yr exceedance levels for 1.0-sec SA are well separated and imply important differences (similar conclusions were obtained with respect to 0.3- and 3.0-sec SA). The differences for PGA are smaller. This latter finding, as discussed by Field (2000) and Field and Petersen (2000), may reflect the influence of sediment nonlinearity in the data.
|
|
Like Steidl (2000) and Lee and Anderson (2000), Field (2000) also tested for a basin-depth effect (with depth also defined by the 2.5 km/sec shear-wave isosurface). A significant trend was found for all four ground-motion parameters. The implied amplification factors are included in Figure 19 (solid line) and generally agree with those of Lee and Anderson (2000). For PGA and 1.0-sec SA, respectively, the deepest basin sites have ground motions that are 1.5 and 2.0 times those at the edge. Field (2000) also found that correcting for the basin-depth effect did not change sigma significantly. This means the amplification factors can be applied directly to the ground-motion exceedance levels (such as those in Figure 21), without redoing the PSHA calculations.
Note that the basin effect for PGA (up to a 50% amplification) is greater than the 20% difference between site classes D and B in Figure 21. Therefore, it would appear that knowledge of basin depth is more important than V30 for PGA. The fact that deep sediments amplify PGA at all, as opposed to deamplify via anelastic attenuation, may seem somewhat surprising. One explanation is that general focusing from the overall basin structure dominates effects of attenuation. Nevertheless, the trend is in qualitative agreement with the 5–7 Hz empirical amplification map of Hartzell et al. (1998). The PGA result cannot be an artifact of a correlation between NEHRP category and basin depth, as Field (2000) effectively maximized the influence of the former before inferring the presence of the latter. There remains a possibility, however, that a V30 variation within the NEHRP category is correlated with basin depth.
A potential problem with the Field
(2000) relationship is that,
like Boore et al.
(1997), sediment nonlinearity
is not accounted for in terms of having amplification factors that depend on
the ground-motion level. However, as discussed by Field
(2000), because sediment sites
dominate the database (Steidl and Lee,
2000), nonlinearity may effectively be accounted for in the
magnitude, distance, and/or fictitious depth terms. If this were the case, we
would expect to see an underprediction of rock-site PGAs at higher
ground-motion levels. Unfortunately, there are not enough recordings on rock
to adequately test this possibility
(Field, 2000). Again, the
important question is the accuracy of the model at the magnitudes and
distances that dominate hazard (M 6.75 events within 20 km). If
the lack of explicit nonlinearity is a problem, it most likely manifests
itself as an underprediction of rock-site PGA at high ground-motion
levels.
Joyner
(2000) Basin
Effect. The article by Joyner
(2000) presents an alternative
perspective on the basin-depth effect. Specifically, he argues that for
long-period surface waves, backazimuth distance from the basin edge is the
controlling factor (rather than basin depth). The idea, illustrated in
Figure 23, is that geometrical
spreading is effectively reduced by lateral focusing along the basin edge.
Because distance from the edge is generally correlated with basin depth, the
latter may be a proxy for the former. He provides a model based on regression
analysis of long-period (T 3 sec) data, which implies
amplifications of up to a factor of 3.
|
Applying this model in PSHA would require tracking the backazimuth distance from basin edge for each earthquake/site pair. A model based on basin depth is obviously much less numerically cumbersome. If Joyner's hypothesis is correct, the relevant question is whether applying the basin-depth correction as a proxy will lead us astray. For example, what happens at the far side of a basin? Under the basin-depth model the amplification comes back down, but with Joyner's model, amplification continues to increase. Interestingly, the 3D simulations of Olsen (2000) shown in Figure 9 suggest the latter. For example, the largest amplification for the San Andreas earthquake (with rupture initiating from the NW) is on the far side of the Los Angeles basin (as opposed to the center). This result implies that the basin-depth effect identified by others may indeed be a proxy for distance from the edge where the waves enter the basin.
|
Discussion |
|---|
|
TopAbstractIntroductionDefinition of Site EffectPrevious Research and Important...SCEC Phase III StudiesDiscussionAcknowledgmentsReferences |
|---|
The maps of Hartzell et al. (1998) represent the state of the art in terms of empirical, site-specific amplification factors. However, questions remain whether present data are adequate for such estimates to represent the average for all possible events, especially in light of the results of Wald and Mori (2000). A more justifiable approach, for now at least, is in terms of site-type, rather than site-specific, estimates.
Variability (Epistemic Uncertainty) of PSHA Predictions
Between previously published attenuation relationships and those developed
in the Phase III collection of articles we have several viable site-effect
parameterizations for southern California. Among all attenuation relationships
evaluated by Field and Petersen
(2000), the range of 10%-in-50
yr exceedance values implied by each is shown in
Figure 24 (where the site type
appropriate to each location has been applied). The attenuation relationship
associated with each line is not indicated, intentionally, as the point here
is to show the variability among all viable estimates. Predicted values in
Figure 24 differ by up to a
factor of three.
|
Assuming the source model is reasonably correct, the 10%-in-50 yr
exceedance levels for sites considered here are generally dominated by
M 6.75 earthquakes within 20 km. Because data are very
limited under these conditions (e.g.,
Figure 15 shows only three
such observations for southern California), we can neither say which
attenuation relationship is best, nor can we rule out any particular
relationship. For this reason, all lines in
Figure 24 represent viable
estimates of the true 10%-in-50 yr exceedance level, and the variability among
predictions represents an estimate of the epistemic uncertainty. That is, time
will eventually reveal which, if any, is correct.
Although none of the attenuation relationships can be ruled out, each undoubtedly has its strengths and weaknesses. For example, and as discussed earlier, the Boore et al. (1997) model has the disadvantage of not explicitly accounting for nonlinearity and lacking a magnitude-dependent distance decay (Anderson, 2000). Nevertheless, it performs as well as the others in terms of predicting southern California strong-motion data (Lee et al., 2000). It also has the advantage of parameterizing the site-conditions with a continuous variable (V30) rather than with just two or three discrete site types, as in other relationships. For such reasons, experts will likely disagree on which model is best in any given situation. It is even possible that all models are biased at the magnitudes and distances that dominate the hazard.
Detailed Site Classifications
In spite of our inability to choose a preferred attenuation relationship,
there are several notable findings with respect to accounting for site
effects. For example, Field
(2000) has found that
corrections based on the site-classification map of Wills et al.
(2000) are both justified
statistically and important in terms of implied ground-motion levels (the
exception being PGA, which shows only two distinct categories). This is
opposite to the conclusions of Steidl
(2000) and Lee and Anderson
(2000) with respect to the
detailed geology map of Tinsley and Fumal
(1985). It would appear that
either the latter map is overly detailed, in the sense that amplification
factors for the different units are not unique, or that there is not yet
enough strong-motion data to reveal its superiority (detailed geology is known
for only a subset of observation sites). That the Wills et al.
(2000) map covers all of
California and is based on the 1994 NEHRP categories used in present building
codes, is an advantage. However, as with any map, one should be aware of its
limitations. For example, they estimate that site-specific
V30 values have a 25% chance of falling outside the
range defined for the mapped unit.
Petersen et al. (1999) have already used the Wills et al. (2000) map, in conjunction with the Boore et al. (1997) attenuation relationship, to obtain site-specific hazard maps for the entire state of California. The 10%-in-50 yr exceedance levels obtained using this approach for the first half of the profile of sites are shown in Figure 25 (green line). Note that the site category specific to each location has been applied rather than using uniform site conditions across the entire profile. The evaluation and customization of the Boore et al. (1997) attenuation relationship, performed by Field (2000) with respect to southern California data, generally supports the Petersen et al. (1999) maps (ignoring the basin depth effect discussed subsequently). The exception is with respect to PGA, where the model of Field (2000) implies less of a difference between type B and type D sites than in the Boore et al. (1997) relationship.
|
Also shown for comparison in Figure 25 are the "firm rock" 10%-in-50 yr values (black line) reflected in the 1996 CDMG/USGS hazard maps (Petersen et al., 1996; Frankel et al., 1996). These latter values are close to, but not exactly the same as those applied in the 1997 NEHRP building code provisions (BSSC, 1998; Leyendecker et al., 2000). The effect of applying the NEHRP amplification factors (Tables 2 and 3) to the rock-site exceedance levels, as specified in the code, is also plotted in Figure 25 (blue line). The results are surprisingly close to the Petersen et al. (1999) exceedance levels.
Basin-Depth Effect
Another important finding is the basin-depth effect
(Fig. 19).
Figure 25 includes the
10%-in-50 yr exceedance levels implied by the Field
(2000) attenuation
relationship using both the Wills et al.
(2000) classification and the
basin-depth correction (red line). This model implies that for all
ground-motion parameters, the deepest basin sites along the profile have the
greatest ground-motion levels. This is in contrast to all the other estimates
in Figure 25, which imply the
greatest level is at the northeast edge of the basin. The difference between
the 10%-in-50 yr exceedance estimates of Field
(2000) and those obtained with
the other site-effect models ranges up to a factor of 2.4. Interestingly,
this manifests more as a reduction along the edge than an increase at the
deepest basin sites, which is entirely true for 3.0-sec SA.
The basin-depth effect has been recognized in the context of attenuation relationships previously (e.g., Trifunac and Lee, 1978; Campbell, 1997). With the Phase III studies (Field, 2000; Lee and Anderson, 2000; Steidl, 2000) and including the long-period 3D finite-difference scenario simulations of Olsen (2000), we have a large body of evidence in support of a basin-depth effect. However, the fact that PGA is influenced by basin structure as well is apparently unique to the Phase III studies (Field, 2000; Lee and Anderson, 2000; Steidl, 2000). The model of Field (2000) implies that basin depth has a greater influence on PGA than surface geology (20% versus 50% amplification, respectively). This is somewhat surprising in that we might expect PGA to be reduced, via anelastic attenuation, rather than amplified at deeper basin sites. Perhaps general focusing from basin concavity dominates the influence of anelasticity.
The physical mechanism for the basin effect is not yet clear, as depth may be a proxy for something else. In fact, the actual physical attribute may differ between longer and shorter period ground motion. For example, Joyner (2000) argues that the backazimuth distance from the basin edge, which generally correlates with depth, is the relevant parameter at long periods. If true, applying the correction will be much more numerically cumbersome because the basin-edge distance will have to be computed separately for each earthquake scenario. Therefore, the relevant question seems to be if basin depth is a proxy for something else, will applying it produce misleading results, or will it be reliable enough for the purposes of PSHA? If Joyner's (2000) hypothesis is correct, the biggest discrepancies will most likely occur at the far sides of basins.
As discussed by Field and Petersen (2000), a comparison of the basin-depth amplification implied by the Phase III studies with that in previous publications (e.g., Trifunac and Lee, 1978; Campbell, 1997) is complicated by differences in depth definitions. This underscores the need to have a consistent, carefully defined, and widely available definition of basin depth. The 2.5 km/sec shear-wave velocity isosurface in the 3D model of Magistrale et al. (2000) provides one such standard.
All of the models that have a basin-depth term predict increased shaking above the deepest parts of the basin. This may cause some confusion in that basin edges are known to amplify ground motion via focusing effects. As exemplified previously in Figure 4, the subsurface basin-edge structure near Santa Monica, California, caused large pockets of amplification during the 1994 Northridge earthquake (Gao et al., 1995). However, the very same subsurface structure may have defocused energy at adjacent sites (Alex and Olsen, 1998). Recall that with respect to PSHA, we are interested in the amplification pattern averaged over all earthquakes of concern. For this, it appears that amplitudes are greater for sites farther from the edge. However, we might expect ground motion to be intrinsically more variable (i.e., larger sigma) near the edges.
Influence of Prediction Error (Sigma)
For the southern California sites examined, Field and Petersen
(2000) demonstrated that
changing the attenuation-relationship prediction error (sigma) by more than
0.1, in natural log units, produces a greater than 10% change in the
10%-in-50 yr exceedance level. As implied by differences between originally
published sigma values and those calculated by Lee et al.
(2000) with southern
California data, epistemic uncertainties of sigma may well exceed this amount,
especially at the magnitudes and distances dominating the hazard. Therefore,
further refinements in our understanding of sigma, including the degree of
magnitude dependence, will likely have an important impact on seismic hazard
estimates.
All Phase-III attenuation-relationship studies (Field, 2000; Lee and Anderson, 2000; Steidl, 2000) concluded that the detailed-site and/or basin-depth corrections produce only a small reduction in sigma. None of the models invokes a change in sigma for the detailed-site or basin-depth corrections. This inspired Lee and Anderson (2000) to apply the residual versus residual analysis of Lee et al. (1998), which provides an estimate of the maximum amount sigma can be reduced by accounting for site effects, without the requirement of knowing what the site corrections are. Their results support the contention that site-effect corrections, at least in southern California, cannot be relied upon to make important reductions in sigma. In other words, the intrinsic variability caused by basin-edge-induced surface waves, focusing and defocusing effects, and scattering in general, create an intrinsic variability that cannot be reduced in any model that quantifies ground motion with so few parameters.
It is possible that some part of sigma comes from a misclassification of
site types in the database. For example, Wills et al.
(2000) estimate a 25%
chance of misclassification with respect to their site-effect map. In effect,
these errors have been folded into the prediction error (sigma) of the Field
(2000) attenuation
relationship. However, it seems doubtful that such misclassification makes a
relatively strong contribution compared to the intrinsic variability of ground
motion caused by scattering.
Caveats
Although all attenuation relationships evaluated in the Phase III studies
are viable, that of Field
(2000) seems most advantageous
in that it incorporates both the detailed site classification of Wills et
al. (2000) and a
basin-depth effect. However, the model does not explicitly account for
nonlinear sediment effects, which as discussed by the author, may manifest as
an underprediction of rock-site amplitudes at higher levels of shaking.
In addition, all Phase III attenuation relationships assume that the southern California strong-motion database is representative of average, long-term behavior. The hope has been that we have learned something unique about the region (e.g., that basin depth is significant and important; that the detailed geology of Tinsley and Fumal (1985) is not useful). However, we must acknowledge the possibility that database limitations may have led us astray.
Finally, it is important to note that our findings are relevant to dominant magnitudes and distances implied by the hazard model and to the site conditions that typify southern California. For example, NEHRP class E is not present in the area and has, therefore, been ignored. The Wills et al. (2000) class DE (V30 = 180 m/sec) does exist (e.g., near Long Beach harbor), but strong-motion observations are generally lacking for this category. Understanding the influence of these site types is very important, especially in regions such as the San Francisco Bay area.
Future Research
The large variability (or epistemic uncertainty) in exceedance levels
predicted by different attenuation relationships highlights the importance of
understanding ground motion under conditions that dominate the hazard (e.g.,
M 6.75 earthquakes at distances less than 20 km). Also
important is the influence of sediment nonlinearity at high ground-motion
levels. Because southern California data are presently inadequate to resolve
these issues, we must either wait for more observations or include data from
other regions.
In their "Proposal for Modifying the Site Coefficients in the NEHRP Provisions," Joyner and Boore (written comm.) have already taken the latter approach of using a broader range of data. Reviewing recent work by themselves and others, they find support for the degree of nonlinearity in the NEHRP Fa amplification factors (Table 2), but find no evidence of nonlinearity for Fv (Table 3). Another remaining question is whether applying the site correction within the hazard calculations, as opposed to after the hazard calculations (as in present building codes), will lead to important differences.
Attenuation relationships are constantly being updated, particularly now
given the recent spate of M 7 events. These include the Kocaeli
earthquake in Turkey (e.g., Toksöz
et al., 1999), the Hector Mine earthquake in southern
California (e.g., Scientists from the
USGS, SCEC, and CDMG, 2000), and the Chi-Chi earthquake in Taiwan
(Shin et al., 2000).
In addition to providing interim models, the Phase III studies can serve as a
guide to authors as they make further refinements to their attenuation
relationships. Specifically, a site categorization based both on
V30 and on a basin-depth parameter seems well supported by
data. In fact, for PGA the basin-depth effect seems more important than
near-surface conditions. However, additional research is needed to determine
whether basin-depth is a proxy for something else (such as distance from the
edge, or near-surface variations not accounted for in the models), and whether
applying it anyway will lead one astray.
Although some additional refinements will be forthcoming, especially in terms of identifying the true mean and standard deviation of ground motion at the magnitudes and distances dominating hazard, a significant intrinsic (or aleatory) uncertainty will remain. That is, due to basin effects, subsurface focusing, and scattering in general, the prediction uncertainty associated with any model that represents ground motion with only a few parameters will remain high. Of course it is possible that sigma of an attenuation relationship could be reduced appreciably by adding more and more parameters to the model. However, eventually it becomes easier, and certainly more elegant, to model ground motion more explicitly from first principles of physics. In fact, the latter approach is probably our only hope for dramatically reducing the uncertainty of ground-motion predictions. Such waveform modeling is also in line with the trend toward dynamic analysis in the engineering community, as complete seismograms are necessary to compute the full nonlinear response of a structure. However, important uncertainties will likely remain with waveform modeling as well, as ground motion is known to be sensitive to the exact distribution of rupture on a fault. Nevertheless, waveform modeling represents our best hope for making more accurate estimates of ground motion at a site. It will also help constrain attenuation relationships at the larger-magnitude/short-distance conditions that dominate hazard and are underrepresented in the data. The accuracy and maximum frequency of waveform modeling will inevitably increase in the future with more refined structural models and advances in high-performance computing.
|
Acknowledgments |
|---|
|
TopAbstractIntroductionDefinition of Site EffectPrevious Research and Important...SCEC Phase III StudiesDiscussionAcknowledgmentsReferences |
|---|
|
Footnotes |
|---|
(alphabetical order) John G. Anderson, Thomas L. Henyey, David D. Jackson,
William B. Joyner, Yajie Lee, Harold Magistrale, Bernard Minster, Kim B.
Olsen, Mark D. Petersen, Jamison H. Steidl, Lisa A. Wald, and Chris J.
Wills
Manuscript received September 12, 2000
|
References |
|---|
|
TopAbstractIntroductionDefinition of Site EffectPrevious Research and Important...SCEC Phase III StudiesDiscussionAcknowledgmentsReferences |
|---|
Abrahamson, N. A., and K. M. Shedlock (1997). Overview, Seism. Res. Lett. 68,9 –23.
Abrahamson, N. A., and W. Silva (1997). Empirical response spectral attenuation relations for shallow crustal earthquakes, Seism. Res. Lett. 68,94 –127.
Aki, K. (1957). Space and time spectra of stationary stochastic waves with special reference to microtremors, Bull. Earthquake Res. Inst. 35,415 –456.
Aki, K. (1988). Local site effects on strong ground motion, in Proc. Earthquake Engineering and Soil Dynamics II, Park City, Utah, June 27–30, 103–155.
Aki, K. (1993). Local site effects on weak and strong ground motion, Tectonophysics 218,93 –111.[CrossRef][Web of Science][GeoRef]
Aki, K., and B. Chouet (1975). Origin of coda waves: source, attenuation, and scattering effects, J. Geophys. Res. 80,3322 –3342.[CrossRef][Web of Science]
Aki, K., and I. Irikura (1991). Characterization and mapping of earthquake shaking for seismic zonation, in Proc. of the 4th International Conf. on Seismic Zonation, Stanford, California, Vol. 1, August 25–29, 61–110.
Aki, K., and P. G. Richards (1980). Quantitative Seismology, Vol. 1, W. H. Freeman, San Francisco.
Aki, K., G. R. Martin, B. H. Chin, N. Abrahamson, A. C. Cornell, and M. Mahdyiar (1995). Probabilistic seismic hazard analysis and the development of earthquake scenario time histories for southern California sites, TASK H-7 of the Southern California Earthquake Center Report on the Characteristics of Earthquake Ground Motions for Seismic Design.
Alex, C. M., and K. B. Olsen (1998). Lens-Effect in Santa Monica? Geophys. Res. Lett. 25,3441 –3444.[CrossRef][Web of Science]
Anderson, J. G. (2000). Expected shape of regressions
for ground-motion parameters on rock, Bull. Seism. Soc.
Am. 90, no. 6B,S43
–S52.
Anderson, J. G., and S. E. Hough (1984). A model for
the shape of the Fourier amplitude spectrum of acceleration at high
frequencies, Bull. Seism. Soc. Am.
74,1969
–1994.
Anderson, J. G., Y. Lee, Y. Zeng, and S. Day (1996).
Control of strong motion by the upper 30 meters, Bull. Seism. Soc.
Am. 86,1749
–1759.
Andrews, D. J. (1986). Objective determination of source parameters and similarity of earthquakes of different size, in Earthquake Source Mechanics, S. Das, J. Boatwright, and C. H. Scholz (Editors), American Geophysical Union, Washington, D.C., 259–268.
Archuleta, R. J. (1998). Direct observation of nonlinear soil response in acceleration time histories (abstract), Seism. Res. Lett. 69,148 .
Bard, P.-Y. (1994). Effects of surface geology on ground motion: recent results and remaining issues, in Proc. 10th European Conf. on Earthquake Engineering 1,305 –325.
Bard, P.-Y. (1998). Microtremor measurements: a tool for site effect estimation? Proc. of the 2nd Int. Symp. on Effects of Surface Geology on Seismic Motion, Yokohama, Japan, 1–3 December, Vol. 3, 1251–1282.
Bazzurro, P., and C. A. Cornell (1999). Disaggregation
of Seismic Hazard, Bull. Seism. Soc. Am.
89,501
–520.
Beresnev, I. A., and K.-L. Wen (1996). Nonlinear soil
response: a reality? Bull. Seism. Soc. Am.
86,1964
–1978.
Beresnev, I. A., G. M. Atkinson, P. A. Johnson, E. H. Field (1998). Stochastic finite-fault modeling of ground motions from the 1994 Northridge, California earthquake. II widespread nonlinear response at soil sites, Bull. Seism. Soc. Am. 88.
Boore, D. M., W. B. Joyner, and T. E. Fumal (1993). Estimation of response spectra and peak accelerations from western North American earthquakes: an interim report, U.S. Geol. Surv. Open-File Rept. 93-509, 72 pp.
Boore, D. M., W. B. Joyner, and T. E. Fumal (1997). Equations for estimating horizontal response spectra and peak acceleration from western North American earthquakes: a summary of recent work, Seism. Res. Lett. 68,128 –153.
Bonilla, L. F., J. H. Steidl, G. T. Lindley, A. G. Tumarkin, and R.
J. Archuleta (1997). Site amplification in the San Fernando
Valley, California: variability of site-effect estimation, Bull.
Seis. Soc. Am. 87,710
–730.
Bonilla, L. F., D. Lavallée, and R. J. Archuleta (1998). Nonlinear site response: Laboratory modeling as a constraint for modeling accelerograms, in Proc. of the 2nd Int. Symp. on Effects of Surface Geology on Seismic Motion 2, edited by K. Irikura, K. Kudo H. Okada and T. Sasatani, A. A. Balkema: Netherlands, 793–800.
Borcherdt, R. D. (1970). Effects of local geology on
ground motion near San Francisco Bay, Bull. Seism. Soc.
Am. 60,29
–61.
Borcherdt, R. D. (1985). Predicting earthquake ground motion: an introduction, U.S. Geol. Surv. Profess. Pap. 1360, 93–99.
Borcherdt, R. D. (1993). On the estimation of site-dependent response spectra, in Proc. International Workshop on Strong-Motion Data, Menlo Park, California, Port and Harbor Research Institute, Japan, vol. 2, 399–427.
Borcherdt, R. D. (1994). Estimates of site-dependent response spectra for design (methodology and justification), Earthquake Spec. 10,617 –653.[CrossRef]
Borcherdt, R. D. (1996). Preliminary amplification estimates inferred from strong ground motion recordings of the Northridge earthquake of January 17, 1994, in Proc. of the International Workshop on Site Response Subjected to Strong Ground Motion, Port and Harbour Research Institute, Yokosuka, Japan, 16–17 January, 1996, Vol. 1.
Borcherdt, R. D., and G. Glassmoyer (1992). On the
character of local geology and their influence on ground motions generated by
the Loma Prieta earthquake in the San Francisco Bay region, California,
Bull. Seism. Soc. Am.
82,603
–641.
Bullen, K. E. (1965). An Introduction to the Theory of Seismology, Cambridge University Press, Cambridge.
Building Seismic Safety Council (BSSC) (1995). 1994 Edition NEHRP Recommended Provisions for Seismic Regulations for New Buildings, FEMA 222A/223A, developed for the Federal Emergency Management Agency, Washington, D.C.
Building Seismic Safety Council (BSSC) (1998). 1997 Edition NEHRP Recommended Provisions for Seismic Regulations for New Buildings, FEMA 302/303, developed for the Federal Emergency Management Agency, Washington, D.C.
Campbell, K. W. (1997). Empirical near-source attenuation relationships for horizontal and vertical components of peak ground acceleration, peak ground velocity, and pseudo-absolute acceleration response spectra, Seism. Res. Lett. 68,154 –179.
Chang, S. W., and Bray, J. D. (1997). Implications of recent strong motion data for seismic building code design at deep, stiff soil sites, Proc. CUREe Northridge Earthquake Research Conference, Los Angeles, California.
Chin, B.-H., and K. Aki (1996). Reply to
"Comment on Simultaneous study of the source, path, and site effects on
strong ground motion during the Loma Prieta earthquake: a preliminary result
on pervasive nonlinear effects" by L. Wennerberg, Bull.
Seism. Soc. Am. 86,268
–273.
Cornell, A. (1968). Engineering seismic risk analysis,
Bull. Seism. Soc. Am.
58,1583
–1606.
Cramer, C. H., and M. D. Petersen (1996). Predominant
seismic source distance and magnitude maps for Los Angeles, Orange, and
Ventura counties, California, Bull. Seism. Soc. Am.
86,1645
–1649.
Day, S. M. (1996). RMS response of a one-dimensional
halfspace to SH, Bull. Seism. Soc. Am.
86,363
–370.
Dobry, R., R. D. Borcherdt, C. B. Crouse, I. M. Idriss, W. B. Joyner, G. R. Martin, M. S. Power, E. E. Rinne, and R. B. Seed (2000). New site coefficients and site classification system used in recent building seismic code provisions, Earthquake Spectra 16,41 –68.
Drake, D. (1815). Natural and Statistical View, or Picture of Cincinnati and the Miami County, Illustrated by Maps, Looker and Wallace, Cincinnati.
Field, E. H. (1996). Spectral amplification in a
sediment-filled valley exhibiting clear basin-edge induced waves,
Bull. Seism. Soc. Am.
86,991
–1005.
Field, E. H. (2000). A modified ground-motion
attenuation relationship for southern California that accounts for detailed
site classification and a basin-depth effect, Bull. Seism. Soc.
Am. 90, no. 6B,S209
–S221.
Field, E. H., and S. E. Hough (1996). The Variability of PSV Response Spectra Across a Dense Array Deployed During the Northridge Aftershock Sequence, Earthquake Spectra, 13,243 –257.[CrossRef]
Field, E. H., and M. D. Petersen (2000). A test of
various site-effect parameterizations in probabilistic seismic hazard analyses
of southern California, Bull. Seism. Soc. Am.
90, no. 6B,S222
–S244.
Field, E. H., P. A. Johnson, I. A. Beresnev, and Y. Zeng (1997). Nonlinear ground-motion amplification by sediment during the 1994 Northridge earthquake, Nature 390,599 –602.[CrossRef][GeoRef]
Field, E. H., S. Kramer, A.-W. Elgamal, J. D. Bray, N. Matasovic, P. A. Johnson, C. Cramer, C. Roblee, D. J. Wald, L. F. Bonilla, P. P. Dimitriu, and J. G. Anderson (1998a). Nonlinear site response: where we're at (a report from a SCEC/PEER seminar and workshop), Seism. Res. Lett. 69,230 –234.
Field, E. H., Y. Zeng, P. A. Johnson, and I. A. Beresnev (1998b). Pervasive nonlinear sediment response during the 1994 Northridge earthquake: observations and finite-source simulations, J. Geophys. Res. 103,26869 –26883.[CrossRef]
Field, E. H., D. D. Jackson, and J. F. Dolan (1999). A
mutually consistent seismic-hazard source model for southern California,
Bull. Seism. Soc. Am.
89,559
–578.
Frankel, A. (1993). Three-dimensional simulations of
ground motions in the San Bernardino Valley, California, for hypothetical
earthquakes on the San Andreas fault, Bull. Seism. Soc.
Am. 83,1020
–1041.
Frankel, A. (1994). Dense array recordings in the San
Bernardino Valley of Landers-Big Bear aftershocks: basin surface waves, Moho
reflections, and three-dimensional simulations, Bull. Seism. Soc.
Am. 84,613
–624.
Frankel, A., C. Mueller, T. Barnhard, D. Perkins, E. V. Leyendecker, N. Dickman, S. Hanson, and M. Hopper (1996). National seismic-hazard maps: documentation, U.S. Geol. Surv. Open-File Rept. 96-352.
Fumal, T. E., and J. C. Tinsley (1985). Mapping shear-wave velocities of near-surface geologic materials, U.S. Geol. Surv. Profess. Pap. 1360, 127–150.
Gao, S., H. Liu, P. M. Davis, and L. Knopoff (1996). Localized amplification of seismic waves and correlation with damage due to the Northridge earthquake, Bull. Seism. Soc. Am. 85,S209 –S230.
Graves, R. W., A. Pitarka, and P. G. Somerville
(1998). Ground motion amplification in the Santa Monica area:
effects of shallow basin edge structure, Bull. Seism. Soc.
Am. 88,1224
–1242.
Gutenberg, B. (1957). Effects of ground on earthquake
motion, Bull. Seism. Soc. Am.
47,221
–250.
Hanks, T. C. (1975). Strong ground motion of the San
Fernando, California, earthquake: ground displacements, Bull.
Seism. Soc. Am. 65,193
–225.
Harmsen, S. C. (1997). Determination of site
amplification in the Los Angeles urban area from inversion of strong-motion
records, Bull. Seism. Soc. Am.
87,866
–887.
Hartzell, S. (1998). Variability in nonlinear sediment
response during the 1994 Northridge, California, earthquake, Bull.
Seism. Soc. Am. 88,1426
–1437.
Hartzell, S., A. Leeds, A. Frankel, and J. Michael
(1996). Site response for urban Los Angeles using aftershocks of
the Northridge Earthquake, Bull. Seism. Soc. Am.
86,S168
–S192.
Hartzell, S., E. Cranswick, A. Frankel, D. Carver, and M. Meremonte
(1997). Variability of site response in the Los Angeles urban
area, Bull. Seism. Soc. Am.
87,1377
–1400.
Hartzell, S., S. Harmsen, A. Frankel, D. Carver, E. Cranswick, M.
Meremonte, and J. Michael (1998). First generation site-response
maps for the Los Angeles region based on earthquake ground motions,
Bull. Seism. Soc. Am.
88,463
–472.
Haskell, N. A. (1960). Crustal reflection of plane SH waves, J. Geophys. Res. 65,4147 –4150.
Hough, S. E., C. Dietel, G. Glassmoyer, and E. Sembera (1995). On the variability of aftershock ground motion in the San Fernando Valley, Geophys. Res. Lett. 22,727 –730.[CrossRef]
Hudson, D. E. (1972). Local distribution of strong
earthquake ground motions, Bull. Seism. Soc. Am.
62,1765
–1786.
Idriss, I. M., and H. B. Seed (1968). Seismic response of horizontal layers, Proc. Am. Soc. Civil Eng. J. Soil Mech. Found. Div. 94,1003 –1031.
Joyner, W. B., R. E. Warrick, and T. E. Fumal (1981).
The effect of Quaternary alluvium on strong ground motion in the Coyote Late,
California, earthquake of 1979, Bull. Seism. Soc. Am.
71,1333
–1349.
Joyner, W. B., and T. E. Fumal (1985). Predictive mapping of earthquake ground motion, U.S. Geol. Surv. Profess. Pap. 1360, 203–220.
Joyner, W. B. (2000). Strong motion from surface waves
in deep sedimentary basins, Bull. Seism. Soc. Am.
90, no. 6B,S95
–S112.
Kagami, H., C. M. Duke, G. C. Liang, and Y. Ohta
(1982). Observation of 1- to 5-second microtremors and their
application to earthquake engineering. II. Evaluation of site effect upon
seismic wave amplification due to extremely deep soils, Bull.
Seism. Soc. Am. 72,987
–998.
Kagami, H., S. Okada, K. Shiono, M. Oner, M. Dravinski, and A. K.
Mal (1986). Observation of 1- to 5-second microtremors and their
application to earthquake engineering. III. A two-dimensional study of site
effects in the San Fernando Valley, Bull. Seism. Soc.
Am. 76,1801
–1812.
Kato, K., K. Aki, and M. Takemura (1995). Site
amplification from Coda Waves: validation and application to S-wave
site response, Bull. Seism. Soc. Am.
85,467
–477.
Lee, Y., and J. G. Anderson (2000). Potential for
improving ground-motion relations in southern California by incorporating
various site parameters, Bull. Seism. Soc. Am.
90, no. 6B,S170
–S186.
Lee, Y., Y. Zeng, and J. G. Anderson (1998). A simple
strategy to examine the sources of errors in attenuation relations,
Bull. Seism. Soc. Am.
88,291
–296.
Lee, Y., J. G. Anderson, and Y. Zeng (2000).
Evaluation of empirical ground-motion relations in southern California,
Bull. Seism. Soc. Am.
90, no. 6B,S136
–S148.
Leyendecker, E. V., R. J. Hunt, A. D. Frankel, and K. S. Rukstales (2000). Development of maximum considered earthquake ground motion maps, Spectra 16,21 –40.
Liu, H.-L., and T. H. Heaton (1984). Array analysis of
the ground velocities and accelerations from the 1971 San Fernando,
California, earthquake, Bull. Seism. Soc. Am.
74,1951
–1968.
Magistrale, H., S. Day, R. W. Clayton, and R. Graves
(2000). The SCEC southern California reference three-dimensional
seismic velocity model version 2, Bull. Seism. Soc.
Am. 90, no. 6B,S65
–S76.
Margheriti, L., L. Wennerberg, and J. Boatwright
(1994). A comparison of coda and S-wave spectral ratios as
estimates of site response in the southern San Francisco Bay area,
Bull. Seism. Soc. Am.
84,1815
–1830.
McGuire, R. K. (1995). Probabilistic seismic hazard
analysis and design earthquakes; closing the loop, Bull. Seism.
Soc. Am. 85,1275
–1284.
McGuire, R. K., and K. M. Shedlock (1981). Statistical
uncertainties in seismic hazard evaluations in the United States,
Bull. Seism. Soc. Am.
71,1287
–1308.
Meremonte, M., A. Frankel, E. Cranswick, D. Carver, and D. Worley
(1996). Urban seismology: Northridge aftershocks recorded by
multiscale arrays of portable digital seismographs, Bull. Seism.
Soc. Am. 86,1350
–1363.
Milne, J. (1898). Seismology, first Ed., Kegan Paul, Trench, Trube, London.
Navaro, O., T. H. Seligman, J. M. Alvarez-Tostado, J. L. Mateos,
and J. Flores (1990). Two-dimensional model for site-effect
studies of microtremors in the San Fernando Valley, Bull. Seism.
Soc. Am. 80,239
–251.
Ni, S.-D., J. G. Anderson, Y. Zeng, and R. V. Siddharthan
(2000). Expected signature of nonlinearity on regression for
strong ground-motion parameters, Bull. Seism. Soc. Am.
90, no. 6B,S53
–S64.
O'Connell, D. R. H. (1999). Replication of apparent
nonlinear seismic response with linear wave propagation models,
Science 283,2045
–2050.
Okada, H. T., S. Matsushima, and E. Hidaka (1987). Comparison of spatial autocorrelation method and frequency-wave number spectral method of estimating the phase velocity of Rayleigh waves in long-period microtremors, Geophys. Bull. Hokkaido Univ. 49,53 –62.
Olsen, K. B. (2000). Site amplification in the Los
Angeles basin from three-dimensional modeling of ground motion,
Bull. Seism. Soc. Am.
90, no. 6B,S77
–S94.
Park, S., and S. Elrick (1998). Predictions of
shear-wave velocities in southern California using surface geology,
Bull. Seism. Soc. Am.
88,677
–685.
Petersen, M. D., W. A. Bryant, C. H. Cramer, T. Cao, Michael S. Reichle, A. D. Frankel, J. J. Lienkaemper, P. A. McCrory and D. P. Schwartz (1996). Probabilistic seismic hazard assessment for the State of California, Calif. Div. Mines Geol. Open-File Rept. 96-08; U.S. Geol Surv Open-File Rept. 97-706, 33 pp.
Petersen, M., D. Beeby, W. Bryant, C. Cao, C. Cramer, J. Davis, M. Reichle, G. Saucedo, S. Tan, G. Taylor, T. Toppozada, J. Treiman, and C. Wills (1999). Seismic shaking hazard maps of California, Calif. Div. Mines Geol. Map Sheet 48.
Petersen, M. D., C. H. Cramer, M. S. Reichle, A. D. Frankel, and T.
C. Hanks (2000). Discrepancy between earthquake rates implied by
historic earthquakes and a consensus geologic source model for California,
Bull. Seism. Soc. Am.
90,1117
–1132.
Phillips, W. S., and K. Aki (1986). Site amplification
of coda waves from local earthquakes in central California, Bull.
Seism. Soc. Am. 76,627
–648.
Reid, H. F. (1910). The California earthquake of April 18, 1906: report of the state earthquake investigation commission, Carnegie Institute, Washington, D.C., Publ. 87, Vol. 2.
Reiter, L. (1990). Earthquake Hazard Analysis: Issues and Insights, Columbia University Press, New York, 254 pp.
Rogers, A. M., J. C. Tinsley, W. W. Hays, and K. W. King (1979). Evaluation of the relation between near-surface geologic units and ground response in the vicinity of Long Beach, California, Bull. Seism. Soc. Am. 61,1603 –1622.
Rogers, A. M., R. D. Borcherdt, P. A. Covington, and D. M. Perkins
(1984). A comparative ground response study near Los Angeles
using recordings of Nevada nuclear tests and the 1971 San Fernando earthquake,
Bull. Seism. Soc. Am.
74,1925
–1949.
Rogers, A. M., J. C. Tinsley, and R. D. Borcherdt (1985). Predicting relative ground response, U.S. Geol. Surv. Profess. Pap. 1360, 221–248.
Sadigh, K., C. Y. Chang, J. A. Egan, F. Makdisi, and R. R. Youngs (1997). Attenuation relationships for shallow crustal earthquakes based on California strong motion data, Seism. Res. Lett. 68,180 –189.
Scientists from the USGS, SCEC, and CDMG (2000). Preliminary report on the 16 October 1999 M 7.1 Hector Mine, California, earthquake, Seism. Res. Lett. 71,11 –23.
Schnabel, P., H. B. Seed, and J. Lysmer (1972).
Modification of seismograph records for effects of local soil conditions,
Bull. Seism. Soc. Am.
62,1649
–1664.
Scrivner, C. W., and D. Helmberger (1999). Variability
of ground motions in southern California: data from the 1995 and 1996
Ridgecrest sequence, Bull. Seism. Soc. Am.
89,626
–639.
Seekins, L. C., L. Wennerberg, L. Margheriti, and H.-P. Liu
(1996). Site amplification at five locations in San Francisco: a
comparison of S-waves, codas, and microtremors, Bull.
Seism. Soc. Am. 86,627
–635.
Senior Seismic Hazard Analysis Committee (SSHAC) (1997). Recommendations for probabilistic seismic hazard analysis: guidance on uncertainty and use of experts, U.S. Nuclear Regulatory Commission, U.S. Dept. of Energy, Electric Power Research Institute; NUREG/CR-6372, UCRL-ID-122160, Vol. 1–2. Also a review of the document by National Academy Press, Washington, D.C., 73 pp.
Shin, T. C., K. W. Kuo, W. H. K. Lee, T. L. Teng, and Y. B. Tsai,2000 ). A preliminary report on the 1999 Chi-Chi (Taiwan) earthquake, Seism. Res. Lett. 71,24 –30.
Spudich, P. A., and S. H. Hartzell (1985). Predicting earthquake groundmotion time-histories, U.S. Geol. Surv. Profess. Pap. 1360, 221–247.
Spudich, P. A. (1997). What seismology may be able to bring to future building codes, Presented at ATC-35 Ground Motion Initiative Workshop, Rancho Bernardino, California 30–31 July 1997.
Steidl, J. H. (1993). Variation of Site Response at the UCSB Dense Array of Portable Accelerometers, Earthquake Spectra 9,289 –302.[CrossRef][GeoRef]
Steidl, J. H. (2000). Site response in southern
California for probabilistic seismic hazard analysis, Bull. Seism.
Soc. Am. 90, no. 6B,S149
–S169.
Steidl, J. H., and Y. Lee (2000). The SCEC Phase III
strong-motion database, Bull. Seism. Soc. Am.
90, no. 6B,S113
–S135.
Su, F., and K. Aki (1995). Site amplification factors
in central and southern California determined from coda waves,
Bull. Seism. Soc. Am.
85,452
–466.
Su, F., J. G. Anderson, and Y. Zeng (1998). Study of
weak and strong ground motion including nonlinearity from the Northridge,
California earthquake sequence, Bull. Seism. Soc. Am.
88,1411
–1425.
Tinsley, J. C., and T. E. Fumal (1985). Mapping Quaternary sedimentary deposits for areal variations in shaking response, U.S. Geol. Surv. Profess. Pap. 1360, 101–126.
Toksöz, M. N., R. E. Reilinger, C. G. Doll, A. A. Barka, and N. Yalcin (1999). Izmit (Turkey) earthquake of 17 August 1999: first report, Seism. Res. Lett. 70,669 –679.
Toro, R. G., N. A. Abrahamson, and J. F. Schneider (1997). Model of strong ground motions from earthquakes in central and eastern North America: best estimates and uncertainties, Seism. Res. Lett. 68,41 –57.
Tsujiura, M. (1978). Spectral analysis of coda waves from local earthquakes, Bull. Earthquake Res. Inst. Tokyo Univ. 53,1 –48.
Trifunac, M. D., and V. W. Lee (1978). Dependence of the Fourier amplitude spectra of strong motion acceleration on the depth of sedimentary deposits, University of Southern California, Department of Civil Engineering, Report No. CE 78-14, Los Angeles.
U.S. Geological Survey (USGS) (1985). Evaluating earthquake hazard in the Los Angeles region, U.S. Geol. Surv. Profess. Pap. 1360.
Vidale, J. E., and D. V. Helmberger (1988). Elastic
finite-difference modeling of the 1971 San Fernando, California earthquake,
Bull. Seism. Soc. Am.
78,122
–141.
Wald, D. J., and R. W. Graves (1998). The seismic
response of the Los Angeles Basin, California, Bull. Seism. Soc.
Am. 88,337
–356.
Wald, L. A., and J. Mori (2000). Evaluation of methods
for estimating linear site-response amplifications in the Los Angeles region,
Bull. Seism. Soc. Am.
90, no. 6B,S32
–S42.
Wennerberg, L. (1996). Comment on "Simultaneous
study of the source, path, and site effects on strong ground motion during the
Loma Prieta earthquake: a preliminary result on pervasive nonlinear
effects" by B.-H Chin and K. Aki, Bull. Seism. Soc.
Am. 86,259
–267.
Wills, C. J., M. Petersen, W. A. Bryant, M. Reichle, G. J. Saucedo,
S. Tan, G. Taylor, and J. Treiman (2000). A site-conditions map
for California based on geology and shear-wave velocity, Bull.
Seism. Soc. Am. 90, no. 6B,S187
–S208.
Wood, H. D. (1908). Distribution of apparent intensity in San Francisco, in the California earthquake of April 18, 1906, report of the State Earthquake Investigation Commission, Carnegie Institute, Washington, D.C., Publ. 87, 220–245.
Wood, H. D. (1933). Preliminary report on the Long
Beach earthquake, Bull. Seism. Soc. Am.
23,42
–56.
Working Group on California Earthquake Probabilities (WGCEP)
(1995). Seismic hazards in southern California: probable
earthquakes, 1994 to 2024. Bull. Seism. Soc. Am.
85,379
–439.
Working Group on California Earthquake Probabilities (WGCEP) (1999). Earthquake probabilities in the San Francisco Bay region: 2000 to 2030: a summary of findings, U.S. Geol. Surv. Open-File Rept. 99-517.
Yamanaka, H., M. Dravinski, and H. Kagami (1993).
Continuous measurements of microtremors on sediments and basement in Los
Angeles, California, Bull. Seism. Soc. Am.
83,1595
–1609.
Yamanaka, H., M. Takemura, H. Ishida, and M. Niwa
(1994). Characteristics of long-period microtremors and their
applicability in exploration of deep sedimentary layers, Bull.
Seism. Soc. Am. 84,1831
–1841.
Yoshida, N., and S. Iai (1998). Nonlinear site response and its evaluation and prediction, in Proc. Second Int. Symp. on Effects of Surface Geology on Seismic Motion, Yokohama, Japan, 1–3 December, Vol. 1, 71–90.
Yu, G., J. G. Anderson, and R. Siddharthan (1993). On
the characteristics of nonlinear soil response, Bull. Seism. Soc.
Am. 83,218
–244.
Zeghal, M., and A. W. Elgamal (1994). Analysis of site liquefaction using earthquake record, Proc. Am. Soc. Civil Eng. J. Geotech. Eng. Div. 120,996 –1017.
This article has been cited by other articles:
|
|
 |
|
  I. D. Papanikolaou, D. I. Papanikolaou, and E. L. Lekkas Advances and limitations of the Environmental Seismic Intensity scale (ESI 2007) regarding near-field and far-field effects from recent earthquakes in Greece: implications for the seismic hazard assessment Geological Society, London, Special Publications, January 1, 2009; 316(1): 11 - 30. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 A. Michelini, L. Faenza, V. Lauciani, and L. Malagnini Shakemap Implementation in Italy Seismological Research Letters, September 1, 2008; 79(5): 688 - 697. [Full Text] [PDF]
|
|
|
|
 |
|
 F. Pettenati and L. Sirovich Validation of the Intensity-Based Source Inversions of Three Destructive California Earthquakes Bulletin of the Seismological Society of America, October 1, 2007; 97(5): 1587 - 1606. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. Ge, J. Pujol, S. Pezeshk, and S. Stovall Determination of Shallow Shear-Wave Velocity at Mississippi Embayment Sites Using Vertical Seismic Profiling Data Bulletin of the Seismological Society of America, April 1, 2007; 97(2): 614 - 623. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 G. M. Atkinson Challenges in seismic hazard analysis for continental interiors Geological Society of America Special Papers, January 1, 2007; 425(0): 329 - 344. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
G.-Q. Wang, G.-Q. Tang, D. M. Boore, G. Van Ness Burbach, C. R. Jackson, X.-Y. Zhou, and Q.-L. Lin Surface Waves in the Western Taiwan Coastal Plain from an Aftershock of the 1999 Chi-Chi, Taiwan, Earthquake Bulletin of the Seismological Society of America, June 1, 2006; 96(3): 821 - 845. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
K. Tsuda, R. J. Archuleta, and K. Koketsu Quantifying the Spatial Distribution of Site Response by Use of the Yokohama High-Density Strong-Motion Network Bulletin of the Seismological Society of America, June 1, 2006; 96(3): 926 - 942. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. B. Scott, T. Rasmussen, B. Luke, W. J. Taylor, J. L. Wagoner, S. B. Smith, and J. N. Louie Shallow Shear Velocity and Seismic Microzonation of the Urban Las Vegas, Nevada, Basin Bulletin of the Seismological Society of America, June 1, 2006; 96(3): 1068 - 1077. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
H.-H. Tsang and A. M. Chandler Site-Specific Probabilistic Seismic-Hazard Assessment: Direct Amplitude-Based Approach Bulletin of the Seismological Society of America, April 1, 2006; 96(2): 392 - 403. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
G. M. Atkinson Single-Station Sigma Bulletin of the Seismological Society of America, April 1, 2006; 96(2): 446 - 455. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. B. Scott, M. Clark, T. Rennie, A. Pancha, H. Park, and J. N. Louie A Shallow Shear-Wave Velocity Transect across the Reno, Nevada, Area Basin Bulletin of the Seismological Society of America, December 1, 2004; 94(6): 2222 - 2228. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
W. J. Lutter, G. S. Fuis, T. Ryberg, D. A. Okaya, R. W. Clayton, P. M. Davis, C. Prodehl, J. M. Murphy, V. E. Langenheim, M. L. Benthien, et al. Upper Crustal Structure from the Santa Monica Mountains to the Sierra Nevada, Southern California: Tomographic Results from the Los Angeles Regional Seismic Experiment, Phase II (LARSE II) Bulletin of the Seismological Society of America, April 1, 2004; 94(2): 619 - 632. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
B. Savage and D. V. Helmberger Site Response from Incident Pnl Waves Bulletin of the Seismological Society of America, February 1, 2004; 94(1): 357 - 362. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
Empirical Corrections for Basin Effects in Stochastic Ground-Motion Prediction, Based on the Los Angeles Basin Analysis Bulletin of the Seismological Society of America, August 1, 2003; 93(4): 1679 - 1690.
|
|
|
|
|
|
J. Gomberg, B. Waldron, E. Schweig, H. Hwang, A. Webbers, R. VanArsdale, K. Tucker, R. Williams, R. Street, P. Mayne, et al. Lithology and Shear-Wave Velocity in Memphis, Tennessee Bulletin of the Seismological Society of America, June 1, 2003; 93(3): 986 - 997. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
D. M. Boore Phase Derivatives and Simulation of Strong Ground Motions Bulletin of the Seismological Society of America, June 1, 2003; 93(3): 1132 - 1143. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
Tests of Source-Parameter Inversion of the U.S. Geological Survey Intensities of the Whittier Narrows 1987 Earthquake Bulletin of the Seismological Society of America, February 1, 2003; 93(1): 47 - 60.
|
|
|
|
|
|
Updated Near-Source Ground-Motion (Attenuation) Relations for the Horizontal and Vertical Components of Peak Ground Acceleration and Acceleration Response Spectra Bulletin of the Seismological Society of America, February 1, 2003; 93(1): 314 - 331.
|
|
|
|
|
|
Ground Motions at Memphis and St. Louis from M 7.5-8.0 Earthquakes in the New Madrid Seismic Zone Bulletin of the Seismological Society of America, April 1, 2002; 92(3): 1015 - 1024.
|
|
|
|
|
|
Unexpected Values of Qs in the Unconsolidated Sediments of the Mississippi Embayment Bulletin of the Seismological Society of America, April 1, 2002; 92(3): 1117 - 1128.
|
|
|
|
|
|
Nonlinearity at California Generic Soil Sites from Modeling Recent Strong-Motion Data Bulletin of the Seismological Society of America, March 1, 2002; 92(2): 863 - 870.
|
|
|
|
|
|
H. Magistrale, S. Day, R. W. Clayton, and R. Graves The SCEC Southern California Reference Three-Dimensional Seismic Velocity Model Version 2 Bulletin of the Seismological Society of America, December 1, 2000; 90(6B): S65 - S76. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. H. Steidl and Y. Lee The SCEC Phase III Strong-Motion Database Bulletin of the Seismological Society of America, December 1, 2000; 90(6B): S113 - S135. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
E. H. Field A Modified Ground-Motion Attenuation Relationship for Southern California that Accounts for Detailed Site Classification and a Basin-Depth Effect Bulletin of the Seismological Society of America, December 1, 2000; 90(6B): S209 - S221. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
E. H. Field and M. D. Petersen A Test of Various Site-Effect Parameterizations in Probabilistic Seismic Hazard Analyses of Southern California Bulletin of the Seismological Society of America, December 1, 2000; 90(6B): S222 - S244. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
