Bulletin of the Seismological Society of America; February 2006; v. 96; no. 1;
p. 11-32; DOI: 10.1785/0120040166
© 2006 Seismological Society of America
Comparison of Seismic and Geodetic Scalar Moment Rates across the Basin and Range Province
Aasha Pancha1,
John G. Anderson1 and
Corné Kreemer2
1 Seismological Laboratory and
Department of Geological Sciences
University of Nevada
Reno, Nevada
89557
pancha{at}seismo.unr.edu
jga{at}unr.edu
(A.P.,
J.G.A.)
2 Nevada Bureau of Mines and
Geology
Mail Stop 178
University of Nevada
Reno, Nevada
89557-0088
kreemer{at}unr.edu
(C.K.)
 |
Abstract
|
|---|
Scalar moment rates estimated from a 146-year seismicity catalog agree,
within uncertainties, with the deformation rate of the Basin and Range province
determined by using space geodesy. Seismic-moment rates have been estimated from
a new catalog of earthquakes complete for M 
5. The catalog was
compiled from 15 preexisting catalogs, supplemented by the review of 44 journal
articles. Throughout the catalog compilation, care was taken to obtain the
moment magnitude or a reasonable, and not inflated, equivalent. Seventy-six
percent of the moment release occurred during 10 earthquakes of magnitude
MW 6.79. The spatial distribution of earthquakes and
their moment release matches the geodetic pattern of deformation. All three are
concentrated in a 
200-km-wide zone along the western boundary of the Great
Basin, with this zone widening to the north. Several techniques, ultimately
traceable to Kostrov and Brune, are used to translate the geodetic strain rates
into rates of seismic-moment release. The agreement between geodetic and
seismic- moment rate suggests that, within uncertainties, the rate of historic
earthquakes within the Basin and Range province, taken as a whole, provides a
reasonable estimate for the future rate of seismicity. These results support the
hypothesis that even a few years of detailed geodetic monitoring can provide a
good constraint on earthquake occurrence rate estimates for large-enough
regions.
|
Introduction
|
|---|
Earthquake occurrence rates are an essential part of seismic-hazard
analysis. There are now three major types of data available to estimate these
occurrence rates: historical seismicity, geological slip rates on active faults,
and geodetic deformation rates. Each approach has limitations, but in principle
they should all yield similar estimates. In the following, we compare these
three approaches in the Basin and Range region of the western United States.
Comparisons of seismicity and geology
(e.g., Anderson, 1979;
Doser and Smith, 1989) or
comparisons of seismicity and geodesy (e.g.,
Ward, 1998a,
1998b;
Shen Tu et al., 1998;
Kreemer et al., 2000,
2002;
Masson et al., 2005)
have been conducted. This study improves on previous studies by including a
decade of geodetic data, an improved seismicity catalog, and an attempt to
characterize all of the active faults.
The adequacy of seismic catalogs to estimate average regional earthquake
occurrence rates is governed by the catalog duration
(Smith, 1976;
Ward, 1998a) and the regional
strain rate (Ward, 1998a). For
seismicity rates estimated from the historical earthquake catalogs to be valid,
the average recurrence interval is required to be shorter than the historical
record. For an individual fault a complete earthquake cycle is required.
Alternatively, for a region containing multiple faults, the historical
seismicity record is required to be long enough to capture a statistical sample
of all phases of the seismic cycle, including of course earthquakes, but
different parts of the cycle can be represented by different faults. With this
constraint, the catalog duration is almost always too short to give a reliable
occurrence rate estimate for regions the size of an urban area, as desired for
seismic-hazard analysis.
Fault slip rates may be used to estimate average regional earthquake
occurrence rates
(e.g., Brune, 1968;
Wallace, 1970;
Anderson, 1979;
Molnar, 1979,
Doser and Smith, 1982). For such
geological estimates of seismicity to be reliable, all major faults must be
recognized and characterized correctly. Where faulting is concentrated on a few
major through-going structures, as in coastal California north or south of the
Transverse Ranges, there is reason for confidence that this goal is close to
being achieved. In the Basin and Range, fault characterization is
incomplete.
Two conditions for geodesy to give reliable estimates of earthquake
occurrence rates are necessary. First, the geodetic measurements should sample a
large enough spatial scale so that they are not affected by nonlinear strain
accumulation during the earthquake cycle on individual faults. Second, they
should sample a long enough time interval that measurement uncertainties have a
minimal effect on the estimated velocities. In the Great Basin, geodetic data
meeting these conditions are obtained with as little as a few years of
observations using the Global Positioning System (GPS), but the
deformation is not uniquely assignable to specific faults. Agreement between the
strike of active Quaternary faults and the azimuth of contemporary deformation
lead Hammond and Thatcher (2004)
to conclude that geodetic motion can be used to infer deformation over many
earthquake cycles. Contemporary strain rates may be used to predict average
earthquake moment rates using methods ultimately traceable to
Kostrov (1974) or
Brune (1968), assuming that all
of the strain that is accumulated is ultimately released in earthquakes
(e.g., Anderson, 1979;
Ward, 1994;
Working Group on California Earthquake Probabilities, 1995;
Savage and Simpson, 1997;
Shen-Tu et al., 1998;
Ward, 1998a,
1998b).
The Basin and Range province extends from the rigid Sierra Nevada block in
the west to the Colorado Plateau in the east
(Fig. 1). The province is an
actively deforming region of Cenozoic extension and shear, dominated by normal
faulting throughout with strike-slip deformation superimposed primarily along
the western margin of the Great Basin
(Stewart, 1988). High heat flow,
negative Bouguer gravity anomalies, thin crust and lithosphere, and
high-attenuation low-velocity upper mantle characterize the region
(Catchings and Mooney, 1991;
Jones et al., 1992;
Chulick and Mooney, 2002;
Zandt et al., 1995).
From the geodynamic viewpoint, buoyancy forces within the crust and lithosphere
(Wernicke, 1992;
Sonder and Jones, 1999),
tractions applied to the plate edge
(Wernicke, 1992), and forces
applied to the base of the lithosphere
(Wernicke, 1992;
Sonder and Jones, 1999) are all
potentially contributing to drive the extension and shear observed in the
region. Topographic and geodetic data, along with plate-motion constraints,
indicate that extension is driven in part by gravitational potential energy, but
plate-boundary interaction stresses modify extension directions
(Flesch et al., 2000).
In addition to spreading, about 25% of the Pacific–North American
(PA–NA) relative plate motion (12 mm/yr) is taken up by
displacement and deformation in the Basin and Range province
(Dokka and Travis, 1990;
Dixon et al., 2000;
Bennett et al., 2003).
View larger version (138K):
[in this window]
[in a new window]
|
Figure 1. Map of the western United States, showing topography and earthquakes with
M 4.8 (blue circles with radius proportional to magnitude). The
study area, outlined with a bold polygon, encloses all major earthquakes that
can be associated with deformation of the Basin and Range province.
|
|
Because deformation is distributed over a region nearly 1000 km wide, most
major Basin and Range faults have recurrence times of several thousand years
(Wallace, 1984; McCalpin and
Nishenko, 1996;
Lee et al., 2001;
Dixon et al., 2003). We
propose, however, that the deformation rate is fast enough that meaningful
comparison of average seismicity rates estimated using seismic, geological, and
geodetic data can still be accomplished for this region as a whole. The
distributed seismicity of the region is assumed to be caused by a sufficient
number of faults at different stages of the earthquake cycle to compensate for
the long recurrence interval of the individual faults. This is reasonable
because there are more than 400 major range-front faults distributed throughout
the region (dePolo, 1998).
Unfortunately many of the slip rates available for the region are based on
reconnaissance techniques
(dePolo, 1998) rather than on
more detailed trenching. Geodetic strain measurements averaged over the region
should be representative of the total geological strain across the entire
region, considering that geodetic strain rates based on a decade of observations
are broadly consistent with global plate models based on rates of seafloor
spreading.
Shen-Tu et al. (1998)
and Humphreys and Weldon (1994)
showed that fault slip rates in the western United States add up to be close to
geological and geodetic estimates of the PA–NA motion. Although
the geodesy data contain transients and localized areas of higher strain, these
are small anomalies compared with the greater region.
To compare the three methods, we compile the best available GPS,
geology, and seismicity data. GPS data from several studies in the
Basin and Range area are combined for this study to model the present-day
deformation field. Best estimates of slip rates on the most active faults
characterized are obtained from input to the 1996 and 2002 U.S. Geological
Survey (USGS) seismic hazard maps
(Frankel et al., 1996,
2002;
Haller et al., 2002).
To characterize the historical seismicity, this study compiles the most
complete possible seismic-event catalog for the Basin and Range with strong
emphasis on obtaining the most appropriate moment magnitude
(MW) for each event. We utilize geodetic data from multiple
stations in the Basin and Range to define the geodetic deformation on a fine
spatial scale (5-km grid). This is in contrast to previous studies for the Basin
and Range that utilized only a small number of data for this region
(Ward, 1998a;
Shen Tu et al., 1998).
Besides the comparison of the entire region, we also compare the spatial
distribution of earthquakes and their moment release with crustal deformation
rates.
|
Earthquake Data
|
|---|
In considering the Great Basin, we also include part of the Mojave Desert
where deformation is more related to the northward motion of the Sierra Nevada
Mountains than to the main motion of the San Andreas fault
(Fig. 1). The southern extent
of the area considered passes between the 1992 Landers earthquake and the 1992
Big Bear earthquake, such that the Big Bear event is excluded from our
earthquake catalog. Although the Landers earthquake represents stress transfer
out of the San Andreas system into the eastern Californian shear zone
(ECSZ), the Big Bear earthquake event represents deformation in the
Mojave Desert
(Hauksson et al., 1993).
Seismic moment, M0, of an earthquake is defined in terms
of source parameters as the product of average shear modulus µ of
the crustal rock around the earthquake, area Ae of the fault
ruptured in the earthquake, and D, the average slip during the
earthquake (Brune, 1968), that
is,
| (1) |
In the context of this article, moment rate is estimated over time intervals of
decades or longer from the sum of the moments of all earthquakes divided by the
interval. Seismic moment can therefore also be related to the rate of crustal
deformation.
We estimated seismic-moment rates from a new catalog of earthquakes from 1850
to the end of 1999, intended to be complete for magnitude M 5
(Fig. 1). Earthquakes within
the study region with M 4.8 in any of 15 pre- existing catalogs
were selected (Table 1). After
removing duplicate entries, the catalog contained a total of 800 earthquakes
since 1855, including 487 earthquakes with M 5.0
(www.seismo.unr.edu/htdocs/BandR.html).
By allowing a lower cutoff level of M 4.8, we sought to ensure that
magnitude differences arising from the use of different catalogs is accounted
for. In this way, no significant events should have been neglected from the
catalog.
This new catalog was supplemented by the review of 44 published journal
articles to obtain MW values for many of the more prominent
earthquakes (Slemmons, 1957;
Tsai and Aki, 1966;
Savage and Hastie, 1966,
1969;
Bolt and Miller, 1975;
Hanks et al., 1975;
Hart et al., 1977;
Langston and Butler, 1976;
Hanks and Kanamori, 1978;
Toppozada et al., 1981;
Doser and Smith, 1982;
Barrientos et al., 1985;
Boatwright and Choy, 1985;
Doser, 1985;
Doser and Smith, 1985;
Ekstrom and Dziewonski, 1985;
Nabelek et al., 1985;
Patton, 1985;
Stein and Barrientos, 1985;
Barker and Wallace, 1986;
Doser, 1986;
Sipkin, 1986;
Ward and Barreintos, 1986;
Doser, 1987;
Doser and Kanamori, 1987;
Barker and Doser, 1988;
Doser, 1988;
Pacheco and Nábelek, 1988;
Patton and Doser, 1988;
Doser, 1989a,
1989b;
Doser and Smith, 1989;
Westaway and Smith, 1989;
Rogers et al., 1991;
Smith and Arabasz, 1991;
Kanamori et al., 1992;
Beanland and Clark, 1993;
Wells and Coppersmith, 1994;
Caskey et al., 1996;
Mason, 1996;
dePolo and dePolo, 1999;
dePolo et al., 2003;
Ji et al., 2002;
Ichinose et al., 2003).
Only best estimates of the moment magnitude were considered from the literature.
Some of the larger events consisted of a number of subevents. In these cases,
the moments of each of the individual subevents were summed and the moment
magnitude was calculated from that total.
The initial compiled catalog contained multiple entries from the same
earthquake. Discrepancies were noted between catalog listings for single events.
Timing differences of up to one day were observed, as well as differences in
location, especially for early events. Some events were not listed in their
primary catalogs. Hence, a small amount of subjectivity, based on the
similarities of both the location and timing of events, was introduced for event
association between catalogs. Errors were often noted in secondary sources.
Where available, primary sources were therefore preferred.
Emphasis was placed on the accuracy of the magnitudes within each catalog
listing, as discussed in the next section. The main objective was to include all
the large earthquakes within the region and gain a reasonable estimate of
MW or a reasonable equivalent. Preferred locations were
those from primary catalogs, except where geological data have been used in
relocations. In general, less emphasis was placed on the accuracy of the timing
of events.
Large uncertainties surround some large historic events. Several catalogs
include an earthquake in 1852 in western Nevada with M 7.3. The
anecdotal evidence for this earthquake is not sufficient to assign a magnitude
and location that is reliable enough to use in this study. The occurrence of the
1903 M 6.5 earthquake
(Slemmons et al., 1959;
Rogers et al., 1991) is
based on geological mapping, field studies, and interviews with residents.
Although omitted by many other catalogs, we include this event in our final
catalog as its occurrence is sufficiently credible. Because of its smaller size,
it does not contribute greatly to the final cumulative seismic-moment release of
the region.
Earthquakes that are potentially related to volcanic processes, including
those associated with activity around Mammoth Lakes and Mt. St. Helens, were
included in the catalog. The Mt. St. Helens events were of magnitude M
5.3 or less and, hence, contribute little to the overall seismic- moment
release. The largest events near Mammoth Lakes (M 6) occur
outside the caldera, so that they may appropriately be considered to contribute
to the tectonic deformation of the region. Events in the locality of the Nevada
Test Site, occurring at times of known nuclear blasts, were removed from the
final database. Three additional events were removed, as they were located on
the Nevada Test Site and occurred either exactly on the hour or half hour. All
other events in the vicinity are assumed to be of tectonic origin or triggered
by the blasts.
Amplitude spectra of surface waves were used by
Patton (1985) to determine
seismic moments of western United States events with ML and
mb between 4.3 and 5.5. Whereas magnitude estimates from
other sources were M 4.8, the moment magnitudes estimated by
Patton (1985) were often less
than this. This discrepancy arises because of the high- frequency content of
these smaller events. Based on the rules for magnitude selection below, these
smaller moment magnitudes are used in the analyses.
Doser and Smith (1982) found
that some events with ML < 4.8 can be modeled to give an
estimate of MW > 4.8; these events are included in the
new catalog. Thus, we may not have achieved completeness in the
MW 4.8–5.5 range. However, these events would not have
an impact on the main results of this study because of their small size.
Geological parameters given by
Wells and Coppersmith (1994)
and Mason (1996) were used to
calculate moment- release values for significant earthquake events from
equation (1) using a shear
modulus of µ = 3 x 1011 dyne cm2.
To determine Ae for normal faults, the dip was assumed to be
60°, whereas for strike-slip events, the dip was assumed to be 90°.
Mason (1996) did not give
estimates of the vertical depth of the faulting. Those given by
Wells and Coppersmith (1994)
were therefore used in calculation of the seismic moment from source parameters
listed by Mason (1996). Best
estimates of the fault length and displacement, as given by Mason, were used. In
the case of the
Wells and Coppersmith (1994)
data, the surface fault length and average displacement were used. For four
small earthquakes where average displacements were not available, maximum
displacements were used.
Equation (1) was also applied to
other earthquake source parameter data listed within the literature.
These calculated moment values and those within the literature were converted
to moment magnitude estimates, so that they could be compared with other
magnitude estimates for each respective event using the relation first defined
by Kanamori (1977):
| (2) |
|
Magnitude Assignment
|
|---|
For most earthquakes, we estimated the seismic moment M0
from magnitude MW, so careful attention was paid to the
magnitudes of each event in the catalog, as small biases in magnitudes can
result in a large bias in the strain rate
(Wang et al., 1982).
Moment magnitude estimates were selected when available. For the largest events,
for which many MW estimates are available, we established
criteria to select the favored MW value. The selection
criteria are described below. For events without MW
estimates, care was taken to avoid inflated magnitude estimates, usually by
using the smallest magnitude from any catalog. This yields a lower- bound
estimate for the occurrence rate of moderate earthquakes. Exceptions were made
in cases where the primary catalog source was preferred. In addition,
MS estimates were preferred over mb
because they are more representative of MW for
large-magnitude events
(Kanamori, 1983).
Careful selection criteria were established to retain the best
MW estimate from the literature and catalog listings for the
largest events. The Harvard long-period surface-wave estimates of the seismic
moment have been consistent for the past 28 years; hence, these estimates were
given primary preference. Second preference was given to other surface- wave
moment tensor estimates followed by any other surface-wave estimates.
Long-period surface waves are considered to be more representative of the
average faulting process than body waves and thus were given precedence over
moment estimates based on body waves. Within each of these
MW categories, the catalog record with the minimum-magnitude
listing was retained. After surface waves, body wave and/or Pnl wave,
geological, and leveling data were then considered in the same category. In
these cases, we needed to use judgment based on the quality of the data; because
of concerns that each of these have the potential to underestimate the size of
the earthquakes, we tended to favor larger values. Appendix 1 describes in
detail how preferred MW values were selected for each of the
10 largest earthquake events in the catalog, and are listed in
Table 2.
All magnitudes within the catalog were then treated as moment magnitudes. We
then estimated the seismic moment of each event using the relation
| (3) |
from inverting equation (2)
exactly. Different values of the constant, instead of 16.095, are in the
literature, as discussed by
Anderson (2003) and
Utsu (2003). These differences
are a result of rounding of the coefficients.
Equation (2) is based on the
original definition rounded to two decimal places. We have chosen to use
equation (2) because the Harvard
Centroid Moment Tensor (CMT) Catalog uses it in their determination
of seismic moment for large earthquakes and these have been consistent for the
last 28 years. Although we have been consistent in the use of
equation (2), we note that within
some of the literature and in several catalog listings that a constant
coefficient of 10.7 had been applied.
Figure 2 shows
MW and coda magnitude estimates for 113 moderate-magnitude
earthquakes from 1990 to 2000 in the western Great Basin. Moments are determined
by
Ichinose et al. (2003).
Although these smaller events have relatively little influence on the study
results, we use these results as an indication that our use of network magnitude
estimates in the place of MW does not cause major bias.
View larger version (14K):
[in this window]
[in a new window]
|
Figure 2. Coda magnitude Md versus moment magnitude
Mw for 113 earthquakes from 1990 to 2000 located within the
western Great Basin. Moments were determined by Ichinose (2003). On average,
Md – Mw = 0.10
± 0.25.
|
|
|
Strain Rate Field Model from GPS Velocities
|
|---|
Geodetic measurements show concentrated deformation at the eastern (50
km) and western (200 km) margins of the Basin and Range, coinciding with
regions of modern seismicity, and with little deformation in between
(Dixon et al., 1995;
Thatcher et al., 1999;
Dixon et al., 2000;
Svarc et al., 2002b;
Bennett et al., 2003;
Hammond and Thatcher, 2004).
Concentration of deformation in the westernmost 200 km of the Basin and
Range and along the eastern boundary may be related to rheological weakness of
the lithosphere
(Thatcher, 2003). Margin
parallel velocities at a latitude of 39–40° N increase from 1 to
2 mm/yr at 117.7° W, representative of the relatively more stable interior
of the Basin and Range, to 12 mm/yr at 120° W
(Bennett et al., 2003;
Hammond and Thatcher, 2004).
Strain rates also increase from north to south along the western boundary of the
region
(Bennett et al., 2003)
because of narrowing of the high- deformation zone from the northern Walker Lane
to the ECSZ in the south.
For the purpose of this study it is appropriate to model the present-day
deformation field by means of a continuous strain rate field based on
GPS velocity observations. For this, we apply a spline interpolation
technique
(Haines and Holt, 1993;
Holt et al., 2000) in
which model velocities are fitted to observed GPS velocities in a
least-squares sense, using the full data covariance matrix. After a continuous
velocity gradient tensor field model has been obtained, we calculated model
velocities for 0.05° (5 km) grid intervals to do the analysis in sections:
Spatial Distribution of Moment and Geodetic Moment Rates.
We combine GPS velocities from multiple studies in the Great Basin
area. Some of these studies are published
(Freymueller et al., 1999;
McClusky et al., 2001;
Oldow et al., 2001;
Svarc et al., 2002a,
2002b;
Mazzotti et al., 2003;
Hammond and Thatcher, 2004;
Savage et al., 2004),
others have been made available otherwise: Eastern Basin-Range and Yellowstone
Hotspot GPS Network (EBRY) (R. Smith, personal comm.,
2003); Southern California Earthquake Center (SCEC) Crustal Motion
Map v.3; Basin and Range Geodetic Network (BARGEN) (R. Bennett,
personal comm., 2003). In addition we have used several unpublished
USGS GPS results from campaign-style surveys: these
consist of the Hawthorne Profile, (part of) the Mammoth network, and networks
presented by
Hammond and Thatcher (2003) and
Hammond et al. (2004).
Each of the geodetic studies used has realized a unique frame of reference
(in general, by assuming North America [NA] to be stable). To be
consistent, we have applied Helmert transformations (when possible) to translate
velocities into the global GPSVEL velocity solution
(Lavallée et al., 2001)
which is in the ITRF2000 frame. We subsequently rotate all velocities into a
North America fixed reference frame, using the ITRF2000 pole obtained from the
GPSVEL solution: 3.0° S, 83.1° W, 0.198°/Ma. For some
studies we have multiplied standard errors in the velocity components with a
factor: EBRY data times 10, BARGEN data times 10,
(Savage et al., 2004)
times 2,
(McClusky et al., 2001)
times 2, and
(Oldow et al., 2001)
times 20.
|
Analysis and Results
|
|---|
The Completeness of the Earthquake Catalog
Figure 1 shows the
epicenters of all earthquakes in the catalog developed in the preceding section.
Earthquakes are concentrated along the southwestern and eastern boundary of the
region. The catalog is more complete in recent years. Completeness as a function
of magnitude was determined from average rate plots, following the method of
Stepp (1972)
(Fig. 3). The average rate in
magnitude intervals was determined from the most recent y years of
data. Considering this average as a function of y, the point at which
the function begins to decline indicates the duration of completeness. From
Figure 3 we estimate that
earthquakes of M 4.8 are complete since 1954, M 5.5
earthquakes are complete since 1932, M 6.0 earthquakes are
complete since 1901, and M 7.0 earthquakes are complete for the
entire duration of the catalog back to 1855.
View larger version (17K):
[in this window]
[in a new window]
|
Figure 4. b-value curves for the study region. (a) Discrete occurrence rates,
where n is the discrete number of earthquakes in the magnitude range
M ±0.25. Error bars show the uncertainty range determined using
the method illustrated in
Figure 3. A different estimate
for the uncertainty in the number of events per year can be inferred from the
plot because earthquake occurrences are approximately a Poisson process (the
approximation is better for M > 6), and for a Poisson process the
variance is equal to the mean. (b) Cumulative earthquake occurrence rates, where
N is the total number of earthquake events of magnitude M or
greater.
|
|
Considering completeness intervals for various magnitudes, the discrete
Gutenberg-Richter relation for the number of earthquakes, n, equal to
magnitude M ±0.25 is log n = 5.66 –
1.00M (Fig. 4a). Using
cumulative rates of occurrence over appropriate catalog durations, we obtain a
relation of log N = 6.66 – 1.15M
(Fig. 4b), yielding 4.4
earthquakes per century with MW 7.0, 0.54 earthquakes
per year with MW 6.0, and 6.6 earthquakes per year with
MW 5.0. These b-value curves are sensitive to
the magnitudes assigned to each earthquake. Of the total moment, 76% was
released during 10 earthquakes of magnitude
MW 6.79
(Table 2), and 90% was released
in the 38 events of MW 6.1. This confirms the
observation that small events do not significantly release accumulating strain
(Brune, 1968;
Anderson, 1979;
Anderson and Luco, 1983;
Shen-Tu et al., 1998).
Spatial Distribution of Moment
Figure 5 shows the
boundaries of four domains (A–D) that we use to compare deformation and
seismicity. The four domains are each 300 km wide.
Figure 6 shows the magnitude of
crustal velocity, as determined from inversion of the geodetic model, along
profiles. These velocities give a smoother picture of the deformation field than
the calculated strain-rate field. A northward broadening of the zone of high
deformations is evident, as observed by
Bennett et al. (2003).
View larger version (31K):
[in this window]
[in a new window]
|
Figure 6. The magnitude of the velocity field determined from inversion of geodetic
data (see text) as a function of XSW, the perpendicular
distance from the southwestern boundary of the study region. The profiles are
located along the upper half of domain A and the centers of domains B, C, and D
(Fig. 5). Modeled velocities
are shown (solid circles) along with one-standard-deviation error bars.
GPS data used to derive the model are also shown (open circles) as
well as their one-standard-deviation uncertainty limits.
|
|
View larger version (25K):
[in this window]
[in a new window]
|
Figure 7. Profiles through domains A (a), B (b), C (c), and D (d)
(Fig. 5), along the western
edge of the province. Each domain extends 300 km inward from the edge of the
study region. For each domain, the top plot shows the cumulative number of
earthquake events within the domain and located at distances greater than
XSW from the southwest boundary. The center plot shows the
magnitude of velocity from
Figure 6. The bottom plot shows
cumulative seismic moment release of all events within the domain located at a
distance greater than XSW from the southwestern boundary of
the study region (Fig. 5). The
thin line in Figure 7b gives
the cumulative moment release with the MW 7.58 Owens Valley
event removed. Right axes of each graph show normalized values.
|
|
View larger version (21K):
[in this window]
[in a new window]
|
Figure 8. Profiles through the eastern domain
(Fig. 5) (a) Cumulative number
of earthquake events within the domain, (b) the magnitude of velocity determined
from inversion of geodetic data through the center of the domain, and (c)
cumulative seismic-moment release within the domain, as a function of the
east–west distance. Modeled velocities are shown (filled circles) along
with one-standard-deviation error bars. Data used to derive the model are also
shown (open circles) as well as their one-standard-deviation error limits.
Scales along the ordinate axes are normalized by the largest values in the total
study region for the latitude range of this domain.
|
|
Figure 7a–d compares
these deformation profiles with the spatial distribution of earthquake numbers
and of moment release within each domain. The seismic moment of each earthquake
is more completely represented as a tensor. Here we use the magnitude of the
maximum eigenvalue. Although tensor information is available for the 10 largest
earthquakes, which release 76% of the total seismic moment, use of tensors
increases the number of degrees of freedom. Therefore a much longer observation
time is required to obtain a reliable comparison with regional components of the
geodetic strain, considering that there is randomness in fault orientations.
The spatial patterns of seismic activity, seismic moment release, and
geodetic deformation are similar along all of the profiles and show a northward
widening of the deformation zone along the western edge of the province. One way
to quantify the similarity of the profiles in
Figure 7 is to tabulate the
distances from the southwest boundary to the point along the profile within
which 75% of the total of each activity measure occurs
(Table 3). For profiles A, C,
and D these widths agree within 20%. Across domain B
(Fig. 7b), 75% of the
earthquake numbers and the geodetic deformation occur within a zone about
90–113 km wide, but the moment release is concentrated by the 1872 Owens
Valley event (Table 2), the
largest event in the catalog. Removal of the 1872 MW 7.58
event results in improved correspondence between the three curves
(Fig. 7b;
Table 3). The 1915 Pleasant
Valley (domain D) and 1872 Owens Valley (domain B) events occurred prior to when
seismic instrumentation was capable of observing aftershocks. If those
aftershocks could be included the distribution of earthquake numbers would
change.
Plots similar to those in
Figure 7 for the eastern domain
(Fig. 5) are shown in
Figure 8. Scales along the
ordinate axes are normalized by the largest values in the study region for this
latitude range. This allows comparison with profiles in
Figure 7. The figure shows that
activity along the eastern half of the Great Basin, across the Wasatch Mountains
(Fig. 5), is significantly
smaller than in the west. The greatest increase on all three rates in
Figure 8 occurs near the
Wasatch Front at 112° W. About 13% of the earthquakes and 4% of the seismic
moment are concentrated east of 112.2° W. Less than about 15% of the
geodetic deformation occurs there.
Malservisi et al. (2003),
in a study of similar GPS data, find that it is not possible to
distinguish between two models: one being elastic strain accommodation on
multiple faults with generally low strain rates (except the Wasatch) and the
other being postseismic creep on the Wasatch fault.
Figures 7 and
8 suggest that spatial
distribution of moderate (M 5) earthquakes and moment release are
correlated in this region. If true, this implies that earthquake numbers and
moment release could be used to constrain the geodetic deformation field and,
conversely, be predicted from geodetic strain rates.
Kreemer et al. (2002)
have suggested that this is true on a global scale, whereas
Masson et al. (2005)
find this relation does not hold at a regional scale for Iran.
Seismic Scalar Moment Rate
The statistical procedure used to estimate the historical seismic-moment rate
is illustrated in Figure 9,
showing cumulative seismic moment as a function of time. As lower- bound
magnitudes of moderate earthquakes were considered, this yields lower-bound
estimates of the moment release rate. A least-squares fit to the points in
Figure 9 (1 point for each
year with an earthquake) has a slope of 6.85 x 1025 dyne cm/yr.
Lines on Figure 9 show a
nonunique, but plausible rationale for moment rates as low as
6.15 x 1025, or as high as 8.84 x
1025 dyne cm/yr.
View larger version (15K):
[in this window]
[in a new window]
|
Figure 9. Plot of cumulative seismic-moment release with time over the study region,
based on preferred moment estimates for each earthquake. Lines show possible
release rates: r1 gives an average rate since 1857 (7.64
x 1025 dyne cm/yr); r2 gives an average
rate since 1871 (8.52 x 1025 dyne cm/yr);
r3 gives the slip-predictable bound (6.15 x
1025 dyne cm/yr); and r4 gives the
time-predictable bound (8.84 x 1025 dyne cm/yr). The time- and
slip-predictable models of moment release usually apply to a single fault, and
extending the concepts to a region with multiple faults does not have the
physical relationship to stress and friction as in the model by
Shimazaki and Nakata (1980).
|
|
To quantify uncertainties associated with these seismic- moment rates, we
repeated the procedure shown in
Figure 9; (1) using upper-bound
estimates of the magnitudes of the smaller events, (2) using smallest and
largest moment estimates for the 10 largest events, and (3) using Monte Carlo
realizations of the moments of the 10 largest events randomly distributed
between the smallest and the largest values. As the estimate of moment rates is
least sensitive to the range of uncertainty of the 790 smaller events in the
catalog (of the total of 800), we focused on the uncertainties associated with
the 10 largest events. Results are given in
Table 4.
The procedure in Figure 9
was automated and repeated for randomly chosen moments of the 10 largest
earthquakes for the Monte Carlo approach. The moment release for each of these
events was randomly selected, assuming a constant probability density between
minimum and maximum Mw estimates. The maximum and minimum
Mw values were selected based on the most reliable and
appropriate estimates of Mw from the literature (Appendix 1,
Table 2). Moment release for
the 790 smaller earthquake events was held constant at the favored values. A
total of 50,000 Monte Carlo realizations was generated. The distributions of
rates from these realizations are shown in
Figure 10 and summarized in
Table 4. Considering one
standard deviation about the mean values and the full set of fitting approaches,
the most likely historical moment rate ranges from 5.8 x 1025
to 11.3 x 1025 dyne cm/yr determined from averaging since 1871.
The extremes are 4.3 x 1025 to 14.9 x 1025
dyne cm/yr.
View larger version (22K):
[in this window]
[in a new window]
|
Figure 10. Distribution of the average seismic moment rate since 1857
(r1) and 1871 (r2) as well as the slip
(r3) and time-predictable (r4) bounds of
the seismic-moment rates determined from 50,000 Monte Carlo simulations. The
distribution designated as r5, not shown on
Figure 9, is derived from a
least-squares fit to the cumulative moments, with each year contributing one
data point. The bin width is 0.1 x 1025 dyne cm/yr.
|
|
Geodetic Moment Rates
The range of moment rates, determined previously, can be compared with moment
rates that can be estimated from the geodetic deformation rates. To do this we
need models that relate the deformation rates to moment rates, which is
nonunique. Acknowledging the nonuniqueness and uncertainty involved with
converting surface strain to a scalar moment rate, this study utilizes four
methods (Anderson, 1979;
Ward, 1998a,
1998b;
Working Group on California Earthquake Probabilities, 1995;
Savage and Simpson, 1997) to
help quantify the moment rate from geodesy and its associated errors. These are
listed in Table 5.
Table 5 shows that for uniaxial
strain (e.g., in the x2 direction) the four methods are very
similar. Anderson (1979) is
different from the other three because he proposed an adjustment for inefficient
fault orientations (parameter k), whereas the other three methods
estimate the minimum rate.
The moment rate estimate from geodetic strain rates is proportional to the
chosen seismogenic thickness. To choose the most appropriate thickness, depth
distributions of microearthquakes from catalog listings from Nevada and Utah
were utilized. Cumulative frequency plots of depth distribution of
microearthquakes (Fig. 11) from
general catalogs show that 98% of events occur at depths less than 15 km for the
entire Utah (1962–1999) region and 17 km for the Nevada region
(1990–1999). Time intervals for data presented in
Figure 11 were selected based
on station coverage. Previous studies have investigated the seismogenic depth
for Utah in more detail. Based on well-constrained focal depths, 15 km is the
preferred source depth used by
Wong et al. (2001) for
Utah.
Arabasz et al. (1992)
found a north–south dependence in focal depth distributions along the
Wasatch Front with 99% of events occurring at 17 km in the south, to 11 km in
the north. Considering the preceding studies and
Figure 11, we assume all
deformation occurs seismically above an average brittle-ductile transition depth
of W = 15 km for the entire study region. The uncertainty
introduced by this assumption is probably under 20%.
We predict the moment rate for the Basin and Range province from the regional
geodetic strain rate tensor models introduced earlier
(Table 5), using a shear
modulus of µ = 3 x 1011 dyne
cm2, W = 15 km, and k = 0.75
(Anderson, 1979). Resulting
moments from geodesy are in the range from 3.91 x 1025 to 6.93
x 1025 dyne cm/yr.
Geological Moment Rates
To determine the geological moment release rate we utilize fault parameters
used as input to the 1996 and 2002 USGS seismic hazard maps
(Frankel et al., 1996,
2002;
Haller et al., 2002).
Data for California come from the 1996 model, whereas all other data for the
study region come from the 2002 model
(Haller et al., 2002).
Although improvements in geological fault characterizations are ongoing, the
USGS database represents an important landmark and plays a key role
in national building codes. The resulting geological moment rate for the region
is 2.55 x 1025 dyne cm/yr.
Comparison of Moment Rates
Moment rates from the seismic, geodetic, and geological methods are compared
in Table 6 and
Figure 12. As discussed
previously these moment rates are intended to display the full range of
uncertainties. Thus we believe that the results in
Figure 12 are a robust
comparison of these differing techniques which we later use to infer the
long-term seismicity rate. Within uncertainties, seismic and geodetic rates are
in agreement. Geological rates are much lower than the seismicity and geodetic
rates. This is not surprising considering the limiting paleoseismic data, which
are necessarily based only on faults that have been well characterized, a
minority of all the faults in the Basin and Range.
View larger version (17K):
[in this window]
[in a new window]
|
Figure 12. Comparison of the range of moment rates determined from the historical
seismicity with those determined from geodesy and geology
(Table 6). Both the extreme
values (thin line) and the most likely bounds (thick line) on the seismicity
rate are shown.
|
|
|
Maximum Magnitude for the Great Basin
|
|---|
We consider whether recent suggestions in the literature regarding the
maximum magnitude of earthquakes within the Basin and Range are consistent with
our results.
Anderson and Luco (1983)
related three functional forms of the Gutenburg-Richter curves to the moment
rate. These models depend on (1) the rate of occurrence at a reference
magnitude, (2) a b-value, and (3) the maximum magnitude
Mmax. Major differences among the models occur in the way
they are truncated as they approach Mmax. The integral of
the area under these curves defines the moment release rate, based on the
specified frequency-magnitude relationship. Note that these models are not
physical laws to which earthquake statistics must ultimately conform. However,
assuming that the frequency-magnitude distribution characterized by the seismic
catalog is representative of the region, we apply these curves to the current
catalog (1) to determine which of the
Anderson and Luco (1983) models
is most representative of the Basin and Range seismicity and (2) to determine
what values of Mmax come out of fitting each of these curves
to the observations.
We compare the historical cumulative magnitude distribution
(Fig. 4b) with the
Anderson and Luco (1983) models
(Fig. 13). The curves are
normalized using a moment release rate of 11.3 x 1025 dyne
cm/yr, corresponding to the upper limit of our most likely historical moment
rate range obtained from the historical seismicity. Increasing
Mmax, while continuing to match a moment release rate of
11.3 x 1025 dyne cm/yr, results in lowering of the curves. The
comparison of these models to the historical b-value curve indicates
that model 1 best matches the data when Mmax 7.58, model 2
matches when Mmax 8.0, and model 3 matches when
Mmax 8.2. Lowering the moment release rate to 5.8 x
1025 dyne cm/yr lowers the curve requiring Mmax
6.8 for model 1 to satisfy the historical seismicity, whereas models 2 and 3
fail to fit the high-magnitude end of the curve.
View larger version (15K):
[in this window]
[in a new window]
|
Figure 13. Cumulative earthquake occurrence rates [N(m)] for the
three functional forms of the Gutenburg-Richter curves of
Anderson and Luco (1983), using
b = 1.00
Figure 4b. These models depend
on (1) N1 = 10a–bM
H (Mmax – M) the rate of occurrence
at a reference magnitude, (2) n2 =
–dN2/dM =
10a–bM H(Mmax =
M) a b-value, and (3) n3 =
–dN3/dM =
(10a–bM – 10a–bMmax)
H(Mmax = M) the maximum magnitude,
Mmax. The plots have been normalized using a moment-release
rate of 11.3 x 1025 dyne cm/yr corresponding to the most likely
maximum estimate determined from historical seismicity. To match the moment
release rate Mmax is set to 7.58, the largest event in the
catalog for N1, Mmax = 8 for
n2, and Mmax = 8.2 for
n3.
|
|
Models 2 and 3 appear to match the cumulative moment curve better than model
1 in Figure 13. However, at
low- occurrence rates the shape of the curve determined by data is poorly
constrained given the duration of observations. We feel that there is not
sufficient data to determine which model best characterizes Basin and Range
seismicity rates.
With consideration of moment rates from historical seismicity and geodesy,
the Anderson and Luco (1983)
models imply that there is no reason to expect an earthquake in the Great Basin
with magnitude greater than Mmax 
8.2. This is
inconsistent with the suggestions of
Wernicke (1995) and
Kagan (1999), through separate
lines of research, that the region could experience earthquakes of magnitudes
much greater than eight.
Kagan (1999) proposed a
universal magnitude-frequency distribution in which the b-values and
maximum moment is the same for all continental regions. He proposed that for
shallow earthquakes the universal value of the effective maximum moment
magnitude is of the order 8.5–9.0. As shown previously, this magnitude is
inconsistent with the historical earthquake rates. An earthquake of this size
also runs into difficulty on physical grounds. Consider for instance that an
event with Mw 8.5 has, by
equation (3), a seismic moment of
7 x 1028 dyne cm. To maximize the fault area and shear modulus,
we consider values larger than those used previously: µ = 4
x 1011 dyne cm2 and a dip of 45° where the
seismogenic thickness is 17 km, yielding W = 24 km. From the
definition of seismic moment
(equation 1), the product of
fault length (L) and mean slip (D) for an event of this size
will be about LD = 7300 m km. A rupture on a fault of 300 km
length (greater than any fault in the Great Basin) would need an average slip of
24 m, which is larger than any observed historical rupture anyplace in the
world. We thus conclude that the Kagan model is not reasonable, both on
statistical and physical grounds.
Wernicke (1995) speculates
that seismogenic low-angle normal faults that form the base of the entire
seismogenic zone play an important role in accommodating Basin and Range
extension. He further speculates that these faults have longer recurrence
intervals than steeply dipping faults because they fail in infrequent, extremely
large magnitude events. Wernicke suggests that the hypothesized ability of
low-angle normal faults at the base of the crust to generate large events with
greater magnitudes has not been tested globally because of the short historical
records. Although low-angle normal faults have been imaged in the Basin and
Range province
(Allmendinger, 1983;
Abbott et al., 2001),
there is no evidence there or elsewhere that such structures experience brittle
failure. A common expectation is that the extension of the region occurs by
creep on these faults below the brittle-ductile transition. If the Wernicke
speculation is correct, then the stress accumulation would roughly double the
seismic-moment rate from the estimates given previously, and the statistical
argument would allow Mmax to increase to about 8.2. However,
evidence for accommodating extension by a creep mechanism
(Buck et al., 2003) at
the strain rates present in the Great Basin suggests that this model is
unlikely.
|
Discussion and Conclusions
|
|---|
The moment rate of earthquakes implied by geodesy is consistent with the
historical seismic estimate. The extremes on the range of moment rate from
historical seismicity, based on mean rates and on linear upper and lower bounds
for the cumulative moment curves allowing for uncertainties in the moments of
the controlling earthquakes, are 4.3 x 1025 to 14.9 x
1025 dyne cm/yr. The most likely rate is between 5.8 x
1025 to 11.3 x 1025 dyne cm/yr. This overlaps the
range determined from the geodetic data, 3.9 x 1025 to
6.9 x 1025 dyne cm/yr
(Fig. 12). This suggests that
the rate of historic earthquakes within the Basin and Range province, taken as a
whole, is the rate that should be expected in the future.
Uncertainties in estimates of moment rates do not arise only on the
seismicity side. Geodetic and seismic measurements sample different aspects of
the deformation field. Seismicity and geological estimates serve only as a
record of brittle deformation, whereas geodesy encompasses both seismic and
aseismic strain accumulation. Recently, significant aseismic deformation has
been observed below Lake Tahoe, California
(Smith et al., 2004),
demonstrating the importance of aseismic strain in the Great Basin. Geodetic
rates cannot uniquely determine slip at depth
(Savage and Simpson, 1997) and
may only give a measure of the instantaneous strain transients, which may not be
preserved throughout the earthquake cycle
(Savage and Lisowski, 1998;
Shen-Tu et al., 1999).
Recent geodetic observations have shown that historical moment release has
occurred where contemporary strain is accumulating
(Hammond and Thatcher, 2004).
Whether the geodetic signature is representative of long- term deformation is
argued by Thatcher (1995) to
depend on fault characteristics and spacing, the extent of the cyclic zone, and
whether the geodetic network completely spans the entire deforming zone.
Geodetic measurements may therefore be sensitive to the duration and sampling of
deformation with agreement also dependent on whether the sample period covered
includes earthquakes that contributed significant post and coseismic
displacements to the observed geodetic velocities. Apart from these
uncertainties due to Earth processes, additional uncertainties are introduced in
the processing decisions in converting individual GPS measurements to
regional strain-rate models. These uncertainties become more important as the
size of the region decreases. The final geodetic uncertainty arises in
converting strain rates to seismic moment rates.
We suggest that it is possible to expand on and quantify the suggestions of
Smith (1976) and
Ward (1998a) that the adequacy
of seismic catalogs to estimate earthquake recurrence rates depends on the area
of the region, catalog duration, and regional strain rates. Where Smith looked
at the product of time and length of the seismic zone, and Ward looked at the
product of time and strain rate, we suggest that it is useful to define a
catalog adequacy parameter
| (4) |
defined as the product of the duration of the earthquake record (T),
the area of the region, and the average strain rate,
, as estimated by
space geodetic methods. For a given strain rate, as the size of the region
decreases, a longer catalog duration is needed. It should be obvious that the
parameter becomes meaningless if the region is too small to contain a
characteristic earthquake. There is no requirement that the strain be
distributed uniformly within the region. For the Basin and Range, T
= 146 years, 
= 7.25 x 105 km2,
and, for the region as a whole
V/L = 1.3 x 10–8/yr, where the
slip rate V = 13 mm/yr is the relative velocity of the Sierra
Nevada block relative to stable North America, and L = 1000 km
is the average width of the region. These parameters yield Z 1.38
km2. For the domains A–D
(Fig. 5), using the same
procedure, Z 0.1–0.25, and since within these areas the
historical and geodetic methods do not agree well
(Fig. 7), these values of
Z are apparently too small. Based on these Basin and Range results, it
seems reasonable to expect that in other regions with Z 1.5
km2, historical seismicity and geodesy will agree within
uncertainties, although of course more testing is needed to confirm this
hypothesis.
The spatial consistency of the distribution of small earthquakes,
deformation, and moment release shown in
Figure 7 is interesting. Given
the shortness of the catalog duration and variability in absolute rates, spatial
similarity between geodetic deformation and seismicity is not necessarily
expected. Even in domain B
(Fig. 7b), where the moment
release is highly concentrated in the Owens Valley because of the 1872
MW 7.74 Owens Valley earthquake, the spatial distribution of
moderate earthquakes follows a broader curve similar to the deformation.
Considering the uncertainties in estimates of the spatial distribution of the
seismic hazard from historical seismicity, geodesy, and geology, consistency of
more than one of these techniques is a key factor in providing confidence for
how seismic hazards are localized. We suggest that it is worthwhile to
investigate conditions for the similarity of seismicity and geodesy to hold and
consider that it is possible that some criteria based on a catalog adequacy, or
related, parameter might be possible.
|
Appendix 1: Magnitudes of the Ten Largest Events
|
|---|
Owens Valley 1872—3 26 10 30
Moment magnitude estimates for this event were available from geology.
Wells and Coppersmith (1994)
give an estimate of MW 7.61, but we obtained
MW 7.58 using their moment because
equation (3) differs from their
conversion from moment to magnitude.
Beanland and Clark (1993)
estimate an MW value of 7.44–7.70. In addition, an
MW estimate of 7.74 was obtained from a moment estimate
based on geology and felt area of the earthquake
(Hanks et al., 1975).
This value is quoted as MW 7.80 by
Toppozada et al. (1981)
and documented as MW 7.76 from
Hanks et al. (1975) in
the U.S. historical catalog. Considering the geological observations to be more
reliable than the felt area for estimating the earthquake size, we use the
Beanland and Clark results to obtain the maximum and minimum estimate for the
moment of this event, and use the Wells and Coppersmith parameters to obtain our
best estimate.
Pleasant Valley 1915—10 3 6 53
Doser (1988) gives a
body-wave estimate of the earthquake size of MW 6.82.
However, Doser and Smith (1989)
model this event as two subevents and obtain a best estimate of
MW 6.89. The lower bound on this best estimate of
MW 6.87 gives us the minimum estimate of the size of
this event. A number of geological estimates were also available.
Doser (1988) and
Doser and Smith (1989) quote a
geological MW 7.15 from geological data using average
displacements, a focal depth of 16 km and a dip of 60°.
Wells and Coppersmith (1994)
also obtain a geological estimate of MW 7.15, whereas our
calculations using the Wells and Coppersmith data give an estimate of
MW 7.14.
Because of the low magnitude of the body-wave estimate we retain the
Wells and Coppersmith (1994)
value of MW 7.15 for the final catalog, which is also the
maximum estimate.
Cedar Mountain 1932—12 21 6 10
Only body-wave and geological estimates were available for this event.
Doser (1986,
1988) and
Doser and Smith (1989) modeled
this earthquake as two subevents. We choose the moment calculated by summing the
individual moments of the two sube
Top
Abstract
Introduction
M 
