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Short Note |
1 Department of Geology, University of
Illinois
1301 W. Green St., 245 NHB
Urbana, Illinois
61801-2939
tseng1{at}uiuc.edu
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Abstract |
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 Top Abstract IntroductionAnalysis and ResultsDiscussions and Geologic...ConclusionsAcknowledgmentsReferences |
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Introduction |
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TopAbstractIntroductionAnalysis and ResultsDiscussions and Geologic...ConclusionsAcknowledgmentsReferences |
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A case in point is the PpPmp phase reflected off the Moho (Fig. 1). Yu and Schuster (2001) and Sheng et al. (2003) pointed out that the reflection point of this phase at the free surface can be treated as a virtual source, thus one can use the PpPmp phase to construct seismic profiles that mimic conventional reflection profiles. In effect, phases such as the PpPmp allow one to construct vertical-component, P- wave receiver functions. Langston and Hammer (2001) used broadband data from isolated stations in southern California to test such a procedure, but probably because of complex crustal structures, the results were not encouraging. Using a broadband array of closely spaced stations (4–8 km) but low- frequency signals (below about 0.2 Hz), Li and Nábelek (1999) showed discernable PpPmp phases across a profile in Cascadia.
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In this study, we demonstrate P-wave receiver-function profiles at frequencies as high as 1.2 Hz and extend this method to short-period data. This is a promising prospect in that (1) P-wave receiver functions, sensitive only to P-wave velocities, use just a single component of data and complement conventional approaches that depend on both P- and S-wave velocities (Ammon et al., 1990) and (2) short-period, vertical-component data are widespread and have been accumulating for many years prior to the broadband era, opening up opportunities for new investigations. Specifically, we will show that the Moho under the Gauribidanur Array (GBA) in southern India is a sharp, subhorizontal interface. By constraining the average P-wave speed in the overlying Archean crust, we also discuss implications of our results for crustal composition.
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Analysis and Results |
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TopAbstractIntroductionAnalysis and ResultsDiscussions and Geologic...ConclusionsAcknowledgmentsReferences |
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This data set is unique; it is the only array data available in the public domain to study seismic properties of the Archean crust in southern India. The absence of data from horizontal components rules out conventional receiver functions and makes P-wave receiver functions a natural choice. However, the narrow passband of short-period instruments imposes a technical limitation. By a combination of carefully selecting deep earthquakes of short, simple rupture history, dense spacing of stations, and low background noise, we constructed several profiles of P-wave receiver functions from sources that have distinct backazimuths (Table 1).
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To remove effects near the source and response of the short-period instrument, we first compute the principal component, or the eigen image, of the seismic profile by singular- value decomposition (Ulrych et al., 1999). This procedure isolates signals that are common to all seismic traces in the profile, akin to but more robust than the average obtained from stacking. In this case, a high ratio between the two largest singular values (27:1) indicates the dominance of the principal component. Starting at the onset of the direct P arrival, we take the first 3.5 sec of the principal component as an estimate of the source wavelet that must be common to all stations (Fig. 3a) (Li and Nábelek, 1999). Oscillatory form of the source wavelet is then removed from each seismic trace by iterative deconvolution in the time domain (Fig. 3b) (Ligorria and Ammon, 1999).
This process sharpens the PpPmp pulse and reduces the background noise (Fig. 3b). The PpPmp phase now stands out as a coherent wavelet among all traces, arriving about 10 sec after the direct P arrivals. On average, amplitude of the PpPmp phase is about twice as large as the intervening coda immediately after the direct P arrival. Furthermore, the intervening coda is incoherent among neighboring seismograms, perhaps related to scattering in the shallow portion of the crust near GBA (Krishna and Ramesh, 2000). In Fig. 3b, the PpPmp phases map out a sharp, subhorizontal Moho based on P-wave receiver functions. This profile is equivalent to a deep-penetrating seismic reflection profile.
Notice that, at this stage, only effects of the source wavelet (including instrument response and structures near the source) are removed by deconvolution. In contrast, a conventional receiver function deconvolves the radial component of data by using the entire wave train on the vertical component. Consequently, the PpPmp phase is obliterated in conventional receiver functions even if its signal is originally present in the data.
In practice, there are some technical restrictions for vertical-component P-wave receiver functions to work properly. Optimally, the focal depth should be deeper than approximately 100 km so source-side reflections and conversions, such as phases pP and sP, do not interfere with the PpPmp phase. Another source of interference comes from reflections off the core (PcP), which becomes an issue at distances beyond about 80 deg. For the same reason, the duration of the source wavelet, including the combined effects of the source time function, attenuation, and the instrument response must be short.
For event 1, the duration of the source time function is only about 2 sec (Kao and Chen, 1994). We test different durations of the source wavelet ranging from 2.5 to 4.0 sec, and there are no discernable differences in the result of deconvolution. For precise control of the passband, we also test deconvolution by using damped spectral division. The results are comparable to those using the time-domain method up to a high corner frequency of about 1.2 Hz (Fig. 4a). In fact, deconvolved waveforms are simple enough to be matched by synthetic seismograms based on a one- dimensional crustal model (Fig. 4c), justified by the simple image of Moho (Fig. 3b) and by negligible amplitude on the tangential component reported by Rai et al. (2003) who studied conventional receiver functions using proprietary data from a single-broadband station in Gauribidanur.
We corroborate the validity of the crustal model using data from another earthquake to the southeast of GBA (event 2, Table 1). In this case, the duration of the source wavelet is estimated to be about 4 sec. Because of interference from another event, the useful portion of the data ends just after the PpPmp phase, which arrives about 0.3 sec earlier then that of event 1. This observation is consistent with the small epicentral distance of event 2 and thus a large angle of incidence below the array (Fig. 4b). There is noticeable coda immediately after the direct P arrival. The coda appears to arise from complications confined in the shallow part of the crust, as noise is low for about 2.5 sec prior to the PpPmp phase whose amplitude and timing are both matched by synthetic seismograms (Fig. 4b). A slight misfit in the timing of the PpPmp phase is only about 0.2 sec, comparable to estimated uncertainties in our measurements (to be discussed in the next section). Such a small fluctuation can be accounted for by a minor variation of 0.7 km in crustal thickness or a change of about 0.1 km/sec in VP.
For the data set at hand, the single greatest limitation is the extremely narrow passband of instruments at GBA. For ground velocity, the response is centered at 1 Hz and drops by about 50 and 20 dB/decade toward the low- and high- frequency ends of the spectrum, respectively. As such, the source time function must not only be short but also smooth for the deconvolution to yield stable results without excessive levels of intervening coda between the direct P and the PpPmp phases. For the ten events listed in Table 1, the PpPmp phase is always coherent across the GBA array and results are consistent among different events. When data from modern broadband arrays are available, the method described here should work even better than the best examples shown in Figures 3 and 4.
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Discussions and Geologic Implications |
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TopAbstractIntroductionAnalysis and ResultsDiscussions and Geologic...ConclusionsAcknowledgmentsReferences |
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As such, precise timing between P and PpPmp phases from our
results leads to a corresponding VP of 6.55 ± 0.09
km/sec (Fig. 4c), using a
generous estimate of error in timing, up to ±1/6 of the dominant period
of pulses (
1 sec). By including uncertainties in crustal thickness, the
uncertainty in VP would be ±0.37 km/sec. Rai et
al. (2003) reported
VP/VS of 1.75 ± 0.03 and an
average crustal VS of 3.75 km/sec for GBA (formal
uncertainty unknown; table 2 of
Rai et al., 2003).
These values imply a corresponding VP of 6.56 km/sec,
consistent with our results, which are independent of VS.
For comparison, the global average of VP under all shields
and platforms is about 6.42 ± 0.20 km/sec
(Christensen and Mooney, 1995).
For many important types of crustal rocks, speeds of P and
S waves (VP and VS) and
the Poisson's ratio increase monotonically with mafic content (e.g.,
Christensen, 1996).
VP/VS of 1.75 ± 0.03 near
GBA is equivalent to a Poisson's ratio (
) of about
0.26 ± 0.01, comparable to that under Hyderabad
(Zhou et al., 2000), a
long-standing broadband station also located on the exposed Archean shield
farther to the north of GBA
(Fig. 2), and elsewhere in
southern India
(Saul et al., 2000;
Kumar et al., 2001). Such values of collectively imply an intermediate to felsic
bulk composition for the Archean crust in southern India. Lower values have been
reported for the Sao Francisco craton in southeastern Brazil (0.23; Assumpcao
et al. [2002])
and the Tanzanian craton (0.24 to 0.26 ± 0.02; Last et al.
[1997]), implying an
even less mafic crust in these regions.
Based on a global study of receiver functions, Zandt and Ammon
(1995) reported that the
Poisson's ratio increases with age of continental crust. Shield regions,
including both Archean and Proterozoic crust, have the highest Poisson's ratio
of 0.29 ± 0.02. Because lower values of , 0.26 or less,
seem to be common in several Archean shields, the average Archean crust appears
to be less mafic than the younger crust formed during the Proterozoic
(Zhou et al., 2000).
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Conclusions |
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TopAbstractIntroductionAnalysis and ResultsDiscussions and Geologic...ConclusionsAcknowledgmentsReferences |
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Acknowledgments |
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TopAbstractIntroductionAnalysis and ResultsDiscussions and Geologic...ConclusionsAcknowledgmentsReferences |
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Manuscript received April 12, 2005
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References |
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TopAbstractIntroductionAnalysis and ResultsDiscussions and Geologic...ConclusionsAcknowledgmentsReferences |
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2f2/a2),
where f is frequency and a is the Gaussian width (set to 5
sec–1). For frequency- domain deconvolution (F.D.), we used a
six-pole, zero-phase Butterworth filter between 0.1 and 1.2 Hz. (c) Crustal
model used to generate synthetic seismograms by the reflectivity algorithm of
Randall (