Waveform Stacking Research Articles

Numerical Modeling for Earthquake Source Image: Implications for Array Design in Determining the Rupture Process

The aim of this study is to develop a numerical method to evaluate the optimum seismic station distribution for imaging the source rupture process of an earthquake. Based on the beam-forming technique, the source rupture distribution of an earthquake can be reconstructed through theoretical travel time correction and waveform stacking. Numerical tests show that this method successfully reconstructs the main displacement distribution from an assumed source rupture plane. In accordance with assumed fault models, seismic waveforms are numerically generated as input data for further source imaging. From synthetic seismograms, we reconstructed the rupture distribution of these assume earthquake sources, and analyzed error systematically. Results of this study indicate that receiver distribution types really affect the successful reconstruction of the slip distribution. Furthermore, parameters such as dip angles and frequency content also play important roles in reconstructing earthquake sources. The proposed method is simple, inverse efficiently, and no initial condition required. Further applications of this method are suggested to image source rupture from near field strong motion observations and to design seismic array to effectively observe seismic rupture properties.

Azimuthal and regional variations of coda waves in New Zealand

We present the results of using seismic waveform data to show that the elliptical nature of isoseismal distributions in New Zealand is related to regional structural trends. The data also suggest that there are regional and azimuthal variations in the attenuation of coda waves, which may need to be considered in ground motion attenuation relations.
 We stacked over 20,000 waveforms from the New Zealand seismographic network. The data were filtered, normalized and stacked. Noisy or clipped records were down-weighted or removed. We also treated dense networks as a single station and generated a single stack for these networks. Stacks of shallow earthquake sources are presented by region and azimuth.
 Variations in coda length throughout New Zealand suggest regions of high scattering. Strong azimuthal dependence in the coda is observed for non-volcanic zone stations. NE-SW waveform stacks, which follow the strike of the subduction zone, contain significantly longer codas than those with NW-SE raypaths. Long coda trains are also observed in the volcanic and geothermal zones yet there is little or no apparent azimuthal variation. These coda are particularly strong throughout the records which explains the difficulty analysts have had in picking S waves.

Short‐period P wave constraints on D″ reflectivity

We present evidence of a P wave reflector in D″ beneath the central and eastern equatorial Pacific obtained from nearly 7000 short‐period seismic recordings of earthquakes in the Tonga‐Fiji and South America subduction complexes. Both regions overlap previous observations of an S wave triplication at similar depths. Double‐array waveform stacking places the reflector 190 ± 20 km above the core‐mantle boundary and allows for a velocity transition zone no thicker than 50 km. The data admit a wide range of compressional (vP) and shear wave velocities (vS); the 2–3% increase in vS suggested by earlier long‐period S wave studies, however, necessitates only a 0.5–0.6% increase in vP. The data stacks represent spatial averages over large areas of the lower mantle, such that reflector intermittence and topography decrease stack amplitude and lower the apparent vP jump. Our results constrain these processes to act over length scales of 10–100 km.

Topography on the 410‐km seismic velocity discontinuity near subduction zones from stacking of sS, sP, and pP precursors

We stack the teleseismic depth phases sS, sP, and pP produced by deep focus earthquakes to image precursory arrivals that result from near‐source, underside reflections off the 410‐km seismic velocity discontinuity (hereinafter referred to as the 410) and use differential time measurements between these phases and their precursors to compute discontinuity depths near seven subduction zones around the Pacific Ocean margin. We begin by selecting seismograms with high‐quality depth phase arrivals recorded by several long‐period networks between the years 1976 and 1996. Filtering the waveforms and stacking them along theoretical travel‐time curves reveals clear precursors which vary in shape and timing. We compute confidence levels to evaluate the reliability of the observed precursory features using a bootstrap method that randomly resamples the seismograms prior to stacking. We measure the differential travel time between the reference pulse and the precursor using a cross‐correlation technique and convert this time to an apparent discontinuity depth using the isotropic Preliminary Reference Earth Model (PREM) at 25‐s period, corrected to an oceanic crustal thickness. The lateral resolution of our long‐period stacks for 410 topography is limited compared to that sometimes achieved in short‐period analyses but is much higher than that obtained from global SS precursor studies. For most subduction zones the results indicate little change in the average depth to the 410‐km discontinuity in the local areas sampled by the precursor bounce points compared to broad regional depths inferred from SS precursor results. This implies that any large variations in depth to the 410‐km discontinuity near subduction zones are limited to a narrow zone within the slab itself where they may be difficult to resolve with long‐period data. Coverage for the Tonga and Peru‐Chile subduction zones is sufficiently dense that we can observe lateral variations in 410 depths. In Tonga the results suggest depth variations perpendicular to the slab of up to 33 km, after correcting for probable lateral heterogeneity in velocity above 400 km depth, and variations parallel to the slab orientation as large as 13 km. The cross‐slab variation is consistent with the elevation of olivine phase transformations in cold regions; the variation along strike suggests a more complex thermal heterogeneity that may be related to the subduction history of this region. We see evidence for additional reflectors above the 410 in some of the waveform stacks, but the inconsistency and weak amplitude of these features preclude definitive interpretations.

Comparison of broadband and short‐period seismic waveform stacks: Implications for upper‐mantle discontinuity structure

Stacks of short‐period and broadband seismic waveforms from four deep (h > 550 km) earthquakes in South America recorded in California exhibit small amplitude signals between the direct P and surface‐reflected pP phases. The anomalous and variable slownesses of these signals in short‐period stacks, as well as differences between short‐period and broadband stacks suggest that the weak arrivals originate by reflection from laterally varying structure in the mantle near the subduction zone. The only structure consistently producing near‐source and near‐receiver reflections is the “410 km” discontinuity, which varies in depth by ±10 km, and has an impedance contrast comparable with that predicted by reference Earth models.

Synthetic seismogram images of upper mantle structure: No evidence for a 520‐km discontinuity

Seismological data used by Shearer (1990, 1991) to infer the existence of a seismic discontinuity at 520 km depth are compared with complete long‐period body wave seismograms calculated for the International Association of Seismology and Physics of the Earth's Interior 1991 (Iaspei91) Earth model. The Iaspei91 model does not contain a seismic discontinuity at or near 520 km depth. The observed P and SH multiples caused by topside reflections and SS precursors caused by underside reflections from the 410‐km and 660‐km discontinuities are well reproduced by the synthetic stacks. The synthetics exhibit clear “phase extrema” between these reflections that correlate well with similar features in the observed waveform stacks. Shearer interpreted these “phase extrema” as separate reflections from a seismic discontinuity at 520 km depth. Cross‐correlation analysis of synthetic seismograms gives an apparent discontinuity depth of about 520 km for P and SH multiples as well as SS precursors. Similarly, amplitude analysis of synthetic upper mantle reflections is in reasonable agreement with the observations reported by Shearer (1991). The phase extrema seen in the synthetics are the result of an extended, multicycle wavelet which is composed of depth phases and other structural phases such as reverberations from the crustal layer, convolved with the instrument response of long‐period stations of the Global Seismograph Network. The comparison of observational data, presented by Shearer (1990, 1991), with the synthetic seismogram stacks of this paper shows that the claim of good seismological evidence for a 520‐km seismic discontinuity as a global feature is not compelling.

Constraints on upper mantle discontinuities from observations of long‐period reflected and converted phases

Stacked images combining over 5 years of long‐period Global Digital Seismograph Network data reveal many phases associated with reflections and conversions from upper mantle discontinuities. These images show travel time and amplitude relative to a reference phase which is aligned and normalized on all seismograms prior to stacking. Results obtained for P, S, SS, and PP reference arrivals resolve numerous phases from discontinuities near 410 and 660 km, while some of the stacks also show evidence for a weaker discontinuity near 520 km. Phases of particular interest include P and SH multiples resulting from topside reflections, precursors to SS from underside reflections, and P‐to‐SV converted phases. These phases can be clearly seen both in the waveform stacks and in cross‐correlation analysis of individual seismograms. Travel times for these arrivals are converted to discontinuity depths relative to velocities in the Preliminary Reference Earth Model, and empirical corrections are applied for the effects of lateral velocity variations in the upper mantle. Average apparent depths to the discontinuities for the different phases agree to within ±3 km for the 410‐km discontinuity, to within ±4 km for the 520‐km discontinuity, and to within ±8 km for the 660‐km discontinuity. The best global averages are obtained from the SS precursor data which indicate discontinuities at 415, 519, and 659 km. Discontinuity depths obtained from the P‐to‐SV converted phases at over 35 individual seismic stations exhibit variations of less than ±20 km. Apparent depths to the 660‐km discontinuity consistently show greater variability than depths to the 410‐km discontinuity, supporting recent laboratory results which indicate that the Clapeyron slope for the 660‐km discontinuity is significantly larger in magnitude than the slope for the 410‐km discontinuity. Precursors to SS (seen between 110° and 180°) are particularly useful for mapping possible lateral variations in discontinuity depths since each arrival can be associated with a single underside reflection point Apparent discontinuity depths computed from SS precursors for different tectonic regions agree to within about ±5 km. The SS precursors have especially good coverage near the subducting slabs in the northwest Pacific. Analysis of apparent discontinuity depths in this area suggests the presence of a broad 1000‐ to 1500‐km‐wide region near the slab in which the 660‐km discontinuity is depressed by about 20 km. Measuring absolute amplitudes for these phases is difficult due to the large corrections required to compensate for the effects of incoherent stacking. Relative amplitude analysis suggests that the P and S wave impedance changes at 410 km are about 0.8–1.1 times the size of the changes at 660 km and that the contrasts at 520 km are between 0.3 and 0.6 of the changes at 410 km.

A new signal averaging algorithm for discrete signals

A technique for the stacking of phase coherent waveforms is presented. The algorithm consists of a sampling process followed by bandpass filtering and is therefore faster than conventional stacking. Expressions for the power spectral density (PSD) and variance of the output noise are derived. The error variance attains the Cramer-Rao bound when the signal and noise spectra satisfy certain conditions. The fast algorithm therefore has the same performance as conventional stacking, but has a computational advantage. Examples illustrating the performance of the algorithm are included.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>