S23B-0303 1340h
Scattering Attenuation And Dispersion Of {\it SH} Waves In 2-D Elastic Media With Densely Distributed Cracks
We compute the synthetic seismograms of multiply scattered {\it SH} waves in 2-D elastic media with densely distributed parallel cracks. We assume two spatial distributions; elastic media with periodic distribution of cracks in a zone and randomly distributed cracks in a rectangle bounded region. The calculated attenuation coefficient $Q^{-1}$ of the primary wave is directly proportional to the crack density in the ranges of $\nu a^2 \leq 0.05$, where $\nu$ and $a$ are the number density and half length of cracks, respectively. This is consistent with that obtained by a stochastic analysis based on Foldy's approximation. When cracks are distributed densely ($\nu a^2=0.075$ and 0.1), our result on $Q^{-1}$ still agrees with it for the random crack distribution models but appears to differ from it for the periodic distribution of cracks especially in the low wavenumber ranges. This suggests that the effect of multiple interactions among densely distributed cracks depends on not only the density but also the spatial distribution of cracks at low wavenumbers. The calculated phase velocity of the primary wave is consistent with that from the stochastic analysis in the ranges of $\nu a^2 \leq 0.1$ and does not depend on the spatial distribution of cracks. This suggests that the multiple crack interactions have a small effect to the phase velocity. Therefore the crack density can be estimated from the values of the phase velocity for the cases of densely distributed cracks even if the effect of the multiple crack interactions is not considered. We can clearly observe the reflected waves in the synthetic seismograms. The reflection coefficient shows a periodical behavior in low wavenumber ranges and its wavenumber dependence is identical to that of an anisotropic layer. The elastic constants and thickness of the cracked zone are estimated by fitting the reflection coefficients to those of a single anisotropic layer for both cases of normal and oblique incidence. The estimated thickness and elastic constants are shown to be reasonable. The elastic constants depend on a crack density, so that it is possible to estimate the density of cracks distributed in a fracture zone when the elastic constants are obtained from the frequency dependence of the reflection coefficients.
S23B-0304 1340h
Modeling of SH Wave Envelopes in Media With Many Cavities: Wave Simulations vs. Radiative Transfer Theory
Since Aki's (1969) pioneering work on the origin of coda waves, synthesis of seismic wave envelopes in the randomly heterogeneous earth has been attracting seismologists' interest. Several models have been proposed for this purpose, but their validation has been mainly restricted to continuous random media. Here, instead, we deal with 2-D circular cavities as a tractable example of discrete heterogeneities. We randomly distribute many cavities within a rectangular area with the concentration varying from 0.004 to 0.2. We then let a plane SH Ricker wavelet impinge on its one side, and synthesize rigorously the RMS seismogram envelopes along the opposite side, using a boundary integral method (Benites, Aki and Yomogida 1992). In our previous work (Eos Trans. AGU, 84 (46), Fall Meet. Suppl., Abstract S11E-0346, 2003), we compared these synthetics with the predictions by a few models, such as the single isotropic scattering model (SISM), thus discussing their validity ranges. In the present study, we now examine other two models: the radiative transfer theory (RTT) and the diffusion model (DM). RTT is numerically solved using a Monte Carlo method (Yoshimoto 2000). Here anisotropic scattering is replaced for simplicity by isotropic one with the aid of the momentum transfer scattering coefficient; this approximation is valid when multiple scattering is dominant. Note that the analytical solutions of SISM and DM are the asymptotic solutions of RTT in the limits of weak and strong multiple scattering, respectively. It is shown that RTT agrees with the wave simulation-based coda envelopes as a whole in many cases examined. The agreement tends, however, to be worse for the early coda part with which single scattering is dominant, as the anisotropy of scattering (depending on frequencies) gets stronger. Concerning the direct wave part, RTT systematically underestimates the envelopes and also cannot reproduce the time delay occurring at low frequencies, probably because of neglecting the constructive interference. It is also shown that DM works as well as RTT does when the distribution area is thicker than the transport mean free path, as expected.
S23B-0305 1340h
Is Markov Approximation Valid for Transmission Fluctuation Problems?
We know that the Markov approximation is a widely-used and a key approximation in the theoretical developments for the wave propagation in random media. In seismology, transmission fluctuation functions are used to infer the statistical structure of the heterogeneities in the Earth mantle. The scale and the pattern of the heterogeneities in the mantle will bear important implications for the mantle material physical properties and even the earth internal dynamics. However, recent numerical simulations and field studies have found some discrepancies with the theoretical predictions for the phase (travel-time) fluctuations across a seismic array of the teleseismic waves. In order to confirm this disagreement and to find the causes that account for the discrepancy, we have carried out extensive numerical experiments and theoretical analysis. The validities of the basic approximations in the theory (Chernov, 1960; Wu and Flatte, 1990), such as the Rytov approximation, one-way approximation, parabolic approximation, and the Markov approximation, have been examined and calibrated. Numerical simulations using full-wave finite difference, wavelet-based full-wave simulations, one-way propagators (generalized screen propagators), Rytov simulations, and parabolic simulations have been conducted to help evaluate the importance of each approximation. We have found that the Rytov and the one-way approximations are generally valid when the medium perturbation is not too large, but a valid parabolic approximation requires a medium with really small perturbations; nevertheless the validities of these approximations are also functions of the wavelengths and the heterogeneity scales. Based on our preliminary study, it seems that the Markov approximation is the most important factor in producing the discrepancy between the theory and the valid numerical experiments. In this presentation, we will isolate and discuss the influences of different approximations in the theoretical derivation and the validity of the Markov approximation in the calculation of the phase fluctuation functions for the transmitted waves.
S23B-0306 1340h
Tensor Strain Seismograms: a New Tool for Earthquake Science
In the expressions for seismic wave propagation in energy dissipating rock, the terms involving particle acceleration and velocity are balanced by local differences in the elastic forces plus those produced by the earthquake source. In homogeneous rock, the spatial differences in elastic forces depend only on the differences in strain. Thus, if one could measure the particle accelerations, velocities, and strain differences, the nature of the source could be solved for directly. In this presentation, we briefly summarize the steps we are taking to build and test an instrument system to make such measurements. Our current working system consists of a standard tensor strainmeter operating at 100Hz, and standard 3-component spring seismograph sampled at similar or higher rates. These sensors are colocated in a two hundred meter deep borehole. Our next generation prototype, which we will begin testing in the SAFOD Pilot Hole in 2005, will also contain accelerometers. We have used the high sampling rate borehole strainmeter and seismometer combinations to record, for example, the 19May04 M~6 earthquake in Taiwan at offsets of a few tens of kms, plus several other Taiwanese events. Separating the strainmeter record into shear and area strains and rotating the seismograms into dynamic coordinates allows rapid identification of different wave types and direct and secondary phases in the seismograms. The M~6 event produced a surprisingly long coda on the strainmeter. Comparing other similar strain and velocity seismograms has allowed various aspects of their codas to be resolved and identified. We see these results as early steps in full-scale, multi-parameter broadband measurements of tectonic displacements, pre- and post-rupture strains, and the elastic velocities and accelerations produced by small and large events. In the long run our aim is to use such data to measure their source characteristics directly.
S23B-0307 1340h
Scattering Wave Energy in a Random Isotropic Scattering Medium
Among many of Aki's theoretical contributions to seismology is his work on the origin of the coda waves (Aki, 1969). Following his work, many new theories have been proposed to explain the seismic scattering waves. For example, Zeng et al. (1991) has extended the single isotropic scattering theory (Aki and Cheout, 1975; Sato, 1977) to multiple isotropic scattering theory. Zeng (1993) and Sato (1994) have proposed a multiple scattering theory that includes P and S waves scattering conversion and examined the evolving energy budget between P and S waves. Later, Sato (1995) extended the theory to consider non-isotropic scattering. In this paper, I will show example of applying the scattering theory to near-field strong ground motion simulation. The result shows that the scattering waves dominate the wave field at later arriving time and of near nodal radiation components. I also extend the scattering theory to include scattered surface waves and surface and body waves scattering conversions. The results show that scattered body wave energy can be well approximated by body to body wave scattering at short distances. At large distances, scattered surface waves will dominate body waves for the near surface stations.
S23B-0308 1340h
Estimation of Local Site Effects Using Coda Waves
Since the pioneering work of Aki (1969), many theoretical and observational studies have been made using coda waves of local seismic events. This has led to great progress in understanding seismic wave scattering as well as to a variety of practical applications (Aki and Chouet, 1975; Chouet et al., 1978; Phillips and Aki, 1986; Zeng et al., 1991; Su et al., 1991; Sato and Fehler, 1998; Mayeda et al., 2003). The fundamental characteristic of coda waves is that their decay depends only on the average properties of the region surrounding the source and station, not on any particular wave path. This property leads to a separability of source, path and site effects on coda waves and offers an effective means for determining the site amplification factor empirically. By comparing the results from direct S waves and coda waves, many studies have shown that coda waves provide more stable estimates of site amplification and coda amplification factor represents that of S waves averaged over various directions of wave propagations (Tsujiura, 1978; Tucker and King, 1984; Su et al., 1996; Bonilla et al., 1997;). On the regional scale, Su and Aki (1995) have established uniformly estimated site amplification factors throughout central and southern California with a common reference using coda waves recorded from local earthquakes. They found that coda site amplifications are well correlated with surface geology. The recent study by Zhang (2004) found a systematic correlation between coda-wave site amplification and NEHRP site classification using digital strong-motion and broadband network recordings of the Chi-Chi, Taiwan earthquake and its aftershock sequences. The results are useful for UBC and IBC design codes. Under the current plan of Earthscope's USArray deployment, a transportable telemetered seismic array will roll across the United States with 1-2 year deployments at each site and will cover the entire continental United States over a period of 8-10 years. The data collected from USArray plus recordings from ANSS and other regional and local networks will be of great importance to study site effect nationwide. This large body of data will offer a great opportunity to establish uniformly estimated site-amplification factors throughout the United States with a common reference.
S23B-0309 1340h
Application of Coda Wave Techniques to Regional Explosion Monitoring
The stability of local (within 100 km) earthquake coda has been well established through observations that have shown coda amplitudes to be independent of distance, path details and azimuth with respect to the focal mechanism (e.g. Aki, JGR, 1969). This behavior is consistent with homogeneous scattering models of coda and allows accurate and high precision measurement of relative amplitudes. Absolute source spectra can be obtained from the relative measurements by applying empirical Green's function (EGF) analysis followed by ties to independently determined moments (Chouet et al., BSSA, 1978; Rautian and Khalturin, BSSA, 1978) for purposes of studying variations in source scaling in different regions. Recently, Mayeda et al. (BSSA, 2003) extended coda techniques from local to regional scales by employing empirical models of coda shape to describe distance effects. We further extend regional techniques: 1) to account for lateral variations in attenuation, and 2) to include empirically derived coda shapes for event clusters. The attenuation maps, as well as relative site terms, are obtained by applying tomographic techniques to amplitude ratio data. Following Aki and Richards (1980; equation 12.166), ratios are taken between stations that record each event, thus removing source effects from the problem. Application of the method to data from over 40 stations and 2250 multiply recorded events covering China and central Asia reduces ratio residuals (RMS) to under 0.1 log10 amplitude units for bands between 0.03 and 6 Hz. For 0.7 to 1 Hz data, variance reduction is 86% relative to the best-fit uniform attenuation model. Attenuation patterns closely follow regional geology, with low Q in Tibet, the East China Basin, the western Tien Shan, and the Baikal rift, and high Q throughout platform regions to the north and in southeast China, as well as the Sichuan, Tarim, Tsiadam and Ordos basins. Our extension to empirically derived coda shape is accomplished by inverting for the amplitude at each elapsed time increment using many events recorded along a common path. No coda shape assumptions are required and the resulting "typecurve" can be compared to individual coda. This gives the highest precision relative amplitudes between events in clusters, but reverts to normal levels of precision between or outside clusters. This technique is especially applicable to test site explosions because saturation of older digital data forces the use of late time segments for many events, and effects of elapsed time, commonly observed for model fits to coda data, is avoided. After applying site and path corrections to amplitude data from over 6500 events that are obtained using a combination of the curve fitting and typecurve methods, and converting to absolute amplitudes as described above, we can directly compare spectra from a wide distribution of sources to study variations in source scaling. We observe apparent stress drop that varies regionally, with lower stress events occurring in limited areas of Tibet, and high stress events in perhaps more brittle regions to the north. These patterns depend on how well path effects are removed and we seek to confirm these results using EGF techniques. Results for Asia explosions rely on data from the Borovoye archive and on ChISS (Soviet, pre-digital era, band pass recording) data from Talgar, and show marked spectral peaks that scale with source size.
S23B-0310 1340h
Numerical Simulation of Seismic Wave Propagation in Non\-Structural Grid System
This report presents a numerical simulation code developed for for seismic wave propagation in highly complex, heterogeneous structures of high resolution. The equations of motion for the 3D wave field are solved using a finite element method. Application of tetrahedral element has some merits in terms of spatial discretization. It can be very easily applied to highly complex geometry, even to that involving spherical geometry, which usually has the grid convergence problems associated with pole and center. This simplicity associated with spatial discretization enables us to include the heterogeneity of small scale and large scale, very easily, without using the sophisticated scheme like multi-grid approach. The present scheme is well suited for the simulation of broadband physical processes. Here, we present the results of benchmark analysis. The results are compared with those of analytic approach.
S23B-0311 1340h
Modeling Small Earthquakes in Southern California with Calibrated High Frequency P waves
With the dense TriNet array in Southern California, the focal mechanism of a Mw $\sim$ 4.0 or larger event can be easily resolved using the full waveform data over relatively long periods (usually 5+ sec for Pnls and 10+ sec for surface waves), where imperfections of the velocity models are tolerated. However, the same strategy becomes less effective when applied to smaller events (Mw $<$ 4.0) due to their poor signal to noise ratio (SNR). Better utilizing waveform data of these smaller events has to be pursued over much higher frequency bands for the sake of good SNR, where, however, any direct use of Green's functions is difficult since the complications caused by the path and site effects are far beyond the current model predictions. In this study, we first determine the focal mechanisms of more than 150 events with Mw $\sim$ 3.60 or larger since 1998 following our improved ``cut and paste'' method. With these well-resolved long-period solutions, we are able to study the un-modeled structural distortions on the waveform data over much higher frequency bands (up to 2 Hz), where the waveform data of an event as small as Mw $\sim$ 3.0 can survive the noise. We found that the azimuthal patterns of P wave amplitude ratios between different events (Mw from 3.60 to 4.50) within an event cluster well follow the differences in their various well-known focal mechanisms. This implies that whatever is causing the distortions on the amplitudes of P waves is relatively stationary and can be represented by a single ``Amplitude Amplification Factor'' (AAF) for the whole cluster at a large fraction of the stations. A detailed investigation is being conducted to learn more about the cause of the AAFs, however, the consistency of the ratios between the AAF on the radial component and that on the vertical component implies mainly a site effect. Taking advantage of these AAFs, we develop a new approach using short-period waveforms of P waves to determine the focal mechanisms of small events, as long as the events occur near well-determined bigger events, which can be used for calibration purposes. We test our new method and check the short-period solutions against the long-period solutions, which shows remarkable consistency.
S23B-0312 1340h
Synthesis of Vector-Wave Envelopes in Random Elastic Media Based on the Stochastic Ray Method
High-frequency seismograms of local earthquakes are mostly composed of incoherent waves that are scattered in the inhomogeneous lithosphere. Although their phase variations are complex, their wave-envelopes are smooth and apparent durations increase with travel distance increasing because of diffraction due to velocity inhomogeneity. When the wavelength is much smaller than the correlation distance of medium inhomogeneity, each potential field of P- and S-wave is independently governed by the parabolic wave equation. The stochastic treatment of the parabolic equation, the Markov approximation, gives the temporal trace of the sum of mean square amplitudes of vector waves for a given frequency band. The use of angular spectrum makes it possible to calculate the mean square amplitude of each vector component in the framework of the Markov approximation. Diffraction of waves can be interpreted as a ray bend by velocity inhomogeneity, where the probability of ray bending is controlled by the power spectra of velocity inhomogeneity. In the case of 2-D random elastic media characterized by the Gaussian autocorrelation function, the equivalence of the stochastic ray method and the Markov approximation is numerically shown for plane waves and cylindrical waves isotropically radiated from a point source. The ratio of transverse-component amplitude to radial-component amplitude gives a quantitative measure of diffraction effect for both P- and S-waves, and the ratio turns over as the lapse time increases. We note that the stochastic ray method is extendable even for the case of a point shear dislocation source: mean square envelopes just after their onsets are different between different components reflecting the source radiation pattern; however, mean square envelopes become equal to each other with lapse time increasing. Vector envelope simulations will be practically useful for studies of earthquake source radiation and medium inhomogeneity in high frequencies.
http://zisin.geophys.tohoku.ac.jp/~sato/
S23B-0313 1340h
Weak Localization of Seismic Waves
In the heterogeneous Earth the wave propagation is complex and wave scattering results in a "seismic coda", which forms the tail of the seismograms. We propose to study the energy distribution of coda waves in space and time. A field experiment was conducted on a volcano in the French Auvergne using 24 aligned geophones. A moment after the energy release at the source (a sledgehammer strike in our case), seismic energy is expected to be uniformly distributed along the sensor network, as predicted by radiative transfer and diffusion theory that are common tools to interpret the coda decay. These theories are consistent with our experimental results except that in the late coda, we observe a persistent energy enhancement around the source within a spot of width a wavelength. This intensity peak is interpreted as follows: when waves have encountered at least two scatterers and are detected exactly at the source, reciprocal paths (between source and receiver) have random but equal phases, which results in constructive interference. Away from the source, the phase difference between reciprocal waves is random, interferences are averaged out, and standard diffusion theory applies. This effect is known as Weak Localisation, also referred to as coherent backscattering in acoustics and optics. Our observations are in good agreement with the near-field theory for weak localization, and also with previous numerical studies. Our work shows the relevance of mesoscopic physics to seismology and its necessity to interpret the seismic coda. We propose a technique for estimating the scattering mean free time, which quantifies the internal heterogeneity without the bias of absorption. This parameter also quantifies the transition from the simple scattering regime where standard imaging techniques are valid to the multiple scattering regime.
http://scitation.aip.org/prl/covers/93_4.jsp
S23B-0314 1340h
"Interactive Seismics", Aki & Richards, Chapter 16
The defining physical character of cold brittle crustal rock hosting geofluid reservoirs and earthquake instabilities is '1/f-noise' spatially-correlated fluctuations in fracture-density. Evidence for 1/f-noise fracture-density fluctuations is manifest in power-law-scaling well-log spectra from $<$1/km to $>$1/cm, spatial correlation of well-core porosity and log(permeability), and the Gutenberg-Richter relation. Unlike spatially-uncorrelated randomness, power-law-scaling spatially-correlated randomness provides no reliable spatio-predictive relation between a sample and the whole. In particular, no point-measurement sequence in a crustal reservoir -- static well-log, temporal pressure-log or strain-log, or earthquake locations - accurately samples a reservoir state. Rather, useful knowledge of a reservoir state requires broadband observation of the whole reservoir as it is perturbed. Such observations could be called 'interactive seismics'. 'Interactive seismics' reservoir monitoring is becoming routine in the oil and gas industry, as embedded sensors record time-lapse source signals to determine where water replaces produced oil and gas. Interactive seismics is feasible with CO2 injection, and may become feasible for active fault zones. Interactive seismics benefits from stable downhole sources and sensors. Imperatives for better hydrocarbon reservoir observation are providing compact, robust, stable seismic sources and vector-sensors, and the means to deploy them downhole. Extensive crosswell seismic data, including monitored travel-times in a tectonically active crust, establish useful performance levels for downhole seismic sourcing at wavelengths 5-50m: crosswell transmission scale $\sim$1km, single-well back-scattering scale $\sim$200m, source wavelet stability \delta S/S $\sim$ 0.03%, and travel-time resolution \delta\tau/\tau $\sim$ 0.03%. Using the attested downhole source parameters, we simulate interactive seismic observation of a 1/f-noise fracture volume undergoing strain increments due to local seismic slip. The simulations use in situ velocity/strain data to estimate how downhole sourcing in the geometry of the prospective SAFOD multi-lateral completion can 1) scan 1/f-noise fracture volumes to locate high-strain response zones that potentially indicate where subsequent slip events will occur, and 2) detect strain-weakening along source-sensor ray-paths that possibly predict incipient slip events. Such development of crustal reservoir seismic observation may in time prompt an Aki & Richards Chapter 16 called, perhaps, 'Interactive Seismics'.
S23B-0315 1340h
Observed and Predicted Travel Times of Pn and P Phases Recorded at NORSAR From Regional Events
The principal objective of this study is to estimate the absolute travel-time path anomalies of regional seismic phases observed at the Norwegian Seismic Array (NORSAR) with respect to the Earth model AK135 and to determine their relationship to the Earth's three-dimensional structure. At least with respect to the large-scale features of the correction surfaces, the agreement between the empirical path anomalies and the model-predicted travel times is quite good. The observed and predicted regional anomalies show strong differences in the P and Pn anomalies observed between explosion source areas in northern and southern Novaya Zemlya, apparently produced by a sharp structural boundary that strongly affects ray paths to NORSAR from these sources. The separation distance between these source areas is on the order of only 300 km, yet the P and Pn median travel time anomalies observed at NORSAR at a distance of about 20 degrees differ by more than 5s. These differences between the two Novaya Zemlya sources are also reflected in typical waveforms observed at NORSAR from these test areas.
S23B-0316 1340h
Synthesis of Scalar-Wave Envelopes in Anisotropic Random Media Using the Markov Approximation
Due to the Earth's inhomogeneity, seismic waves impulsively radiated from a source are distorted with increasing travel distance, characterized by increase of the duration and decrease of the maximum amplitude. Those phenomena have been studied on the basis of the forward scattering in random media. The waveform envelopes are theoretically calculated by using a stochastic approximation referred to as Markov approximation. Although the conventional studies have assumed isotropic random media, they are not realistic enough to represent the anisotropic lithosphere. The present study formulates a method of envelope synthesis using the Markov approximation in anisotropic random media: two-dimensional media and a special case of three-dimensional media. For two-dimensional media, random inhomogeneity are characterized by the root-mean-square value of the fractional velocity fluctuation and the two correlation distances a$_{x}$ and a${_z}$ that are the characteristic scale-length of the inhomogeneity in the x and z directions, respectively. The formulation is made for the Gaussian-type and the von Karman-type random media, where the horizontal correlation-distance is larger than the vertical correlation-distance. The reliability of the formulation is confirmed by the finite-difference numerical simulations of wavefield; the envelopes based on the Markov approximation are in good agreement with the envelope obtained from the wave traces of the finite-difference simulations. As is the case of isotropic random media, the envelopes by the Markov approximation become scale-free when the time axis and the amplitude are normalized by using a characteristic time. It should be noted that the characteristic time is a function of propagation direction in addition to travel distance, frequency and the parameters of random media. It predicts that envelopes are more collapsed when propagating in the horizontal direction than in the vertical direction. For three-dimensional random media (x-y-z space), the case of transverse isotropy characterized by two correlation distances, a$_{h}$ (= a$_{x}$ = a$_{y}$) and a$_{z}$, is studied. The formulation based on the Markov approximation is given when waves propagate along the z direction. When a$_{z}$ $<$ a$_{h}$, the envelopes are less collapsed than in the case of the isotropic random media with the correlation distance of a$_{z}$ or a$_{h}$. This indicates that the intensity of the inhomogeneity is underestimated when one assumes isotropic random media. In past studies, the intensity of the lithospheric inhomogeneity estimated from the envelope duration of the intermediate-depth events are small compared to that estimated from the coda excitation of shallow events. The anisotropic inhomogeneity in the lithosphere may be a key to solve this discrepancy.
S23B-0317 1340h
High-resolution imaging of the deep structure of the Bear Valley section of the San Andreas Fault with joint analysis of fault-zone head waves and direct P arrivals
Understanding the structure of large strike slip faults can be an important step towards the understanding of dynamic earthquake processes. Geologic measurements are limited to selected sites, and surface or shallow fault zones that have undergone the process of exhumation (and thus may not reflect the in situ state). The short length scales and near vertical dip of large strike slip faults also makes conventional geophysical methods ineffective. The utilization of seismic energy trapped within low velocity fault zone (FZ) layers can yield detailed images of the structure. However, recent studies at a number of locations indicate that trapped waves are typically generated only by the top ~3km of the fault zones, above the seismogenic portion of the structures. Major faults that have accumulated significant amounts of slip may not only have damage zone but also juxtapose rocks with different elastic properties. In such structures, fault zone head waves (FZHW) can propagate along material interfaces and arrive at near-fault stations on the slower side before the direct P wave. The FZHW spend the majority of their propagation paths along the fault zone and their incorporation in imaging studies can provide high resolution results on the deep structure of the fault. In this study we perform a joint direct P and head wave travel time inversion of data from a dense temporary array of 49 seismometers deployed by Thurber et al. (1997) in the Bear Valley region of the San Andreas Fault. Within the operational period, ~1200 events were recorded by the array and located. Currently travel time picked were done for 200+ events, yielding ~6304 direct P and ~2017 head wave arrival times. Analysis of the moveout between the direct P and FZHW allows estimates of the velocity contrast and can show variation along strike and with dip. Waveform fits are also produced to further constrain FZ properties. As the FZHW are examined the arrival time picks and picking method are refined with a view to increasing the ray path coverage and performing a joint direct P and head wave travel time inversion. The results obtained so far indicate that the San Andreas Fault in our study area has material interfaces that extend to the bottom of the seismogenic zone and are continuous along strike for several 10s of km. The strength of the material interfaces change with position along strike and depth.
S23B-0318 1340h
Envelope Broadening of High-Frequency P- and S-Waves in Relation to Quaternary Volcanoes in Northeastern Honshu, Japan
Envelope broadening of high-frequency ($\ge$ 2Hz) seismograms of microearthquakes reflects the scattering effect due to small scale medium heterogeneities. The peak delay times from onsets of P- and S-waves ($t_p$ in later) are known as good measure of accumulated forward scattering effect since they are not susceptible to intrinsic attenuation. Recently, we showed that S-waves propagating under Quaternary volcanoes have quite large values of $t_p$ as compared with those propagating in non-volcanic areas in northeastern Honshu, Japan (Takahashi et al., 2003). In this study, extending the envelope analysis to P-wave seismograms in the same region, we examined the scattering effect for P-waves. P-wave's $t_p$ was measured from Root Mean Square envelope of three-component velocity seismograms recorded by Hi-net (NIED). Microearthquakes occurred around the subducting Pacific plate with focal depths of 32$\sim$150km are used for the analysis. We restricted data to those that a clear peak of P-wave appears in the first half of the time window from P to S arrivals. Peak delay $t_p$ is found to increase generally with hypocentral distance $R$, for example the regression line is $\log t_p = 1.5\log R-3.2$ for 8$\sim$16Hz. The deviation of the logarithm of $t_p$ from its regression line $\Delta \log t_p$ represents relative strength of scattering effect along the ray path. Dividing the whole region into small blocks, we evaluate the distribution of minimum values of $\Delta \log t_p$ in small blocks. The result shows relatively large $\Delta \log t_p$s beneath Quaternary volcanoes at a shallow depth of less than 20km in the northern part of study area. Beneath other volcanoes in the southern part, large $\Delta \log t_p$ regions extend to the depth of about 40$\sim$50km. On the other hand, the result of S-wave analysis showed that the large $\Delta \log t_p$s are observed at regions extending to a depth of about 40$\sim$50km beneath most of the Quaternary volcanoes in the study area. This difference found in P- and S-wave scattering implies a regional variation of the ratio of P- to S-wave velocity inhomogeneities and/or a variation of fluid contents which may help us to understand deep structure of volcanoes.
S23B-0319 1340h
3D Seismogram Synthesis and Inversion for Finite Moment Tensors Using Receiver Green Tensors
The Southern California Earthquake Center (SCEC) is developing a Community Modeling Environment (CME) to facilitate the computational pathways of seismic hazard analysis (Maechling et al., this meeting). Major objectives of the CME project are to construct an efficient system for calculating synthetic seismograms from 3D regional models of elastic/anelastic structure (CME Pathway 2) and to use observed waveforms to invert for source structures and improve the 3D models (CME Pathway 4). In this presentation, we describe the implementation of an approach to these problems based on the use of receiver Green tensors $G_{ik}(\mathbf{r}, \mathbf{r}_{\mathrm{R}}; \emph{t})$ and seismic reciprocity. $G_{ik}(\mathbf{r}, \mathbf{r}_{\mathrm{R}}; \emph{t})$ is the \emph{i}th component wavefield at position $\mathbf{r}$ and time \emph{t} for a \emph{k}th component impulsive force at the receiver position $\mathbf{r}_{\mathrm{R}}$. Seismic reciprocity implies that the synthetic seismogram at $\mathbf{r}_{\mathrm{R}}$ excited by a point source with moment tensor $M_{ij}$ at position $\mathbf{r}_{\mathrm{S}}$ at time $t_{\mathrm{S}}$ is $s_k (t) = M_{ij} \partial^S_j G_{ki} (\mathbf{r}_{\mathrm{R}}, \mathbf{r}_{\mathrm{S}}; \emph{t}-\emph{t}_{\mathrm{S}})$. We calculated $G_{ik}$ for 33 broadband stations of the California Integrated Seismic Network in the Los Angeles region using the SCEC Community Velocity Model (CVM), version 3.0 (Magistrale et. al., 2000), and K. Olsen's (Olsen, 1994) finite-difference code. These receiver Green tensors were sampled on a regular mesh of 36 million grid points with a horizontal spacing of 200 m and archived on the Storage Resource Broke (SRB) system at the San Diego Supercomputer Center, where they occupy a total data volume of 24 TB. The SRB provides high-level digital library functionality, including a maintained association of data and metadata and tools for data queries and subset retrieval. We synthesize seismograms by retrieving $G_{ik}$ on small source-centered grid and calculating the source-coordinate gradient $\partial^S_j$ using a five-point-formula. At the same time, we calculate the higher-order gradients needed to invert waveform data for the centroid moment tensor (CMT) the finite moment tensor (FMT). The latter extends the CMT to include the characteristic space-time dimensions and orientation of the source (Chen, Jordan & Zhao, 2004). We discuss how the 3D synthetics can be used to recover frequency-dependent phase-delay and amplitude-reduction differentials from observed waveforms and demonstrate how these data can be inverted for CMTs and FMTs in Southern California. As discussed by Zhao et al. (this meeting), rapid access to receiver Green tensors is also required for the inversion of the same waveform data for improved 3D models of regional Earth structure.
S23B-0320 1340h
Coherence Characteristics Of Body Waves From Local Events
A fundamental issue in seismology and earthquake engineering is the coherence characteristics of body waves from local events that propagate in a sedimentary layer - basement system. To respond this issue, we investigated down-hole array recordings including deep-borehole seismograms obtained in the Kanto region, central Japan and obtained the following results: (1) Coherence characteristics of body waves traveling in a sedimentary layer - basement system are modeled by omega-square model. (2) Corner frequency in the omega-square model decreases as increasing in travel time. However, there is a critical corner frequency that becomes a constant independent of travel time. For example, the critical corner frequencies are about 6Hz and 3Hz for P- and S-waves, respectively. This means that bedrock motions recorded in the pre-Tertiary basement are incoherent in frequencies higher than these critical corner frequencies.
S23B-0321 1340h
Regional difference of total scattering coefficients revealed from the envelope analysis of {\it ScS} waves
Coda envelope reflects the medium heterogeneity in the Earth. The change of coda decay gradient associated with the {\it ScS} arrival becomes smaller as a period becomes shorter and a focal depth becomes shallower around the world. We discovered an offset behavior with coda decay rate change around the {\it ScS} arrival for deep events. To quantitatively explain the regional difference of coda envelope characteristics, we examined seismogram envelopes of regional earthquakes registered by IRIS stations in Kyrgyzstan, Sakhalinsk, and Bolivia with focal depths greater than 150km ranging from 1s to 20s periods for a wide lapse time range up to 2000s. We find that the offset before and after the {\it ScS} arrival is prominent in Kyrgyzstan and Bolivia at 10s period band. We estimated total scattering coefficients using the Direct Simulation Monte Carlo method based on the radiative transfer theory for the two-layer attenuation structure modified from the PREM. The total scattering coefficients of the upper layer for depths shallower than 670km are 7.520\times10$^{-4}$\sim1.129\times10$^{-3}$km$^{-1}$ and 4.510\times10$^{-4}$\sim6.770\times10$^{-4}$km$^{-1}$ for 4s and 10s, respectively, and the values of the lower layer for depths up to the CMB are 4.160\times10$^{-4}$\sim6.230\times10$^{-4}$km$^{-1}$ for 4s at all three places. In Kyrgyzstan and Bolivia, where show the offset, for the lower layer at 10s, we obtained total scattering coefficient as 2.710\times10$^{-4}$km$^{-1}$, which is larger than that of Sakhalinsk on the order of ten. It tells us that much stronger scattering in the lower mantle beneath Kyrgyzstan and Bolivia could be a cause of the offset behavior and coda decay gradient change after the {\it ScS} arrival.
S23B-0322 1340h
Non-uniform spatial distribution of the S-coda-wave energy in Japan estimated from the seismograms of local earthquakes
Seismic coda waves of local earthquakes had been considered as the multiple scattered waves that distribute uniformly in space at large lapse times. However, the analysis using data from the dense seismic network in northeastern Honshu, Japan had revealed that the coda-wave energy in the forearc is much larger in magnitude than that in the backarc (Yoshimoto et al, 2003). Is such non-uniform spatial distribution of coda-wave energy common and observed in other regions? This study analyzed the spatial distribution of coda-wave energy of 9 local earthquakes (magnitude 4.7-7.1) occurred in Japan. We selected the earthquakes with very few aftershocks to accurately investigate the coda-wave characteristics of the single event. The velocity seismograms recorded by the Hi-net, which is operating by the National Research Institute for Earth Science and Disaster Prevention and consists of about 700 borehole seismometers, were used in our analysis. We calculated the coda-wave energy as the squared sum of the coda-wave amplitudes on horizontal components. In the high-frequency range of 16-32 Hz, the spatial distribution of coda-wave energy shows clear regional variations, except for the random scatter due to the effect of site amplification. The magnitude of coda-wave energy is systematically small in the area where the Quaternary volcanoes exist. The difference in magnitude reaches up to one-hundred times. This tendency is observed in the whole area studied. Our result shows that the S-coda-wave energy does not distribute uniformly in space in the tectonically active region. From the spatial correlation between the Quaternary volcanoes and the high heat flux, it is suggested that the structure of the intrinsic attenuation in the crust and the uppermost mantle characterizes the regional variation in coda-wave energy.
S23B-0323 1340h
Beyond Delay Time Tomography: the Estimation of Rock Physics Properties From P- and S- Velocity Models.
The estimation of physical properties of rocks is a task showing manifold applications in studies of the Earth's crust. Joint P- and S- travel time tomography from microearthquake travel times is a basic tool to assess the local velocity structure in seismically active areas and thus, it provides the spatial distribution of elastic properties at a specific time moment. To characterize porosity and fluid content within the shallow crust, both P- and S-wave velocities are required because P-waves are sensitive to changes in pore fluid, whereas being S-waves mainly depending on rock matrix properties they are relatively unaffected by the pore fluid. Specifically, the translation of velocity images into lithology, porosity and pore filling phase images requires quantitative relations relating the rock elastic properties to its bulk properties and pressure conditions: this goal can be achieved by rock physics effective-medium modeling. We present a methodology to estimate the petrophysical properties from passive seismic data by linking, at the tomographic resolution, P- and S- wave velocities to lithology, porosity and fluid phases. To reconstruct rock velocities, models use the Hertz-Mindlin contact theory and the modified Hashin-Shtrikman bounds both for consolidated and unconsolidated rocks as described in Dvorkin et al. 1999. Models require knowledge of both the shear, bulk moduli, and density of the matrix which are computed from those of the individual constituents using the Hill's average formula and those of fluid phases which are determined on pressure and temperature based equations. Before inversion, trends for dry rocks were compared with laboratory measurements at crustal conditions for site-relevant rocks. The effect of the pore fluid is calculated at different reservoir conditions in the low-frequency domain through the Gassmann's poroelastic theory. Rock property images are finally determined by minimizing the difference between the tomographic and the modeled velocities through the use of local and semi-global inversion scheme. The presented technique is applied to the passive dataset collected in the Campi Flegrei hydrothermal system where the seismic velocity structures recovered by delay time tomography now fit the bulk physical properties of three different rock types.
S23B-0324 1340h
Modelling Elastic Media With Arbitrary Shapes Using the Wavelet Transform
We extend the new method proposed by Rosa et al. (2001) for the study of elastic bodies with complete arbitrary shapes. The method was originally developed for modelling 2-D elastic media with the application of the wavelet transform, and was extended to cases where discontinuities simulated geologic faults between two different elastic media. In addition to extending the method for the study of bodies with complete arbitrary shapes, we also test new transforms with the objective of making the related matrices more compact, which are also applied to the most general case of the method. The basic method consists of the discretization of the polynomial expansion for the boundary conditions of the 2-D problem involving the stress and strain relations for the media. This parameterization leads to a system of linear equations that should be solved for the determination of the expansion coefficients, which are the model parameters, and their determination leads to the solution of the problem. Despite the fact that the media we studied originally were 2-D bodies, the result of the application of this new method can be viewed as an approximate solution to some specific 3-D problems. Among the motivations for developing this method are possible geological applications (that is, the study of tectonic plates and geologic faults) and simulations of the elastic behaviour of materials in several other fields of science. The wavelet transform is applied with two main objectives, namely to decrease the error related to the truncation of the polynomial expansion and to make the system of linear equations more compact for computation. Having validated this method for the original 2-D elastic media, we plan that this extension to elastic bodies with complete arbitrary shapes will enable it to be even more attractive for modelling real media. Reference Rosa, J. W. C., F. A. C. M. Cardoso, K. Aki, H. S. Malvar, F. A. V. Artola, and J. W. C. Rosa, Modelling elastic media with the wavelet transform, Geophys. J. Int., 146, pp. 454-488, 2001.
S23B-0325 1340h
Depth Distribution of the Stress Sensitivity of Seismic Wave Velocities in the Crust
Seismic wave velocities in rocks are known to be sensitive to applied stress from laboratory experiments and field observations. The stress sensitivity of the velocity is attributed to opening and closing of such small-scaled defects as pores and cracks in the rocks. Then monitoring temporal changes in seismic wave velocities may provides a method to infer the stress state in the crust. In addition to this, the sensitivity depends also on the degrees of fluid saturation and pressure in the defects. Then there is a possibility that we obtain information on such interesting features of the defects in the crust. However, our knowledge about the sensitivity in the crust is far from the comprehension. To discuss the depth distribution of the sensitivity in the crust, we here compile stress sensitivities obtained by various field experiments. Analyzing the apparent stress sensitivity as a function of the epicentral distance of seismic station or the base line length of experiments, we estimate the depth distribution of the sensitivity. We define here the sensitivity S as S = dlogv/ds, where v is the average velocity along the wave path and s is the stress. The base line lengths in the compiled experiments are in a range from 100m to about 400 km. The observed sensitivities vary from 1 to 0.001 (1/MPa) depending on the base line length. The highest sensitivity is observed in experiments whose base lines are of the order of 100m, which can be explained by high concentrations of the small defects very near the surface. The sensitivity rapidly decreases with the increase of the base line length; the sensitivity decreases sharply with depth. If we assume that the depth distribution is an exponential function of depth, the observed relation between the sensitivities and the base line lengths is well explained by a depth constant (a depth increment with which the sensitivity becomes 1/e ) of the order of 1 km.
S23B-0326 1340h
Attenuation Anisotropy and the Relative Frequency Content of Split Shear-Waves
The variation of frequency-dependent seismic wave attenuation with direction (attenuation anisotropy) contains additional information to that contained in velocity anisotropy. In particular it has the potential to distinguish between different mechanisms that can cause velocity anisotropy. For example, aligned fracturing might be expected to cause both velocity and attenuation anisotropy, whilst preferred crystal orientation should lead only to velocity anisotropy. Attenuation anisotropy may also contain useful information about pore-fluid content and properties. We present a methodology for analysis of attenuation anisotropy, and apply it to a microseismic dataset previously analysed for shear-wave splitting by Teanby et al. (2004). The comparison of the relative frequency content of fast (S1) and slow (S2) split shear-waves is a convenient method for examining seismic attenuation anisotropy. Provided that S1 and S2 initially have the same spectral colouring, that no spectral distortion is introduced by the differences between receiver responses of geophone components, and that spectral distortion due to background noise can be ignored or corrected for, we can attribute any differences in their frequency content to attenuation anisotropy. Attenuation anisotropy should be detected by the different (approximately orthogonal) polarisations of S1 and S2 as they pass through the anisotropic medium. In the presence of attenuation anisotropy S1 and S2 should experience different levels of frequency-dependent attenuation. We quantify the differential attenuation of S1 and S2 using a scheme based on the spectral ratio method. We present results from a microseismic dataset acquired in an abandoned oil well at Valhall, a North Sea oil field. The results are surprising in that sometimes the slower arrival, S2, is richer in high frequencies than the faster, S1. This appears to be contrary to results predicted by theoretical crack models for attenuation anisotropy (e.g. Hudson 1981). The mechanism responsible for these observations is not clear. Our differential attenuation measurements correlate with the angles between the initial shear-wave source polarization and the crack normal, the event back azimuths, and the splitting times.
S23B-0327 1340h
Crustal heterogeneity in active fault regions estimated by inversion of coda envelopes
Coda envelopes from local earthquakes can be inverted to estimate a 3D heterogeneous structure in the crust (Nishigami, 1991, 2000; Asano and Hasegawa, 2004). These studies suggest that the data of dense seismographic networks is effective to image crustal heterogeneities and also it is possible to estimate deep structure of active faults such as downward extension in the crust, segmentation along the fault, and relatively weaker scattering (i.e., more homogeneous or locked) areas which will be ruptured by M 6-7 earthquakes. Recently High Sensitivity Seismograph Network (Hi-net) has been constructed by NIED covering all over Japan. We are aiming at estimating systematic variation in the crustal heterogeneity in Japan and trying to detect a possible structure related to the earthquake generation, using the Hi-net, and University and JMA network data. We analyzed two active fault regions, the Yamasaki fault system in southwest Japan and the Atotsugawa fault system in central Japan. The deviation of coda envelopes from average decay curves was measured as the observational data assuming a single isotropic scattering model. The analysis area, $\sim$200 km in horizontal and $\sim$60 km in depth, was divided into small blocks, and 3D distribution of relative scattering coefficient was obtained by solving the observational equation using a recursive stochastic inversion. The result shows strong scattering along the entire Yamasaki fault system at the seismogenic depth of 10-15 km. For the Atotsugawa fault system, we can find weaker scattering along the Ushikubi fault, which is one branch of the fault system and shows low microseismicity. The resolution will be improved by adding more data including the University and JMA stations, and the deep heterogeneous structure of these active faults will be discussed.
S23B-0328 1340h
New Waveform Analysis Method: the Chirplet Transform. Characterisation of the Induced-Seismicity From the Lacq gas Field (Western Pyrenees, France).
Whole waveform records of waves radiated by induced-seismic events contain considerable information on event location, propagation medium, failure type, source size, and state of stress. Modern seismological studies of induced-seismicity related with hydrocarbons exploitation or storage benefit from time-frequency (TF) analysis techniques such as the windowed Fourier transform or the wavelet transform. These TF representations with fixed windows or kernels perform well only for limited classes of seismograms. Representations with signal-dependent kernels can overcome this limitation. A new five-parameter atomic decomposition of chirplets is developed for compact and precise representation of seismograms with chirp components. The five-parameter chirplet atom is obtained from the unit Gaussian function by successive applications of scaling, fractional Fourier transform, time-shift and frequency-shift operators of various duration. So, the chirplet transform unifies many of the disparate signal representation methods. In particular, the wide-range of TF methods such as the Fourier transform, spectrogram, Wigner distribution, and wavelet transform may each be shown to be a special case of the chirplet transform. We developed a methodology that recognizes the attributes of the waveforms of each seismic events. We first present and illustrate on synthetic examples this new formalism. Next, we illustrate its potentialities on seismograms recorded by 17 seismometers (Mark-Product L-4C - 12 bits) during the monitoring period (1974-1997) of the Lacq gas field (Western Pyrenees, France). Using the chirplet transform, each wave packet of the seismogram (mostly single component, sampling frequency = 150 Hz, duration = 15 s) is decomposed in terms of energy, arrival time, frequency, duration, shape (time-shear) and frequency modulation (frequency-shear). Thus, selected seismograms (N $\sim$ 5500 for 592 well-localized events) are described by a set of sextuplets which provide compact and precise representation of its inner structure, and form the basis for a classification of the seismic traces in the TF plane. Results obtained in terms of trace characterization and event parameter (date, location, magnitude, focal mechanism) are compared with the documented history of the reservoir (exploitation, fluid-injection, pressure, permeabilities and porosities maps, ...). Together, they allow to investigate earthquake induction and geomechanics processes at this site.
S23B-0329 1340h
Imaging of the Philippine Sea Plate beneath the Chugoku and Shikoku Regions in Southwest Japan - Reflection and Forward-scattering Analyses of Local Earthquakes and Teleseismic P Codas -
In this study, we investigate how the Philippine Sea (PHS) Plate subducts beneath the Chugoku and Shikoku regions in southwest Japan, which will be essential for understanding the tectonic settings and the origin of the volcanoes in southwest Japan. Nakamura et al. (1997) showed that there are seismic activities accompanied by the PHS plate subduction to the depth of ~40km beneath the northern part of the Shikoku region. Yamane et al. (2000) detected the leading edge of the high-velocity slab at depths of ~60-80km in the middle of the Chugoku region through travel time tomography. Siomi (2002) found the velocity discontinuity due to the PHS plate subducton to the depth of ~50km by receiver function analysis. However, it is not clear how deep and how far the aseismic slab reaches beneath the Chugoku region. We detected a highly reflective layer at depths of 50-60km beneath the northern part of the Chugoku region by reflection analysis using aftershocks of the 2000 Western Tottori Earthquake (Doi et al., 2003). In the present study, in order to elucidate how deep the PHS plate subducts as well as the relationship between the reflective layer stated above and the PHS plate, we applied the reflection analysis using the waveforms of local earthquakes and forward-scattering analysis of the teleseismic P coda in the wide region from Shikoku to Chugoku. In the reflection analysis, we used 3,364 seismograms from 492 local earthquakes observed at 55 Hi-net stations with the epicentral distances less than ~70km. We applied normal moveout (NMO) correction to the waveform data after correcting the geometrical spreading and anelastic attenuation. We detected a southeast-to-northwest dipping reflective layer in the Shikoku region at depths almost the same as those shown by Nakamura et al. (1997) and Siomi (2002). We also found another reflective layer dipping southeast to northwest at depths of ~50-70km beneath the entire Chugoku region which is considered to be the same as that Doi et al. (2003) found at similar depths. In the analysis of teleseismic P coda, we assumed the coda waves as P to P forward-scattered waves as Revenaugh (1995) did in southern California. The analysis procedure is as follows. First, we averaged the P wave part (~10s) over the stations, by summing all the waveforms with taking the waveform correlation. We assumed that the averaged P waves mostly represent the source and near-source structure effects. Then, we deconvolved the averaged P wave from each waveform to obtain waveforms containing heterogeneities below the station-network. We divided the analysis region into blocks with 5km in horizontal and 2.5km in depth direction and assigned the amplitudes of the envelope of the deconvolved waveforms at the corresponding travel time of scattered waves to each block. We stacked the envelope amplitudes for all the waveform traces, in order to estimate the relative scattering strength in every block. The result thus obtained shows that the high-scattering zone exists in Shikoku region below the reflective layer stated above. There is also another high-scattering area at depths of ~70-80km beneath the Chugoku region where the reflective zone was detected at similar depths. We are going to add more data to obtain images of the aseismic slab in Chugoku region with higher resolution.
S23B-0330 1340h
How do underground explosions excite regional waves: a source array analysis by virtue of a reciprocal theorem
There has been a long-standing question on how the regional S waves are generated by underground nuclear explosions (UNEs). Hundreds of historic UNEs were recorded by individual seismic stations at regional distances. According to the reciprocal theorem (Aki and Richards, 1980), the records can be treated as those collected from a fictitious array at the sources. Array analysis techniques can then be applied to these records to infer the phase velocity composition of regional waves in the near-source region, and constrain the excitation mechanisms. We apply a frequency-wavenumber technique for the array analysis, and analyze short-period records of Balapan explosions from the Borovoye Observatory in Kazakhstan at distances of around 690 km. Pn wave is composed of P wavelets leaving the source region with phase velocities of about 8.0 km/s. P wavelets dominate the seismograms between Pn and Sn. S wavelets with phase velocities of about 4.0 km/s start to emerge in the Sn window, where the dominant energy still originates from P. Toward later Sn coda, the influence of S wavelets increases with time. The Lg waves are built mostly by waves with velocities of about 4.0 km/s, which corresponds to the S phase velocity. The dominant phase velocity in the Rg window is 3.1 km/s. It seems that Rg scattering plays a relatively trivial role in the shear wave development by Balapan explosions. Primary phases (Pn, Sn and Lg) are composed mainly of wavelets leaving the sources along the great-circle direction, while coda waves are increasingly influenced by randomly scattered waves.
S23B-0331 1340h
Discrete Frame-Based Gaussian Beam Methods for Seismic Modeling and Imaging
In this presentation we describe the use of discrete frame-based Gaussian beam summation methods with application to modeling and imaging. In this approach a windowed expansion is used where the individual functions are matched to paraxial Gaussian beams which are then propagated into the medium. The Gaussian windowed expansion is performed on an over-sampled position-wavenumber lattice where over-sampling is required for stability. The only window-based transform allowing critical sampling is a Wilson basis or local cosine transform which requires Gaussian beams to be launched in pairs losing some of localization properties of the method. For over-sampled Gaussian windowed expansions, dual functions must be computed to reconstruct the field, but for sufficiently high over-sampling the dual function becomes closer to a Gaussian function. An early application of windowed expansions using Gaussian beams was given by Hill (1990) for seismic migration. He also derived early sampling criteria for the expansion. Here we will give applications of the method to forward modeling including waves in a layer over half-space for a range of beam parameters. We also provide several applications of seismic imaging using surface sources and teleseismic waves incident from below.