S53B-1256
Synthesis of High-Frequency Vector-Wave Envelopes in von Karman-type Random Media
High-frequency seismogram envelopes of an earthquake are broadened with travel distance increasing. For P- wave, there is an excitation of the transverse-component amplitude with travel distance increasing. These phenomena are explained by scattering due to randomly velocity inhomogeneities, and mathematically described by the statistical treatment of the wave equation in random media. When random media are characterized by a Gaussian auto correlation function, an analytical solution of vector-wave envelopes has been obtained and the resultant vector-wave envelopes show broadening with travel distance; however, they are frequency independent. Here we study the envelope broadening in von Karman-type random media since they have realistic power-law spectrum at large wavenumbers. When the wavelength is smaller than the correlation distance of random media, the wave equation is approximated by the parabolic equation. Considering an ensemble of random media, we introduce the two-frequency mutual coherence function (TFMCF) of potential fields on the transverse plane orthogonal to the global ray direction. Then we statistically derive the master equation for the TFMCF as the ensemble average. Improving the finite difference simulation method and applying a new boundary condition for solving the scalar wave case, we numerically solve the master equation for the case of von Karman-type random media. By using the Fourier transform of TFMCF solution, we can derive accurate synthesis of vector-wave envelopes. Synthesized vector-wave envelopes show broadening and excitation of transverse component with travel distance increasing for the case of P-wavelet radiation from a point source in 3-D random media. The frequency dependence of the synthesized envelopes is controlled by the roll-off of the power spectrum of random inhomogeneity. We find that the peak delay time of transverse component is longer than that of longitudinal component. The envelope broadening of each component and the excitation of the transverse component become larger as the power spectrum becomes richer in short wavelength components. The time integral of the transverse-component mean square envelope with geometric correction increases according to a power of travel distance.
S53B-1257 INVITED
Passive Image Interferometry: Theory and Application to the Source Region of the 2004 Mw = 6.6 Mid-Niigata earthquake
Passive Image Interferometry is a technique to continuously monitor temporal variations of the mean shear wave velocity of the Earth's crust. In a first step, the elastic Green's tensor between two seismometers is computed from the cross-correlation of seismic noise recorded at the two sensors during a certain period. Alternatively, one can also compute the source-receiver co-located Green's function using the auto-correlation function of noise recorded at a single seismometer. In a second step we compare the constructed seismograms of different periods. To do so, we apply the technique of Coda Wave Interferometry, which is able to detect small time changes in the coda of similar seismograms and to convert it to a relative change in mean shear wave velocity. First applications of Passive Image Interferometry show, that using high frequencies (1-10 Hz) one obtains a resolution for relative changes in mean shear wave velocity of about 0.1 percent. In this frequency range one day of noise data is generally sufficient to estimate the source-receiver co-located Green's function, which leads to a temporal resolution of one day. Using lower frequencies (10-3 s), on the other hand, much longer noise time series are required to compute the Green's function. The advantage of using lower frequencies is that Green's functions for larger station distances can be computed, whereas for high frequencies due to the lack of coherence in many cases only source-receiver co-located Green's functions can be constructed. In an application to the Earth's crust in the source region of the shallow 2004 Mw = 6.6 Mid-Niigata earthquake, we use ambient seismic noise recorded at 5 stations of Japanese Hi-net and 1 station of broadband F-net, all located in a distance of less then 20 km from the epicentre of the earthquake. Daily measurements during two month before and two month after the earthquake show a sudden decrease of mean shear wave velocity of some tenth of percent at the time of the Mid-Niigata earthquake. Possible interpretations of this velocity decrease are a decease of crustal stress after the earthquake, a creation of a shallow damage zone by strong ground motion, or the creation of new fractures in the source area of the earthquake.
S53B-1258
Multiples: From Artifact Prediction to Image Reconstruction via Illumination
A typical seismic image assumes that the recorded wavefield has been scattered only once in the subsurface. This assumption places two limitations on the resulting image. The first is that the image will contain artifacts from multiply scattered waves. The second is that the portion of the Earth represented in the image is limited to regions which are illuminated by recorded singly scattered waves. The first limitation has been addressed in a variety of different ways, in particular within the petroleum prospecting industry. The second limitation, however, has received only limited attention. We present a theoretical path from artifact prediction to image reconstruction by including the illumination footprint of the acquisition geometry in the theory of artifact prediction. From this structure it becomes clear how multiply scattered waves can be used to enlarge the region of the Earth that can be imaged from a particular data set. This is particularly important for steeply dipping structures such as faults and salt intrusions; singly scattered waves do not generally illuminate these structures while doubly scattered waves do. We illustrate, with numerical examples, that these ideas fit naturally within a downward continuation migration procedure allowing for the improved image to be computed efficiently.
S53B-1259
Global-, Teleseismic- and Regional-Scale Green's Function Retrieval: on the Sampling of the Surface Integral
Seismic Green's function retrieval or seismic interferometry (SI) refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. SI can be applied independently of the scale and wavetype under consideration. We consider the application of SI with natural transient seismic sources. In this case, 3D SI consists of a surface integration of correlations over source positions. The quality of the retrieved Green's function between two receiver locations depends largely on how well this surface integral is sampled. For an arbitrary inhomogeneous medium, the source sampling needs to satisfy the Nyquist criterion. In many situations, the natural distribution of primary sources, e.g., earthquakes, is not such that this sampling criterion is reached. Fortunately, it does not matter whether this sampling criterion is reached by actual or secondary (Huygens) sources. As has been stated in many papers, the more inhomogeneous the medium, which means more scattering, the better the SI retrieval of the Green's function. In the optimal case when an equipartitioned state is reached, only one source suffices. That is, the medium is so heterogeneous that -with one source only- the medium surrounding the receivers is already indirectly illuminated from all directions. For a natural source distribution, the sampling of the integration surface will never be regular. The problem of integrating over an irregularly sampled surface has long been studied for the application of migration algorithms in exploration geophysics. Solutions found for migration, e.g., binning and triangulation weighing, can also be used for SI. We show formulations for global-, teleseismic- and regional-scale SI. We determine the source sampling required for the different scales and media and evaluate how this source sampling can be reached in practice. Also, we evaluate the effects of an irregular sampling and show how its negative effects can be minimized.
S53B-1260
Scattering Attenuation Due to Weak Discrete Inhomogeneities: Comparison of the Born and Foldy Approximations
There are two approaches for predicting scattering attenuation due to randomly inhomogeneous media. One approach models the media by weak (and usually continuous) perturbation of material properties; the resultant scattering loss is evaluated using the Born approximation. The other treats media with randomly distributed discrete inhomogeneities, such as inclusions and cracks; the first-order solution of the attenuation was obtained by Foldy (1945). Despite the different appearances of the both model media, the Born approximation could be also applied to the inclusions, if the autocorrelation functions for them would be given. In the case of the sparse distributions and the low material contrasts between the inclusions and the matrices, the both approaches would yield virtually the same results. The present study confirms this inference in cases of simple-shaped inclusions, for which the Foldy approximation solutions are analytically obtained. The traveltime correction is not considered here. We first treat the SH wave scattering due to 2-D circular inclusions with the same size. We assume that the S- wave velocity of the matrix is c0, that of a half of the inclusions is c0(1+ξ), and that of the rest is c0(1-ξ), with 0<ξ\ll1. The density perturbation is made proportional to ξ. We also assume the sparse distribution to make the Foldy approximation reliable. The Born approximation solution is evaluated using the autocorrelation function taken from Stoyan et al. (1995). It is shown that the scattering Q values based on the both approximations are highly consistent within the Rayleigh-Gans scattering regime (kaξ\ll1; ka is the wavenumber multiplied by the inclusion radius), as expected. Relying on the Foldy approximation, one may conclude that the Born approximation is approximately valid up to ka~1/ξ and breaks down beyond it. In a special case with density perturbation only (causing no traveltime fluctuation), however, the Born approximations is valid for any ka. We next extend the model to 3-D (spherical inclusions with P-wave velocity perturbation added) and evaluate the scattering attenuation of P waves due to them. The results based on the both approximations are again highly consistent within the Rayleigh-Gans scattering regime, implying the generality of this feature.
S53B-1261
Modification of Radiative Transfer Theory to Include Wave Interference
When seismic waves interact with strong heterogeneity in the Earth, multiple scattering makes deterministic imaging a challenge. Instead, seismologists often resort to the retrieval of statistical inferences about subsurface properties by investigating the evolution of the squared wave field, or energy. Recent investigations in some of the strongest scattering regions of the Earth's subsurface indicate that these diffusion-based or radiative transfer- type models for energy propagation may not hold. This is because these models do not incorporate wave interference terms. We present a modification of radiative transfer theory to include the effects of wave interference. This modification aims to improve statistical inferences about velocity and attenuation of those regions of the subsurface where scattering Q drops into the single digits.
S53B-1262
Fractal Heterogeneities in Sonic Logs and Low Frequency Scattering Attenuation
Wave propagation in a heterogeneous medium involves seismic attenuation and dispersion by scattering. The nature of subsurface heterogeneities has been recognized to satisfy fractal properties. We model the velocity heterogeneities by the von Kármán spatial autocorrelation function depending on the length b (larger size of fractal heterogeneities), the Hurst exponent, and the standard deviation of the velocity variations. The nonlinear parameters estimation on four sonic VP and VS logs data from a clastic overburden in Canada reveals the spatial frequency domain of validity for the fractal description and the presence of several low cycles. We attempt to identify the different scales of the sedimentation process in the well log signal as proposed by O'Doherty and Anstey. Our inversion result shows a good agreement with the fractal model at scales smaller than 10 meters but the importance of local cycles at low spatial frequency. For long wavelengths compared to the size of heterogeneities, the scattering is in the Rayleigh diffusion regime in which the wavefield is dominantly backscattered. This regime is relevant for the frequency band of seismic surveys in our fractal heterogeneities model. High frequencies, required to improve resolution, undergo a more complex loss of energy by intrabed multiples as the wavelengths become similar to the heterogeneities scale. We use analytical derivations of the scattering attenuation based on the mean wavefield theory, whose validity is restricted to the low frequency band, i.e. for small heterogeneities compared to the seismic wavelength. The result estimates the attenuation by 3-D scattering of a scalar wave from isotropic fractal heterogeneities correlated by the von Kármán function. We determine that the loss of resolution with depth is more severe for a high Hurst exponent (smoother medium), for shear waves compared to compressional wave due to their smaller wavelength, and extremely sensitive to the characteristic size b of the fractal heterogeneities. The depth of penetration of the wave decreases dramatically with increasing frequencies. We evaluate the shift of the dominant frequency with depth for a Ricker wavelet propagating in the 3-D fractal heterogeneous medium. These results advise to use low frequency seismic for deep targets under a strongly heterogeneous overburden. The presence of quasi-cycles in the sonic log data at large spatial scales calls for more sophisticated seismic scattering methods accounting for the medium's periodicity.
S53B-1263
The Anisotropic Fractured Rock in Vicinity of the San Jacinto Fault Zone, Southern California From S-Coda Waves
Recently ( AGU Full Meeting 2004, 2005 ) we discussed the influence of seismic scattering in anisotropic rock on the S-coda waves attenuation, coda quality factor Qc and intensity of back scattering energy, Cc. Now we improve our method of anisotropy study based on coda waves of 102 3-components records from 11 local earthquakes, ml = 4.0 - 5.0 of 10 ANZA stations.Examining different parts of coda envelope ( 1. 16 sec - 41 sec, 2. 22 sec - 58 sec ) we found two types of crustal anisotropy.1. The S-coda waves polarized in a plane with the strike 126° and dip 72° has the smallest attenuation, or maximum value of Qc. The largest attenuation has polarization direction that is consistent with a vector normal to that plane. The coefficient of anisotropy equals 14.2 %. We suggest this type of anisotropy is controlled by the San Jacinto Fault Zone.2.A plane with the largest values of Qc has the strike ~ 26° and dip varies from 51° to 79°. Coefficient of anisotropy varies from 3.9 % to 9.3 %. On our suggestion there is a tectonic stress induced anisotropy in vicinity of the Fault Zone.The azimuthal variations of Qc and Cc are best fit with an anisotropic term A × cos ( 2 Az + φ ).
S53B-1264
REGIONAL P-CODA FOR STABLE ESTIMATES OF BODY WAVE MAGNITUDE: EXTENDING THE Ms:mb DISCRIMINANT TO SMALLER EVENTS
The most successful teleseismic discriminant is Ms:mb, and many studies are underway to try and extend surface wave magnitude (Ms) estimation to regional distances. A problem that is encountered at regional distances and small magnitudes is how to estimate mb so that the Ms:mb discriminant is meaningful and consistent with teleseismic measures. Over the past several years, a regional S-coda wave methodology has been developed that provides for the lowest variance estimate of the seismic source spectrum. Thus, regional MW and mb estimates derived from Sn and Lg coda are very stable, even when only a single station is used. However, these mb's&p are inherently biased for earthquakes because they are an S-based measurement, and explosions are relatively depleted in S-waves. Previous research projects have used region-specific mb scales based on direct measurements of Pn and Pg to improve the Ms:mb discrimination, even though the mb estimates often had a large variance. In our preliminary research, we have found that P-coda envelopes for both explosions and earthquakes can be obtained for events from both the NTS and NZ regions without bias. Our next step at NTS will be to derive path corrections, similar to the approach of Mayeda et al. (2003) for Lg-coda. We will compare inter-station scatter of distance-corrected amplitudes as a function of window length. This will provide an empirical measure of error based on window length for each frequency band. For each frequency band, we will regress our coda envelope amplitudes against regional and teleseismic estimates of mb (e.g., mb(Pn), mb(P)) to determine which band provides the lowest variance. This will yield slope and intercept values for each frequency band. We will then derive mb(Pn) and mb(P) (following Denny et al., 1989) to compare against mb(P-coda) to assess performance at the network and single-station level. Most of the nuclear explosions already have an mb(Pn) compiled by Vergino and Mensing (1989). Patton (2001) has estimated mb(Pn) for many historic NTS earthquakes. For recently recorded earthquakes, we will need to estimate mb(Pn) and mb(P). Finally, we will compute Ms(VMAX) from the regional stations and form an Ms(VMAX):mb(Pcoda) discriminant to compare against teleseismic values and trends.
S53B-1265
A Time-Reversed Reciprocal Method for Detecting High-frequency events in Civil Structures
A new method that uses the properties of wave propagation reciprocity and time-reversed reciprocal Green's functions is presented for identifying high-frequency events that occur within engineered structures. Wave propagation properties of a seismic source in an elastic medium are directly applicable to structural waveform data. The number of structures with dense seismic networks embedded in them is increasing, making it possible to develop new approaches to identifying failure events such as fracturing welds that take advantage of the large number of recordings. The event identification method is based on the hypothesis that a database can be compiled of pre-event, source-receiver Green's functions using experimental sources. For buildings it is assumed that the source-time excitation is a delta function, proportional to the displacement produced at the receiver site. In theory, if all the Green's functions for a structure are known for a complete set of potential failure event locations, forward modeling can be used to compute a range of displacements to identify the correct Green's functions, locations, and source times from the suite of displacements that recorded actual events. The method is applied to a 17-story, steel, moment-frame building using experimentally applied impulse-force hammer sources. The building has an embedded, 72-channel, accelerometer array that is continuously recorded by 24-bit data loggers at 100 and 500 sps. The focus of this particular application is the identification of brittle- fractured welds of beam-column connections.
S53B-1266
Spurious arrivals in seismic interferometry
Seismic interferometry makes it possible to extract the Green's function that accounts for wave propagation between receivers from the cross-correlation of field fluctuations recorded at those receivers. In principe, the full Green's function can be obtained, but we show examples that interferometry may lead to spurious arrivals due to cross-terms between different arrivals that do not correspond real physical arrivals. In the examples that we present, these spurious arrivals vanish when a full coverage of noise sources is present. In practical situations, noise sources, as required by theory, do not cover a closed surface around receivers, as required by theory. In that case, spurious arrivals may contaminate the estimated Green's function obtained from the cross-correlation of field fluctuations. http://www.mines.edu/~rsnieder/Publications.html
S53B-1267
Radiative Energy Transfer of Elastic Waves in Random Media – Three-component Envelopes and Numerical Validation
Short period wave propagation through the lithosphere results in complex wavetrains that are mainly composed of waves multiply scattered at small-scale heterogeneities of the Earth medium. Often it is useful to focus on bandpass-filtered envelopes of recorded seismograms instead of the full waveforms, as envelopes are stable features that allow the retrieval of statistical parameters of the lithospheric heterogeneity. Parameters like rms velocity and density fluctuation, correlation distance or scattering attenuation are informations closely related to stratigraphy, stress distribution, crack density, pore fluids etc. We present a Monte Carlo scheme for the solution of the three-dimensional radiative transfer (RT) equations for energy transport in elastic media with randomly fluctuating velocity and density. It includes mode conversions between P and S wave energy, and considers the frequency dependent directional scattering patterns following from Born approximation in continuous random media. By splitting S energy into two parts with orthogonal linear polarization we keep the polarization information of S energy without using the Stokes vector concept. The method offers a convenient way to synthesize complete three-component mean square envelopes of bandpass-filtered high-frequency wavefields in the presence of small-scale random heterogeneity starting from the first P wave onset until the late S wave coda. Validation of the method is achieved through a comparison with average mean square envelopes from full 3D wavefield simulations for the whole envelope shape and with the analytical Markov approximation for time windows around the ballistic arrival times. RT yields accurate envelope shapes even for parameter ranges where strong forward scattering occurs. Peak amplitudes, pulse broadening and coda decay at long lapse times are correctly modelled. A breakdown of RT is observed in the vicinity of a point source: waveform modeling shows that even for a pure compressional source some per cent of outward propagating shear wave energy are generated by near-source scattering that are not explained within the framewok of Born approximation.
S53B-1268
A New Derivation of Noise Correlation and Implications for Seismic Noise Tomography
It has been shown that the Green's function between two receivers can be retrieved by cross-correlating time series of noise recorded at the receivers. One of the most useful and impressive applications of this noise- correlation property is the three-dimensional mapping of seismic velocities, known as seismic noise tomography. This noise-correlation property has been derived assuming that the energy in normal modes is uncorrelated and perfectly equipartitioned or that the distribution of noise sources is uniform in space. We present a simple alternative derivation that facilitates an understanding of the relationship between the noise- correlation property and seismic noise tomography efforts. This new derivation is not unlike some of the earlier derivations, but it is novel in describing the density distribution of noise sources as a function of travel-time delay and facilitates the interpretation of and calculation of the retrieved cross-correlation from arbitrary noise-source distributions. We show that the success of noise tomography follows from proper application of a two-dimensional surface- wave noise-correlation theory, rather than the assumption of noise sources distributed isotropically in three dimensions. We resolve discrepancies between various approaches in the published literature and demonstrate that certain steps, such as calculating the time derivative of the cross-correlation, are not necessary. We further demonstrate that with a non-uniform noise-source distribution or a non-uniform velocity medium, the cross- correlation includes energy originating from elastic structure away from the geometric ray connecting the two receivers. Using our alternative derivation, we are able to quantify the degree to which the sensitivity kernel is different than the geometric ray and find, for example, that the kernel width is period-dependent and that the kernel generally has maximum sensitivity not precisely on the geometric ray, even within a ray theoretical framework. In a system like the Earth, which has neither a uniform source distribution nor uniform velocities, models of seismic-wave speed produced using noise-correlation techniques may therefore, in some regions, be biased.
S53B-1269
Deep Electromagnetic Imaging(EMI) Simulations for Realistic Heterogeneous Earth Models
Electromagnetic Imaging (EMI) is an extremely low frequency version of Ground Penetrating Radar (GPR) that provides deep non-invasive imaging of the subsurface. Recent breakthroughs in low frequency time-domain modeling show that reflections from frequencies in the very low megahertz range (center-band frequencies down to 500 kHz). Simulations of EMI data facilitate an understanding of the effects of complex electromagnetic phenomena in the intermediate frequency range (1-50 MHz) where both conduction and displacement currents affect wave propagation, as well as predicting the performance of radar antennas over a complex heterogeneous subsurface geologic environment. Our results show that specular reflections from objects buried down to a depth of 15-20 m in a heterogeneous environment can be imaged using a robust finite difference time domain algorithm (FDTD) with a source pulse center-band frequency lower than 1 MHz. A highly efficient robust algorithm was developed to enhance the effectiveness of the simulation in surroundings characterized by an arbitrary distribution of all electromagnetic properties (conductivity, permittivity, and permeability). The modeling is facilitated by a graphical algorithm that enables a detailed simulation of each component of the system, including a heterogeneous half-space and the physical details of the transmitter and receiver antennas. In terms of specific targets, the results produced by the simulation demonstrated the applicability of low frequency GPR for detecting cavities in heterogeneous environment down to depths of 20 m using 500 KHz center-band source pulse.
S53B-1270
Site Response in the San Joaquin/Sacramento River Delta
The Sacramento/San Joaquin River Delta lies on the western edge of the Great Valley and contains a system of levees that are thought to be prone to catastrophic failure from a major earthquake in the San Francisco Bay area or on faults along the western border of the Great Valley. To assess this risk we deployed digital recorders and broadband sensors in late 2006 and 2007 at 3 levee sites in the Delta (each site had a top and base sensor) and at one reference site to the west. Cone penetrometer data show that at the base, the soils have low S-wave velocities of 170 to 240 m/s. Upper soil layers are typically peats and aeolian sands. During the nine months of deployment, we recorded 3 local events (45km<r<60km) that occurred on or near to the Hayward Fault. The events range in depth from 5 to 16 km with magnitudes of 3.7 to 4.2. Site response is estimated by ratios of S wave spectra at each site to spectra from a reference site to the west of the Delta (Byron Hot Springs , BYR) or Black Diamond Mine (BDM, part of the Berkeley Digital Seismic Network). Spectra are normalized for distance. Each spectrum is smoothed with an algorithm that tries to preserve peaks; a running mean filter is also applied to the spectra from the reference site to reduce the possibility of holes in the reference spectrum appearing as a resonance in the ratio. Our primary observation is that many of the spectral ratios show large resonances, typically at 1-3 Hz and may represent a substantial risk to the levees. Sites at the tops of levees typically have stronger resonances in the 1-3 Hz range compared to base sites. The character of these ratios, however, differs substantially for each event. For example, the top site at Bethel Isl. has peaks in the site response with amplitudes between 6 and 15 (2-3Hz) for an earthquake located near Berkeley using either reference site, but is only apparent in the ratios using BDM for the other two events. This is because BYR has more amplitude in the 2- 3 Hz band then BDM typically does. The event with a depth of 16.2 km appears to have the smallest resonances when using BYR as a reference. Long-period surface waves arrive as much as 20s late compared to the high- frequency S waves on records from Delta sites producing very long codas on these records. Because of a strong resonance at the top site compared to the base site at Bethel Isl. we investigated whether the resonance could be explained by a topographic effect. Polarizations at top sites are not consistent with the focal mechanism, nor are they simply related to the strike of the levees suggesting that the source of such a marked change in the character of the ground motion on the levees is differences in subsurface geology.
S53B-1271
Reanalysis of the stationary phase method in ambient noise study
Extracting Green's function between stations from the cross correlation has been proven to be an effective method theoretically and experimentally. It has been widely applied in surface wave tomography of the crust and upmost mantle. However, there are still a lot of controversies about why this method works. Assuming the stationary phase approximation, Snieder (2004) evaluated the contribution of scatterers distributed in whole space to cross-station correlation function, and he proposed that it is the constructive interference of waves emitted by the scatterers near the receiver line leads to the Green's function. Instead, we evaluate the cross correlation between station pairs numerical for a diffuse wave field, and our numerical computation indicates that cross correlation differs from Greens¡¯ function substantially in both amplitude and phase when frequency is low, where stationary phase approximation fails to work. We also demonstrate that this inaccuracy of stationary phase approximation can be ignored when the station distance is larger than several wavelengths.
S53B-1272
Analyses and Simulation of 3D Scattering due to Heterogeneous Crustal Structure on Regional Phases; Seismic Source Discrimination
The purpose of our study is basic understanding of wave propagation scattering and its effect on regional phases through step-by-step numerical experiments, with the goal of providing useful insights into ongoing research for seismic source discrimination and development of simple empirical models of scattering that can be used in reducing the scatter in measures of Lg and coda wave magnitude. We performed anelastic 3D finite-difference simulations of wave propagation in highly heterogeneous media for a range of receiver distances using double- couple and isotropic explosion point sources. Using a parallelized computer code and models with flat surface topography we have produced synthetic seismograms up to 4.5 Hz at regional distances up to 300 km. Our numerical experiments with 3D velocity models that include random velocity perturbations and small-scale heterogeneities such as microbasins, design to produce wave scattering in the upper 6km of the crust, clearly show that wave-path scattering alone can produce Lg, P and S coda waves with significant energy even for explosion sources. The energy of Lg coda waves depends on the source depth. P/Lg ratios estimated at different frequencies indicate that at high frequencies this ratio could be a good discriminant between explosions and earthquakes. P/Lg ratios below 1Hz are very similar for shallow explosions and deep earthquakes.
S53B-1273
Spectral-Element Simulations of Wave Propagation in Porous Media
Biot theory has been extensively used in the petroleum industry, where seismic surveys are performed to determine the physical properties of reservoir rocks. The theory is also of broad general interest when a physical understanding of the coupling between solid and fluid phases is desired. One fundamental result of Biot theory is the prediction of a second compressional wave, which attenuates rapidly, often referred to as "type II" or "Biot's slow compressional wave", in addition to the classical fast compressional and shear waves. The mathematical formulation of wave propagation in porous media developed by Biot is based upon the principle of virtual work, ignoring processes at the microscopic level. Moreover, even if the Biot formulations are claimed to be valid for non-uniform porosity, gradients in porosity are not explicitly incorporated in the original theory. More recent studies focused on averaging techniques to derive the macroscopic porous medium equations from the microscale, and made an attempt to derive an expression for the change in porosity, but there is still room for clarification of such an expression, and to properly integrate the effects of gradients in porosity. We aim to present a straightforward derivation of the main equations describing wave propagation in porous media, with a particular emphasis on the effects of gradients in porosity. We also present a two dimensional numerical implementation of these equations using a spectral-element method. Finally, we have performed different benchmarks to validate our method, involving acoustic-poroelastic waves interaction and wave propagation in heterogenous porous media.
S53B-1274
Revisiting Energy Estimates Using the Seismic Coda
Measurements of seismic energy from scattered coda waves indicate that apparent stress increases with increasing seismic moment, a consequential result for several reasons. For one, it may constrain possible forms of fault weakening with increasing slip. Moreover, if larger earthquakes more efficiently generate energy than their smaller counterparts, strong ground motion from large events would be more intense than anticipated from the extrapolation of smaller events. The relatively sparse strong motion data set does not appear to support this conclusion, leading us to reexamine seismic energy estimates. Coda envelope measurements of the source amplitude are much more stable than measurements made using direct waves because the coda averages over both path and source variability. We follow Mayeda et al. [2003] by fitting narrowband coda envelopes at 15 frequency bands for events at a single station to an analytic expression. A(f,t,r)=P(r,f)t- γ(r)eb(r)t describes the time decay of the coda envelope, A(f,t,r), at each frequency band, distance and station, where γ(r) and b(r) are the distance dependent parameters being fit and P(r,f) describes the source amplitude, site response, path effects, scattering, spreading and attenuation. We make empirical distance corrections to tie the observed amplitudes to absolute moment-rate spectra. From this, we estimate the radiated seismic energy. Our analysis differs somewhat from that used previously in that we fit parameters simultaneously, rather than sequentially, and place soft bounds on them due to physical considerations. We analyze broadband data from the western United States and Japan to revisit the scaling of seismic energy using coda waves.
S53B-1275
Multiple scattering of waves in random media: Application to the study of the city-site effect in Mexico City area.
Long-duration, amplifications and spatial response's variability of the seismic records registered in Mexico City during the September 1985 earthquake cannot only be explained by the soil velocity model. We will try to explain these phenomena by studying the extent of the effect of buildings' diffracted wave fields during an earthquake. The main question is whether the presence of a large number of buildings can significantly modify the seismic wave field. We are interested in the interaction between the incident wave field propagating in a stratified half- space and a large number of structures at the free surface, i.e., the coupled city-site effect. We study and characterize the seismic wave propagation regimes in a city using the theory of wave propagation in random media. In the coupled city-site system, the buildings are modeled as resonant scatterers uniformly distributed at the surface of a deterministic, horizontally layered elastic half-space representing the soil. Based on the mean-field and the field correlation equations, we build a theoretical model which takes into account the multiple scattering of seismic waves and allows us to describe the coupled city-site system behavior in a simple and rapid way. The results obtained for the configurationally averaged field quantities are validated by means of 3D results for the seismic response of a deterministic model. The numerical simulations of this model are computed with MISS3D code based on classical Soil-Structure Interaction techniques and on a variational coupling between Boundary Integral Equations for a layered soil and a modal Finite Element approach for the buildings. This work proposes a detailed numerical and a theoretical analysis of the city-site interaction (CSI) in Mexico City area. The principal parameters in the study of the CSI are the buildings resonant frequency distribution, the soil characteristics of the site, the urban density and position of the buildings in the city, as well as the type of incident wave. The main results of the theoretical and numerical models allow us to characterize the seismic movement in urban areas.
S53B-1276
Frequency Dependence of Regional Coda Q: Numerical Modeling and a PNE Example
Mapping of coda properties requires the use of parameterization reflecting the fundamental physics and stable in respect to unconstrained factors. We use numerical modeling of nuclear-explosion coda at regional distances to compare two types of such parameterizations, namely the frequency-dependent coda attenuation (Q1Hz,η) and frequency-independent attenuation with geometric spreading, (γ, Qcoda). The modeling shows that for a constant intrinsic Q of the crust, the resulting coda Q exhibits strong and positive frequency dependence η ~ 1. This spurious frequency dependence is not related to model rheology but is caused by disregard of geometrical propagation effects, such as bending of scattered ray paths. By contrast, in the geometric-spreading approach, coda amplitude inversion using the synthetic records results in spreading parameters, γ = (0.8-1.6) 10-2 s-1, and frequency-independent Qcoda uniquely related to the crustal S-wave Q. Peaceful Nuclear Explosion (PNE) data from two different areas in Russia were found to have similar values of γ = 0.75 10-2 s-1, which are remarkably close to numerical results, and strongly different Qcoda values of 850 (in the East European Platform) and 2500 (the Siberian Craton). Combined with literature results, this suggests that tectonically active zones in both North America and Northern Eurasia could differ from stable areas by their high values of γ, and not so much by η. Modeling also shows that γ could increase in areas where high-attenuation or scattering layers are present within the crust. We therefore suggest that parameters γ and Qcoda could provide high quality, stable, and transportable discriminants for differentiating between crustal tectonic types and for seismic regionalization used in nuclear-test monitoring.