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  • Articles  (13)
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  • Articles  (13)
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  • Springer  (13)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 131 (1989), S. 639-685 
    ISSN: 1420-9136
    Keywords: Finite-difference ; finite-element ; scattering ; random heterogeneity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract This paper reviews applications of the finite-difference and finite-element methods to the study of seismic wave scattering in both simple and complex velocity models. These numerical simulations have improved our understanding of seismic scattering in portions of the earth where there is significant lateral heterogeneity, such as the crust. The methods propagate complete seismic wavefields through highly complex media and include multiply scattered waves and converted phases (e.g.,P toSV, SV toP, body wave to surface wave). The numerical methods have been especially useful in cases of moderate and strong scattering in complex media where multiple scattering becomes important. Progress has been made with numerical methods in understanding how near-surface, low-velocity basin structures scatter surface waves and vertically-incident body waves. The numerical methods have proven useful in evaluating scattering of surface waves and body waves from topography of both the free surface and interfaces buried at depth. Numerical studies have demonstrated the importance of conversions from body waves to surface waves (andvice versa) when lateral heterogeneities and topographic relief are present in the uppermost crust. Recently, several investigations have applied numerical methods to study seismic wave propagation in velocity models which vary randomly in space. This stochastic approach seeks to understand the effects of small-scale complexity in the earth which cannot be resolved deterministically. These experiments have quantified the relationships between the statistical properties of the random heterogeneity and the measurable properties of high-frequency (≥1 Hz) seismograms. These simulations have been applied to the study of many features observed in actual high-frequency seismic waves, including: the amplitude and time decay of seismic coda, the apparent attenuation from scattering, the dispersion of waveforms, and the travel time and waveform variations across arrays of receivers.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 131 (1989), S. 61-76 
    ISSN: 1420-9136
    Keywords: Refraction ; fractal ; raytracing ; scattering ; seismology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The introduction of noise components to a simple crustal velocity model is shown to markedly affect the appearance of synthetic seismograms calculated according to ray theory applied to refraction experiments. Here we simulate noise by a self-similar process with a power spectral density which falls off as inverse wavenumber to a simple power (0–2). The major effect is to destroy the coherency of the arrival branches normally expected from deterministic velocity models; the arrival amplitudes also show large trace-to-trace variations and considerable sensitivity to shot position. Some of these differences can be ascribed to the variety of noise model chosen (i.e., white noise, flicker noise and brown noise). It is argued that there is no clear distinction between coherent noise and geological structure.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 128 (1988), S. 43-47 
    ISSN: 1420-9136
    Keywords: Coda ; fractal ; scattering ; seismogram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Supposing that the distribution of scatterers in a three-dimensional medium is not uniform but fractally homogeneous with fractal dimensionD, we have made the dimensional analysis for the temporal decay of the multiple scattering energy density at the hypocenter.The number of scatters in a sphere of radiusR is assumed to be proportional toR D . Then, the energy density of thekth order scattering decays according to the [(D−2)k−3]th power of lapse time. A fractal dimension ofD=3 corresponds to the uniform distribution. If 2〈D≦3, multiple scattering terms of orderk≧2 dominate over the single scattering term (k=1) at long lapse time. IfD=2, energy density of every order decays according to the — 3rd power of lapse time. The single scattering model survives on conditionD〈2; the single scattering term dominates over the higher order multiple scattering terms even at long lapse time, since the negative power of lapse time fork=1 is the smallest of all.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 128 (1988), S. 7-42 
    ISSN: 1420-9136
    Keywords: Surface waves ; scattering ; layered media
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Malin's (1980) first-order single scattering theory has been extended to study the scattering of surface waves as well as body waves by distributed point scatterers in a layered medium. The scattered waveform itself is generated and examined instead of its energy envelope. The theory used allows 1) mode conversion, 2) wave type conversion, 3) finite scatterer distribution, and 4) the effect of attenuation from scattering as well as intrinsic absorption. The cases studied are for elastic or slightly attenuative media with any kind of source and receiver at any place in the layered structure. This direct calculation of coda waves provides us an immediate description of the relation of coda and scattering. The objectives are to find 1) the effect of layering on scattering, 2) the effect of scatterer distribution on recorded vertical and horizontal motion, 3) the relation of scatteringQ to intrinsicQ, 4) the scattering behavior of surface and body waves, and 5) the superposition of scattering waves to form the coda. The generation of body waves by ‘locked mode’ approximation, which makes the body-wave scattering a subset of the ‘surface-wave’, scattering. Preliminary results explain some observed coda behavior surprisingly well. We find a larger geometrical spreading for near scatterers, which is caused by mode conversion or wave type conversion because of the wide angle scattering. This makes the speading correction higher for early part of coda which may account for the lowQ observed in early coda of regional earthquakes. This study is of practical value as an effort to understand the complicated coda phases.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 128 (1988), S. 81-100 
    ISSN: 1420-9136
    Keywords: Attenuation ; scattering ; crust ; strong motion ; Rg ; coda
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The mechanisms contributing to the attenuation of earthquake ground motion in the distance range of 10 to 200 km are studied with the aid of laboratory data, coda wavesRg attenuation, strong motion attenuation measurements in the northeast United States and Canada, and theoretical models. The frequency range 1–10 Hz has been studied. The relative contributions to attenuation of anelasticity of crustal rocks (constantQ), fluid flow and scattering are evaluated. Scattering is found to be strong with an albedoB 0=0.8–0.9 and a scattering extinction length of 17–32 km. The albedo is defined as the ratio of the total extinction length to the scattering extinction length. TheRg results indicate thatQ increases with depth in the upper kilometer or two of the crust, at least in New England. CodaQ appears to be equivalent to intrinsic (anelastic)Q and indicates that thisQ increases with frequency asQ=Q o f n , wheren is in the range of 0.2–0.9. The intrinsic attenuation in the crust can be explained by a high constantQ (500≤Q o≤2000) and a frequency dependent mechanism most likely due to fluid effects in rocks and cracks. A fluid-flow attenuation model gives a frequency dependence (Q≃Q o f 0.5) similar to those determined from the analysis of coda waves of regional seismograms.Q is low near the surface and high in the body of the crust.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 128 (1988), S. 251-260 
    ISSN: 1420-9136
    Keywords: Coda ; attenuation ; scattering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Coda wave data from California microearthquakes were studied in order to delineate regional fluctuations of apparent crustal attenuation in the band 1.5 to 24 Hz. Apparent attenuation was estimated using a single back scattering model of coda waves. The coda wave data were restricted to ≤30 s following the origin time; this insures that crustal effects dominate the results as the backscattered shear waves thought to form the coda would not have had time to penetrate much deeper. Results indicate a strong variation in apparent crustal attenuation at high frequencies between the Franciscan and Salinian regions of central California and the Long Valley area of the Sierra Nevada. Although the codaQ measurements coincide at 1.5 Hz (Q c =100), at 24 Hz there is a factor of four difference between the measurements made in Franciscan (Q c =525) and Long Valley (Q c =2100) with the Salinian midway between (Q c =900). These are extremely large variations compared to measures of seismic velocities of comparable resolution, demonstrating the exceptional sensitivity of the high frequency codaQ measurement to regional geology. In addition, the frequency trend of the results is opposite to that seen in a compilation of codaQ measurements made worldwide by other authors which tend to converge at high and diverge at low frequencies, however, the worldwide results generally were obtained without limiting the coda lengths and probably reflect upper mantle rather than crustal properties. Our results match those expected due to scattering in random media represented by Von Karman autocorrelation functions of orders 1/2 to 1/3. The Von Karman medium of order 1/3 corresponding to the Franciscan codaQ measurement contains greater amounts of high wavenumber fluctuations. This indicates relatively large medium fluctuations with wavelengths on the order of 100 m in the highly deformed crust associated with the Franciscan, however, the influence of scattering on the codaQ measurement is currently a matter of controversy.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 128 (1988), S. 295-307 
    ISSN: 1420-9136
    Keywords: Coda ; scattering ; attenuation ; Alaska
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Coda wave quality factor (Q c ) was investigated by using digital data (100 sample sec−1) recorded by a vertical component short-period station installed for this study. The station was located in the greater Fairbanks area in central Alaska. From several hundred earthquakes recorded by this station in about a year, 27 earthquakes were selected for the above study; 7 of these selected earthquakes were located along the Alaska Wadati-Benioff zone (Pacific plate). The other 20 earthquakes were located in the area of intraplate seismicity (North American plate). The data was filtered using 9 pass-bands with center frequency varying from 1.5 Hz to 16 Hz with octave bandwidth. The values ofQ c obtained from the coda amplitude decay rates measured on the filtered data after corrections due to the recording instrument and source-receiver separation show appreciable frequency dependence. The value ofQ c varies in the range of 253 and 1190 corresponding to the frequency interval from 1.5 Hz to 16 Hz for the study area. This variation is close to that reported by others for the Kanto region of Japan. Moreover, the characteristics ofQ c obtained in the present case seem to be independent of epicentral distance and hypocentral depth.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 128 (1988), S. 309-331 
    ISSN: 1420-9136
    Keywords: Coda decay ; amplitude decay ; scattering ; local earthquakes ; reflection/refraction surveys
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Three types of seismic data recorded near Coalinga, California were analyzed to study the behavior of scattered waves: 1) aftershocks of the May 2, 1983 earthquake, recorded on verticalcomponent seismometers deployed by the USGS; 2) regional refraction profiles using large explosive sources recorded on essentially the same arrays above; 3) three common-midpoint (CMP) reflection surveys recorded with vibrator sources over the same area. Records from each data set were bandpassed filtered into 5 Hz wide passbands (over the range of 1–25 Hz), corrected for geometric spreading, and fit with an exponential model of amplitude decay. Decay rates were expressed in terms of inverse codaQ (Q c −1 ).Q c −1 values for earthquake and refraction data are generally comparable and show a slight decrease with increasing frequency. Decay rates for different source types recorded on proximate receivers show similar results, with one notable exception. One set of aftershocks shows an increase ofQ c −1 with frequency. Where the amplitude decay rates of surface and buried sources are similar, the coda decay results are consistent with other studies suggesting the importance of upper crustal scattering in the formation of coda. Differences in the variation ofQ c −1 with frequency can be correlated with differences in geologic structure near the source region, as revealed by CMP-stacked reflection data. A more detailed assessment of effects such as the depth dependence of scattered contributions to the coda and the role of intrinsic attenuation requires precise control of source-receiver field geometry and the study of synthetic seismic data calculated for velocity models developed from CMP reflection data.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 126 (1988), S. 465-497 
    ISSN: 1420-9136
    Keywords: Attenuation ; scattering ; coda ; cracks ; inhomogeneities ; heterogeneities ; seismograms ; earthquake prediction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The study of coda waves has recently attracted increasing attention from seismologists. This is due to the fact that it is viewed as a new means by which the stress accumulation stage preceding a large earthquake can be measured, since the scattering paths nearly uniformly cover a fairly large region around the focus and observation stations, compared with the direct ray paths. To date, we have had many reports on the temporal variation of the relation between coda duration and amplitude magnitude, and that of the coda attenuationQ c −1 which is estimated from coda amplitude decay. Some of these have shown a precursor-like behavior; however, others seem to have shown a coseismic change. We have critically reviewed these reports, and discussed what these observational facts tell us about the change in the heterogeneous crust. We found significant temporal variations, not only in the mean but also in the scatter ofQ c −1 , associated with the mainshock occurrence. The formation of new cracks, the reopening and growing of existing cracks, the interaction of these cracks, and the pore water movement through these cracks might correspond to such variations. In addition, we may expect an inhomogeneous distribution of crack clusters in a fairly large region, compared with the aftershock region. The gradual appearance of such crack clusters seems to be the most plausible mechanism by which coda decay gradients are caused to largely scatter in the stress accumulation stage.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 128 (1988), S. 119-132 
    ISSN: 1420-9136
    Keywords: Rayleigh ; scattering ; wedge corner ; reflection ; transmission
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Theoretical calculations were performed on reflected and transmitted Rayleigh waves and scattered body waves, in the case where a two-dimensional Rayleigh wave is incident to a wedge-shaped medium having a wedge angle between 250° and 290° and arbitrary value of Poisson ratio. The reflection and transmission coefficients of Rayleigh waves were also experimentally measured in cases of wedges with 190° to 330° wedge angles. The method of theoretical analysis and the techniques of experiment are based on those developed in our preceding research (W-1. W-2 and W-3). Compared with the results where the wedge angle is smaller than 180° (W-1 and W-2), all features show consistent variation with wedge angle.
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  • 11
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 128 (1988), S. 147-156 
    ISSN: 1420-9136
    Keywords: Random media ; waves ; scattering ; causality ; dispersion ; attenuation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Basic ideas of the causal approach to wave propagation in random media are first overviewed. This approach appeals from the outset to the linearity, causality, and passivity of the effective medium and is therefore particularly simple from the conceptual viewpoint. The energy analysis and the Kramers-Kronig relations play the major role in this method, which does not resort to ensemble averaging. Then the dispersion of plane wave propagation in randon media is evaluated by extending Wu's results on attenuation induced by scattering. These results are particularly suitable for seismic waves, for which the so-called mean-field approach may not provide adequate modeling. The presence of intrinsic losses is also incorporated. The analysis also includes the case of propagation of a small-amplitude discontinuity.
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  • 12
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 128 (1988), S. 195-229 
    ISSN: 1420-9136
    Keywords: Finite difference ; scattering ; marine seismics ; Stoneley waves ; random heterogeneities ; incoherence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract We present finite difference forward models of elastic wave propagation through laterally heterogeneous upper oceanic crust. The finite difference formulation is a 2-D solution to the elastic wave equation for heterogeneous media and implicitly calculatesP andSV propagation, compressional to shear conversion, interference effects and interface phenomena. Random velocity perturbations with Gaussian and self-similar autocorrelation functions and different correlation lengths (a) are presented which show different characteristics of secondary scattering. Heterogeneities scatter primary energy into secondary body waves and secondary Stoneley waves along the water-solid interface. The presence of a water-solid interface in the model allows for the existence of secondary Stoneley waves which account for much of the seafloor ‘noise’ seen in the synthetic seismograms for the laterally heterogeneous models. ‘Random’ incoherent secondary scattering generally increases aska (wavenumber,k, and correlation length,a) approaches one. Deterministic secondary scattering from larger heterogeneities is the dominant effect in the models aska increases above one. Secondary scattering also shows up as incoherence in the primary traces of the seisograms when compared to the laterally homogeneous case. Cross-correlation analysis of the initialP-diving wave arrival shows that, in general, the correlation between traces decreases aska approaches one. Also, because many different wave types exist for these marine models, the correlation between traces is range dependent, even for the laterally homogeneous case.
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  • 13
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 125 (1987), S. 499-577 
    ISSN: 1420-9136
    Keywords: High frequency seismic waves ; coda waves ; attenuation ; scattering ; heterogeneity ; absorption ; inhomogeneity ; coda quality factor ; Lg quality factor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The analysis and interpretation of coda waves have received increasing attention since the early seventies. In the past few years interest in this subject has spread worldwide, and the study of high-frequency seismic coda waves has become a very important seismological topic. As a conclusion of the studies accomplished in this time, coda waves are considered the result of scattering processes caused by heterogeneities acting on seismic waves.P andS waves play a particularly important role in this interaction. The process introduces an attenuation which, added to the intrinsic absorption, gives the observed apparent attenuation. Therefore, coda waves constitute a thumbprint left by the heterogeneities on the seismograms. Coda waves offer decisive information about the mechanism of how scattering and attenuation take place. This review describes coda waves in detail, and summarizes the work done in this subject to 1986. The relation between coda waves and attenuation in the context of research on seismic scattering problems is stressed. Particular attention has been given to the application of coda waves to estimate source and medium parameters. The state-of-the-art of the temporal variations of coda wave shape, and the possible use of these variations as an earthquake precursor also are presented. Care has been taken to introduce the statistical models used to deal with the heterogeneities responsible for scattering.
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