Seismic Wave Propagation and Scattering in the Heterogeneous Earth : Second Edition

Abstract

Scattering due to randomly distributed small-scale heterogeneities in the earth significantly changes seismic waveforms of local earthquakes especially for short periods. Scattering excites long lasting coda waves after the direct arrival and broadens the apparent duration of oscillation with increasing travel distance much longer than the source duration time. Models of propagation through deterministic structures such as those with horizontally uniform velocity layers cannot explain those observed phenomena. Our goal in writing this book is to put a focus on the phenomena of seismic wave scattering by distributed heterogeneities in the earth, especially in the lithosphere, where stochastic treatment is essential to describe both heterogeneous media and wave propagation through them. Stochastic approaches and deterministic approaches are complementary for the construction of a unified image of the earth's structure.Keiiti Aki was a distinguished pioneer who extensively developed various stochastic methods for short-period seismology. His strong encouragement and continuous support for us were essential in motivating us to write the first edition of this book. Before Kei passed away in 2005, he kindly cited our book when he argued for the importance of the study on seismic wave scattering caused by small-scale heterogeneity in his letter to V. I. Keilis-Borok, ". . . To a geodynamicist, the earth's property is smoothly varying within bodies bounded by large-scale interfaces. Most seismologists also belong to this "smooth earth club," because once you start with an initial model of smooth earth your data usually do not require the addition of smallscale heterogeneity to your initial model. As summarized well in a recent book by Sato and Fehler (1998), the acceptance of coda waves in the data set is needed for the acceptance of small-scale seismic heterogeneity of the lithosphere. There are an increasing number of seismologists who accept it, forming the "rough earth club." I believe that you are also a member of the rough earth club, judging from the emphasis on the hierarchical heterogeneity of the lithosphere. . . . "(Aki 2009).The first edition of this book was fortunately accepted in the geophysical community as a textbook, especially for graduate students. Furthermore it has been often cited in the physics community since this book introduced various aspects of wave scattering in real heterogeneous media. During the decade following the vii viii Preface to the Second Edition publication of the first edition, there were developments in stochastic methods and analyses focusing on seismogram envelopes. Radiative transfer theory has been used not only for the study of coda envelopes but also for the analysis of whole seismogram envelopes. These studies made it possible to resolve the spatial variation of scattering strength. There have been developments in the statistical description of wave propagation in random media that reliably predict the delay of peak amplitude from the onset and the broadening of seismogr...

Source Mechanisms of Induced Earthquakes at The Geysers Geothermal Reservoir

“…Numerical simulations have shown that topography such as that found at The Geysers can cause variations in the amplitudes of seismic waves of more than 50 % at frequencies above 2 Hz (BOORE 1972(BOORE , 1973BOUCHON et al 1996). The effects of heterogeneity in velocity has also been investigated with numerical calculations (FRANKEL and CLAYTON 1986;O'CONNELL 1999;SATO et al 2012) and effects similar to those shown in Fig. 7 can be produced by velocity variations of only about 5 %.…”

“…For instance, the observed seismograms in Fig. 7 show many of the features considered by SATO et al (2012) as indicative of high frequency scattering by correlated random heterogeneity, including the codas of P and S waves that last longer than the expected source duration, an S coda that is more prominent than that of P, and a tendency for equipartition of motion on the different components. The fact that the seismograms at each station have certain distinctive characteristics, such as frequency content, shape of phase arrivals, and duration of phases, that are independent of the source suggests that much of this scattering is taking place near the seismic station.…”

Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation

“…Understanding the propagation of classical waves through strongly scattering media is of great importance for many applications such as imaging, characterization, or communication with all kinds of waves [1][2][3][4][5].…”

Simulations of P-SV wave scattering due to cracks by the 2-D finite difference method

“…Random inhomogeneities inside the Earth's lithosphere scatter high-frequency seismic waves and thereby cause phenomena such as the attenuation, dispersion, and generation of coda waves (Sato et al, 2012). The modeling of such inhomogeneities can be categorized into two concepts: random spatial fluctuation of medium parameters (called random media), and discrete scatterers such as cracks, inclusions, or cavities.…”

“…The modeling of such inhomogeneities can be categorized into two concepts: random spatial fluctuation of medium parameters (called random media), and discrete scatterers such as cracks, inclusions, or cavities. Although the concept of random media has been popularly adopted in theoretically modeling seismic scattering (Sato et al, 2012), it assumes quite often a continuous heterogeneity. In contrast, the real Earth's interior obviously has a discontinuous nature.…”