Computer Science – Sound
Scientific paper
Nov 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002geoji.151..673.&link_type=abstract
Geophysical Journal International, Volume 151, Issue 2, pp. 673-673.
Computer Science
Sound
Scientific paper
This book, published recently by Springer Verlag, is devoted to the description of elastic wave propagation and scattering in random media, consisting of a stack of thin layers. It is well known that the stratigraphic filtering effects in such media can be satisfactorily described by the classical O'Doherty-Anstey (ODA) formula, which provides a very good approximation both for forward propagating and for scattered wavefields. The main goal of the book under consideration is to study the potential of the ODA approximation for the solution of a wide class of seismological problems. The authors have managed to treat this topic in a comprehensive manner and presented a set of important results in a didactically simple way, emphasizing the physics of wave-propagation and scattering problems. Throughout the text the authors do not claim for mathematical strictness in derivations, however they have managed to obtain a number of useful generalizations of the original ODA approximation for various applications.The book consists of eleven chapters. Chapter 1 shortly outlines the main problems under consideration and gives a very short historical review. Basic concepts of wave propagation through the random media are presented in Chapter 2. Like Chapter 1, this chapter is not lengthy, but nevertheless contains two important points which were still not reflected in seismological literature in a proper way. The first of these points is the notion self-averaged values, which are especially important for seismological problems, dealing with the single realization of medium parameter, but thinking on statistical ensemble of such media. The second point is the estimate for the length of localization of elastic waves in a fine-layered media. This length happens to be so large (about 10-15 km), that it practically excludes observations of Anderson strong localization phenomenon in seismology.Chapter 3 analyses properties of normally incident waves in a stack of layers. The authors start with the Goupillaud model and present the rigorous solution in an explicit form. It looks quite instructive, both for students and for experienced readers, to compare the ODA formula with the exact solution. Based on the ODA approximation, the authors first revealed the universal behavior of near coda, arriving just after primary, and estimated the variance of far coda, which are shown to reduce continuously in time.Chapter 4 deals with the attenuation and phase of transmissivity of scalar waves obliquely incident on a layered media. The main result is the derivation of the equations for the amplitude and phase of propagating elastic waves as well as their solution under reasonable prepositions. As a result, the authors obtained generalized ODA formulae for scalar waves. It is worth noticing that in fact these formulas can be considered as a `seismological generalization' of the Rytov approximation widely used for description of light fluctuations in a turbulent atmosphere.Chapter 5 is devoted to mode conversion which can take place at any interface. Studying the influence of 1-D randomly stratified media on elastic plane waves, the authors used a combination of the invariant imbedding method and the small-perturbation expansion and obtain one more generalization of ODA formulas-this time on multimode wave propagation.The subject of analysis of Chapter 6 is the frequency-dependent properties of stratigraphic filtering. The authors revealed a few important features of stratigraphic filtering in a frequency domain, in particular, the frequency-dependent velocity anisotropy, the frequency-dependent shear-wave splitting and the dispersion and attenuation of the time-harmonic transmissivity. All these features characterize the frequency-dependent behavior of generalized primaries of seismic events.Chapter 7 develops the results of Chapter 8 as applied to analysis of transient transmissivity. Comparison of numerical results with analytical ones demonstrates good agreement between them and allows the authors to reveal conditions when approximating formulae, say the Gaussian approximation for the Gaussian approximation of the waveform works well.In Chapter 8 generalized ODA formulae from Chapters 4 and 5 are used for the correction of the offset-dependent reflection response for the effect of two-way stratigraphic filtering. The authors follow the lines of Widmaier, however, they simplified and shortened his treatment. Separate section is devoted to the problem how to distinguish the effects of scattering from intrinsic absorption. Chapter 9 takes into account the effects of poroelasticity and outlines features of stratigraphic filtering in poroelastic vertically heterogeneous structures. Anelastic effects related to the interaction of a viscous fluid with the porous matrix causes multimode propagation even for a vertical incidence of the P wave.Whereas the main subject of previous Chapters was the medium transmissivity, Chapter 10 analyses reflectivity of multilayered structures and suggests a few useful numerical receipts, based on ODA approximation, which demonstrates acceptable agreement with the existing experimental data. Thus the book demonstrates `how does one take into account the influence of small- (or even multi-) scale heterogeneities of reflector overburdens' (cited from the Chapter 11, titled `Instead of Conclusions'). Together with the authors the reviewers believe that `readers will have gained some more intuition or deeper understanding' on the wave propagation and scattering in multilayered random media. The book under review is not equally good in all its parts. It seems to us that the title sounds somewhat wider, than the real content of the book, devoted to only plane-layered random media. Some fragments of the text looks as if it was written in haste, though it may produce some positive effects, since it allows to us peer into creative laboratory of the researchers. On the whole the book will be useful not only for students, but also for professional scientists as a compact guide on quite new areas in elastic wave theory, dealing with fine-layered random media.
Hubral Peter
Shapiro Serge A.
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