ISSN 1069-3513, Izvestiya, Physics of the Solid Earth, 2011, Vol. 47, No. 4, pp. 354–369. © Pleiades Publishing, Ltd., 2011. Original Russian Text © A.V. Gorbatikov, A.A. Tsukanov, 2011, published in Fizika Zemli, 2011, No. 4, pp. 96–112. 354 INTRODUCTION The surface seismic waves carry a major part of the energy of the seismic event on one hand, and attenuate much less than the body waves on the other hand. That is why surface–wave seismology represents a very important part of the seismological practice. A consid- erable part of recent research concerning surface waves was devoted to the study of the natural microseismic field of the Earth since the surface waves predominantly contribute to this field. In this regard, the study of the interaction between the surface Ray- leigh waves and the velocity inclusions is becoming increasingly important. Thus, considerable progress was achieved in surface wave tomography, a method based on the estimation of Green’s function of a medium from the cross-correlation function. The approach goes back to the works on the quantum field theory. One can find the review of corresponding stud- ies in [Peskin, 2001]. The achievements of these works were later used in the fields of hydroacoustics, ultra- sonic research, and seismology [Munk, 1995; Weaver and Lobkis, 2001; Snieder, 2004]. For example, hav- ing measured the cross-correlation functions between different points for the microseismic background field consisting mainly of Rayleigh surface waves, one can reconstruct the morphology of the lateral velocity het- erogeneities of the Earth’s crust [Shapiro and Camp- illo, 2004; Shapiro et al., 2005; Koroleva et al., 2009]. The sphere of practical problems dealing with the question of the interaction of surface waves with the heterogeneities is very broad. It ranges from the assess- ment of ground-shaking effects caused by strong earthquakes to the use of surface waves for the pur- poses of structural problems. The necessity for the solution of this problem is also associated with the argumentation and development of many rigorous and phenomenological methods dealing with general and applied geophysical studies. In this context, the wide practice of the application of the Nakamura method [1989] and similar techniques is worth noting. Historically, most methods of surface wave tomog- raphy make use of the phase information contained in seismograms. Attempts to take advantage of the amplitude information are very rare. Nevertheless, the involvement of the amplitude data has a substantial potential for the development of these techniques. When we consider the Rayleigh waves’ scattering by the velocity heterogeneities, the concept of the velocity itself loses its meaning in the immediate neighborhood of the scatterers, since the generated (reflected, refracted, converted) waves are not yet spa- tially separated according to their types here and the concept of the velocity of a wave of an “averaged” type Simulation of the Rayleigh Waves in the Proximity of the Scattering Velocity Heterogeneities. Exploring the Capabilities of the Microseismic Sounding Method A. V. Gorbatikov a and A. A. Tsukanov b, c a Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Bol’shaya Gruzinskaya ul. 10, Moscow, 123996 Russia b Faculty of Physics, Moscow State University, Moscow, 119991 Russia c OAO Zarubezhneft’, Moscow, Russia Received May 24, 2010; in final form, October 11, 2010 Abstract—The interaction between the fundamental mode surface Rayleigh waves and the buried heteroge- neities with various sizes and different velocity contrasts was studied on base numerical simulation. The field of surface oscillations in the proximity of the scattering heterogeneities was computed as a function of fre- quency. The synthetic seismograms were used for numerical simulation of the microseismic sounding tech- nology proposed earlier, implying that the solution of the inverse problem for the structure of the medium containing inclusions can be derived from the information contained in the ambient microseismic field. It is assumed that the depth of the layer to be reconstructed is linked with the frequency of the microseisms by a simple relation with the help of a numerical coefficient equal to 0.4–0.5. The combined results of the simu- lation of a direct problem together with the simple inverse problem solution show that the microseismic sounding technique ensures adequate estimation of the medium structure. Previously, the technology was based on the experimental data only and was phenomenological in character. Some relations between the velocity parameters of the original model heterogeneities and their reconstructed images were also studied. DOI: 10.1134/S1069351311030013