1063-7710/05/51S1-S $26.00 © 2005 Pleiades Publishing, Inc. 0115 Acoustical Physics, Vol. 51, Suppl. 1, 2005, pp. S115–S121. Translated from Akusticheskiœ Zhurnal, Vol. 51, Suppl., 2005, pp. 132–139. Original Russian Text Copyright © 2005 by Markov. English Translation Copyright © 2005 by Pleiades Publishing, Inc. INTRODUCTION Many rocks contain mobile fluids in their pores. The propagation of elastic waves in such media has a num- ber of distinctive features, as compared to a single- phase elastic medium. A correct description of these features is possible in the framework of the Frenkel– Biot theory [1–5]. According to the latter, two longitu- dinal waves propagate in a fluid-saturated porous medium. The longitudinal wave of the first kind in the geoacoustic frequency range is associated with in- phase oscillations of the solid skeleton and the fluid in the pores. The longitudinal wave of the second kind corresponds to antiphase particle displacements of the solid and fluid phases, and, hence, this wave is charac- terized by strong attenuation. As a rule, only longitudi- nal waves of the first kind are recorded in geoacoustic measurements. However, in an inhomogeneous medium, the generation of the rapidly attenuating lon- gitudinal waves of the second kind at the boundaries of inclusions leads to an additional energy dissipation and to changes in the amplitudes of the observed waves. The propagation of elastic waves in a fluid-saturated porous medium containing a crack in the form of a plane-parallel liquid layer was studied in [6]. The crack model in the form of a Biot medium with a very high porosity was considered in [7, 8]. In [6, 7], it was shown that the attenuation of elastic waves may be caused by filtering flows of the fluid near the boundaries of inclu- sions. The effective wave numbers of elastic waves propagating in a periodically layered fluid-saturated porous medium were calculated in [9–12]. The propa- gation of longitudinal waves in a medium containing spherical inclusions that differ in the properties of the fluid was first considered by White [13]. The results obtained by White were refined in [14], where the effective compressibility was determined for a water- saturated medium containing spherical gaseous inclu- sions whose size was much greater than the character- istic size of the pores. A complete solution to the prob- lem of elastic wave scattering by a fluid-filled cavity in a fluid-saturated porous medium was obtained in [15, 16], and the solution for the case of porous inclu- sions with contrasting elastic properties, in [17, 18]. B. Ya. Gurevich and his coauthors considered the propagation of elastic waves in fluid-saturated porous media with weak-contrast spherical [19] and spheroi- dal [20] inclusions. In [15], the multiple scattering theory version proposed by I. A. Chaban [21] was used to calculate the effective wave number of a lon- gitudinal wave of the first kind propagating in a medium with pores and cavities. This paper presents the calculation of the effective wave number of a longitudinal wave of the first kind propagating in a fluid-saturated porous medium with spherical inclusions on the basis of the equations of the multiple scattering theory [22]. The characteristic size of inclusions is assumed to be much greater than the size of pores. The inclusions differ from the matrix in elastic and hydrodynamic properties. The second sec- tion of the paper briefly describes the solution of the Propagation of Longitudinal Elastic Waves in a Fluid-Saturated Porous Medium with Spherical Inclusions M. G. Markov Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, CP 07730, México, DF e-mail: mmarkov@imp.mx Received April 23, 2004 Abstract—The Frenkel–Biot theory is used to study the propagation of a longitudinal harmonic wave of the first kind in an isotropic porous matrix with inclusions contrasting in elastic properties and hydrodynamic per- meability. The generation of elastic waves of the second kind at the boundaries of inclusions is taken into account. The effective wave number of the longitudinal wave is calculated using the equations of the multiple scattering theory. The characteristic size of inhomogeneities is assumed to be much greater than the size of pores. The parameters of the model used for calculations correspond to sandstone with centimeter-scale inho- mogeneities. The presence of such inhomogeneities is typical of sedimentary rocks. Calculations show that, in the frequency range of acoustic logging, the effective attenuation factor of the longitudinal wave may noticeably exceed the attenuation factors of longitudinal waves of the first kind in both matrix and inclusions. From the results obtained, it follows that, when studying the propagation of elastic waves in fluid-saturated porous media, it is necessary to take into account the hydrodynamic effects associated with the filtering flows that arise at the boundaries of inhomogeneities. © 2005 Pleiades Publishing, Inc.