Computation of the dynamic green's tensor of a stochastically inhomogeneous elastic medium: PMM vol. 43, no. 5, 1979, pp. 916–922

Abstract

The problem of finding mean Green's tensor of the microinhomogeneous elastic unbounded medium is considered. In the case of a statistically isotropic homogeneous medium the problem reduces to that of finding the eigenvalues of the elastic and polarization operators and of calculating the inverse Fourier transforms. The method of changing the field variables was used to sum all one-point and two-point sequences in the expansion for the elastic operator and its eigenvalues. A general expression for the mean Green's tensor is obtained for a particular correlation function. The problems of obtaining an approximate expression for this tensor in terms of the first roots and of finding the asymptotic formulas in terms of the wavelengths (frequencies) are discussed. Methods of obtaining the Green's function for the inhomogeneous and randomly-inhomogeneous media were discussed in [1– 5]. Use of the methods of the Green's function in stochastic systems is the subject of [6– 8].