Space-angular distribution of seismoacoustic waves excited by a vibration source in a semibounded gas-saturated porous medium

Abstract

Specifying the formulation of the problem, let us note that as a fluid that fills the pores we consider air whose density is known to be several orders lower than that of the frame material, but whose acoustic velocity is higher than the velocity of compression wave propagation in the frame. Therefore, we speak of soil whose granules contact each other at several points, and in view of the reduced rigidity in the contact region compared with the rigidity of the forming continuous material, the effective compressibility of such a medium becomes rather significant and the velocity of longitudinal waves can drop below an acoustic velocity in air, which is confirmed experimentally for geologic materials deposited at depths from 1 to 1.Sin or higher [6]. Below we consider a gas-saturated two-phase medium that fills the lower halfspace the plane free boundary of which is subjected to the vertically oriented oscillating force P exp(-/~t), which is uniformly distributed across a circular platform with radius a. In this case, using the known methods, we calculate the radiation field of all types of elastic waves, in particular, P waves of the first and second kinds and S waves. For the case of a P wave of the first kind, it is easier to calculate the amplitude and phase dependences of radiated fields for the Fra~mhofer region, using the known asymptotic methods. In essence, the fmding of the field structure is reduced to estimating the integral expressions used to describe the field in the sector of angles that are adjacent to the direction of the main ray plotted according to the rules of geometric optics to connect the source and the observation point. In view of the wide use of the above methods (we speak of the method of the standard integral and the method of the stationary phase), including integral calculation on their basis, we mention [5, 7], in which they are described in detail. Calculating as in [5, 7] and using