Slow wave diffraction at a borehole

It is known that in a cracked layer consisting of alternating fluid and elastic layers and located inside an elastic medium an interference slow wave propagates. It was shown that a number of phenomena observed on crosshole sounding of the media with oil-collectors can be explained by the initiation of a slow wave. Interest in slow waves is related to different geophysical applications (volcanic activity, wave propagation in oil-bearing rocks and so on). A slow wave is a surface wave, the amplitude of which decreases exponentially in both directions away from the layer. The energy of the propagating wave is partially trapped by the elastic medium and, for sufficiently low frequencies, this part of the energy can be significant. A wave of the same nature arises in a fluid layer sandwiched between two elastic halfspaces. At its incidence on a borehole intersecting the cracked or fluid layer, the slow wave excites intricate interference oscillations in the borehole which are related to the response of the elastic medium with a fluid-filled borehole to the incident pertubation. We solve this problem in the low frequency approximation for λ≫a, where λ is a wavelength, and a is the radius of the borehole. Earlier the problem of the excitation of a tube wave in a fluid-filled borehole by the Rayleigh wave propagating along the free surface of an elastic half-space was considered. The problem of slow wave diffraction at a borehole is more complicated because of the dispersion of the phase velocity of the slow wave. In this case we are unable to provide the solution in the time domain in an explicit form and the inverse Fourier transform must be applied