Excitation of Rayleigh and Stoneley surface acoustic waves by distributed seismic sources

Abstract

Using the integral Fourier-transform technique, we obtain a solution in integral form to the problem of excitation of elastic waves in a homogeneous isotropic solid half-space and the bordering homogeneous gas by the time-dependent forces which are arbitrarily distributed in a solid over the plane parallel to the interface of the media. Different configurations of the force sources are analyzed from the viewpoint of excitation of different types of seismoacoustic waves. Expressions for the time-averaged radiated powers of the Stoneley wave at the gas–solid interface and the Rayleigh wave at the solid–vacuum interface as well as analytical expressions for the Rayleigh wave displacements, which are valid for large distances from the source, are obtained for the harmonic dependence of forces on time. Excitation of a Rayleigh wave by the point sources oriented vertically, i.e., along the normal to the surface of elastic half-space, and horizontally, i.e., parallel to this surface, is analyzed in detail. Analytical expressions for the Rayleigh-wave radiated power are obtained. The dependences of these powers on the source orientation and depth are derived. It is shown that the Rayleigh-wave radiated power decreases with distance between the point of the force application and the boundary and turns to zero for a source depth of about 17.5% of the wavelength of the transverse wave in the case of a horizontally oriented subsurface source and a medium with identical Lame parameters λ and μ. This power increases and reaches a relative maximum when the source depth becomes equal to about 42.4% of the wavelength of the transverse wave and then exponentially falls off as the source depth increases. This maximum is about 5.5% of the surface-source radiated power.