Asymptotic Ray Theory for Seismic Surface Waves in Laterally Inhomogeneous Media

Abstract

A recurrence procedure is outlined for constructing asymptotic series for surface wave field in a half-space with weak lateral heterogeneity. Both horizontal variations of the elastic parameters and of the wave field are assumed small on the distances comparable with the wavelength. This is equivalent to the condition that the frequency ω is large. The Surface Wave Asymptotic Ray Theory (SWART) is an analog of the asymptotic ray theory (ART) for body waves. However the case of surface waves presents additional difficulty: the rate of amplitude variation is different in vertical and horizontal directions. In vertical direction it is proportional to the large parameter ω. To overcome this difficulty the transformation ‘equalizing’ vertical and horizontal coordinated is suggested, Z = ωz. In the coordinates x,y,Z the wave field is represented as an asymptotic series in inverse powers of ω. The amplitudes of successive terms of the series are determined from a recurrent system of equations. Attention is paid to similarity and difference of the procedures for constructing the ray series in SWART and ART. Applications of SWART to interpretation of seismological observations are discussed.