SCATTERING BY CRACKS BENEATH FLUID–SOLID INTERFACES

Abstract

The scattering of incident plane elastic, or fluid, body waves and interfacial waves by an arbitrarily orientated subsurface crack is considered. The crack lies in an infinite elastic half-space that is coupled to an overlying fluid half-space. Material parameters relevant for water–metal and water–rock combinations are taken and far field scattering patterns are given; these demonstrate beam formation along critical angles. For light, or moderate, fluid coupling, it is shown that the beams form along different critical angles depending upon the magnitude of the coupling. In addition, reciprocity relations relating the far field scattering coefficients viewed along an angle θ, and generated by one type of plane wave incident along φ, to the scattering coefficient viewed along φ, generated by another plane wave incident along θ, are found. Reciprocity relations involving interfacial waves are also given. Power flow theorems are derived; these relate the time averaged scattered power to a combination of far field scattering coefficients. This is used to determine the proportion of scattered power converted into the different types of scattered wave. The reciprocity and power flow theorems provide a powerful consistency check upon the numerical accuracy of the results. The boundary value problem is recast as a system of coupled integro-differential equations for the unknown jump in displacement across the crack faces. These integral equations are solved in an efficient and fast numerical manner by performing the integrations over the crack faces analytically, thus reducing the computational effort substantially.