### Scattering by cracks beneath fluid-solid interfaces

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 theta, and generated
by one type of plane wave incident along phi, to the
scattering coefficient viewed along phi, generated by another
plane wave incident along theta, 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.

#### Journal of Sound and Vibration, 209, 343-372, 1998

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