Abstract
Time-domain Helmholtz-Kirchhoff integral (H-K integral) for forward surface scattering is extended to a refractive medium. Ray theory is applied to obtain the Green’s function, while the normal derivative in the integral is evaluated analytically using a ray geometry along with the ray-based Green’s function. This approach allows for stationary phase approximation which reduces the surface integration to a line integration. For high-frequency signals with a narrow bandwidth, an asymptotic form of the time-domain H-K integral then can be derived using the Fourier transform. The pressure field scattered from a sinusoidal surface wave in a constant-gradient sound speed profile is evaluated and compared to the result based on a conventional ray model.
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