Wave scattering from a ground with a Gaussian bump or trough in an inhomogeneous medium

A closed-form solution of the Helmholtz equation is obtained for the case of a time-harmonic line source embedded in a medium with the linear sound-speed profile. Substituting the closed-form expression of the Green’s function into the Helmholtz-Kirchhoff integral equation, the exact solution of the scattered fields from a ground with a Gaussian shaped bump or trough in such a medium is obtained. An extension of the method of moments, which can solve the Helmholtz-Kirchhoff integral equation for sound scattering in the inhomogeneous medium, has been developed. Using these new tools, the effects of scattering in the region beyond a bump or trough are studied for situations when the background medium is upward refracting. Numerical results show that a soft ground with a bump or a hard ground with a trough in the upward refracting medium may cause some enhanced field regions beyond the bump or trough. The phenomenon is not observed when the background medium is homogeneous. Numerical results also show that a hard ground with a bump or a soft ground with a trough in the inhomogeneous medium may not cause any major difference when compared with results from the case using the homogeneous medium as the background medium.