SOUND-PROPAGATION OVER A SURFACE WITH VARYING IMPEDANCE - A PARABOLIC EQUATION APPROACH

This paper describes modifications to a finite element solution for the wide angle parabolic equation (PE). The modifications to the PE allow the computationally efficient solution of the problem of sound propagation over ground whose impedance varies with range. In particular, the set of linear algebraic equations that propagate the field outward in range is solved with a UL (upper, lower triangular) decomposition, instead of the standard LU (lower, upper triangular) scheme. This approach allows the change in impedance to affect only a single element in the decomposition. Consequently, all previous calculations in the decomposition can be saved in proceeding from one range step to the next. Results are presented for several cases, in which the ground suffers an abrupt change in acoustic impedance at some distance along the propagation path. Comparisons to existing experimental data are made and the method presented here matches the published data quite well. Other diffraction cases are presented for which no experimental data are available, however the results are fairly self-consistent and serve to indicate the versatility of this method. The approach described in this paper represents an accurate and efficient method for solving problems involving sound propagation over ground having a range-dependent surface impedance.