ANALYSIS OF TIME-DOMAIN ACOUSTIC WAVEFIELDS IN HORIZONTALLY CONTINUOUSLY LAYERED CONFIGURATIONS BASED ON THE MODIFIED CAGNIARD METHOD

A combination of the Neumann series and the modified Cagniard method is used to derive a theoretically exact space-time domain solution for the 3-D acoustic wave propagation problem in horizontally continuously layered media. Firstly, integral transformations (among which is a one-sided temporal Laplace transformation) are applied to the space-time domain basic acoustic equations. Secondly, a system of transform domain integral equations is derived, which is solved using a convergent Neumann series. Finally, the individual terms of this series are transformed back to the space-time .domain using the modified Cagniard method. The space-time domain series turns out to be convergent for every continuously layered configuration and at any time instant. In contrast to the standard angular wave number-frequency domain analysis, in the present analysis, difficulties due to turning points, etc., are avoided.