Impedance formulation and clipping technique in the fast field program

Abstract

The propagation of a sound wave in a layered media excited by a point pressure source can be formulated into a Fourier integral. A powerful method for evaluating this integral is to use the Fast Fourier Transform, resulting in the so‐called “Fast Field Program (FFP)” [F. R. DiNapoli and R. L. Deavenport, J. Acoust. Soc. Am. 67, 92–105 (1980)]. In the existing scattering matrix formulation, the FFP requires the multiplication of matrices containing exponential factors exp (+γh) and exp (−γh), where γ is the attenuation constant along the vertical direction of a layer, and h is the layer's thickness. These factors often exceed the computer's capability in handling large/small numbers, thus resulting in erroneous FFP solutions. In the present paper, we describe a new formulation of the FFP that is inherently numerically stable and is completely free from the difficulty mentioned above. The central step in our formulation is to calculate the equivalent impedance for each layer in succession starting from the top/bottom layers toward the source. This technique results in terms containing (γh) rather than (−γh), which goes to unity smoothly as γh → ∞. In addition, we introduce a “clipping technique.” For a given horizontal wavenumber, it removes layers that are not physically significant by terminating the preceding layer at its characteristic impedance.