Efficient calculation of scattering into an acoustic shadow zone using empirical orthogonal functions and the Markov approximation

Abstract

In many previous studies, the mean sound level of a signal scattered by turbulence into an atmospheric refractive shadow zone has been calculated using a Monte Carlo procedure. This procedure involves generating many (typically 10 to 100) random realizations of the turbulent field, using a parabolic equation (PE) code to solve for the sound field corresponding to each realization, and then averaging. Unfortunately, this method is computationally intensive because of the large number of PE runs required. In this paper, a different approach, based on combining a distorted-wave Born approximation, a ‘‘quasi’’-Markov approximation, and decomposition of the turbulence into empirical orthogonal functions, is described. Here ‘‘quasi’’ refers to the fact that the Markov approximation is applied only in the nominal (horizontal) direction of propagation, since the exact direction of propagation is variable. Initial results are promising in that the mean scattered field can be calculated in a small fraction of the time required for a single PE run. However, the new approach underpredicts the Monte Carlo result by 5 to 10 dB. Possible sources of the discrepancy include the Markov approximation, multiple scattering, and inexact treatment of boundary effects.