Multidimensional Filtering of Acoustic Records in Seismic Signal Processing

Abstract

In the paper the problem of acoustic wave propagation within a homogeneous medium is considered. Examples of application are referred in the field of acoustics and in seismic signal processing. The wave migration in the frequency domain corresponds to linear all pass phase filtering and phase specifications are derived for the ideal two-dimensional case. The resulting hyperbolic impulse response is symmetrical with respect to the time axis and two-dimensional half-plane recursive filters are proposed to solve the wave equation backwards in the time variable. Numerical examples are referred to analyse the practical constraints of the proposed processing system which is compared against parabolic approximations of the two-dimensional wave equation. In most application a general three-dimensional model of spherical waves is much more suitable. The proposed solution in the 3-D case is still based on recursive filtering so that it can be profitably used also for large amounts of data. The linear processing method described here is limited to homogeneous media so that it does not represent the best solution for the wave migration in geophysical prospecting, even if it has been proved an efficient method for preliminar estimation. On the other hand it seems particularly useful for some other acoustics problems such as impulse analysis of loudspeakers.