Evanescent Effects in Acoustical Wave Propagation*

Abstract

KUHN, M.J. 1987, Evanescent Effects in Acoustical Wave Propagation, Geophysical Prospecting 35, 167-186.The propagation of transient acoustic pressure waves in a layer enclosed between two, not necessarily identical, half-spaces is considered. The source and the receivers are always located in the same half-space and at the same depth. The source excitation function is a narrow causal spike. Several thicknesses of the layer are examined including the case in which the embedded layer vanishes.The phenomena of 'constricted' head waves and wide-angle reflections in the layer are examined in detail using a 'numerical experimentation ' approach. First, a closed-form solution is numerically evaluated. Then this solution is developed in series and each term is evaluated separately using the same numerical techniques. When the contribution of an individual high-order term becomes unimportant, all higher order terms are discarded, and the response is constructed by superposition of the previously computed low-order terms only.Propagation by wide-angle reflections from inside the layer is of interest. When the thickness of the layer is reduced to a fraction of the wavelength, these events consist typically of a low amplitude, high frequency, geometrical acoustics arrival, followed by higher amplitude, low frequency, non-geometrical coda. When all important low-order terms are added, the non-geometrical events tend to interfere destructively, leaving a waveform nearly identical to that obtained by integration of the closed-form solution.When the thickness of the embedded layer is measured in fractions of the dominant wavelength, none of the individual terms of the series development can be duplicated by asymptotic ray tracing. However, because the codas of the various terms interfere destructively, the total response may be well-represented by the addition of a few low-order rays, using asymptotic approximation. This discovery extends the usefulness of Huygens-Kirchhoff ray tracing to modeling of wave propagation in thin layers.

Critical Behavior of the Randomly Spin Diluted 2D Ising Model: A Grand Ensemble Approach

“…Let us mention in closing that it is easily adapted to the study of correlated disorder. Preliminary results for a 1-d system, where comparison with an exact solution is possible [29] do look encouraging. We are currently also using our method to study the wetting transition in the presence of surface disorder, which has recently been a subject of some controversy in the literature.…”