Premium
MODELLING 1D WAVE PROPAGATION IN A SYSTEM OF ABSORBING LAYERS 1
Author(s) -
McGEE T. M.
Publication year - 1991
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1991.tb00299.x
Subject(s) - reflection (computer programming) , recursion (computer science) , filter (signal processing) , absorption (acoustics) , domain (mathematical analysis) , notation , algorithm , frequency domain , time domain , computer science , optics , geology , transmission (telecommunications) , mineralogy , acoustics , mathematical analysis , mathematics , physics , telecommunications , arithmetic , programming language , computer vision
A bstract The purpose of this paper is to derive relationships useful for the analysis of shallow transmission and reflection seismic data. Since the effects of absorption cause such data to be non‐stationary, the derived results do not rely on frequency‐domain representations being independent of the time origin. Rather, results are expressed in the z ‐domain and are suitable for implementation in the time domain. In order to give an unambiguous system of notation a classic approach to the problem of 1D wave propagation in a layered system is fully described. Absorption is included in a general but realistic way and the implications of representing it digitally are considered in detail. Computational efficiency is improved by grouping the layers in blocks of similar absorptive effect. The transmissivity and reflectivity of systems composed of such blocks are obtained and a dereverberation filter identified. The filter is described succinctly in terms of a non‐linear recursion relationship. The sequences obtained by convolving the filter with the transmissivity and reflectivity are discussed in detail. The results are illustrated by nominally realistic synthetic examples computed in the time domain.