Deconvolution With Propagated Geometric Factors

Abstract

ABSTRACT The deconvolution process is basic to the improvement of the thin bed response of induction logging tools. Past approaches to this problem (Smith, Bostick 1964) have focussed on the design of inverse filters based on the Doll Geometric factor (Doll 1949). As is well known, the Doll Geometric factor does not accurately model the response of the induction tool particularly in formations with conductivities greater than 1 mho/meter. Recently (Thadani, Hall 1981), new techniques based on the solution of Maxwell's equations have been developed that permit the computation of propagated geometric factors i.e. geometric factors that fully incorporate propagation effects. These techniques make it possible to accurately compute the vertical investigation characteristic or response function of the induction tool in a large class of cylindrically symmetric formation geometries, including the thin invaded bed formation model. In this paper, it is shown by the application of the above techniques that the response function of the induction tool is a function of both the formation parameters and the relative position of the tool with respect to the formation. In particular, it is shown that the shape of the response function becomes asymmetric with respect to the center of the tool as the conductivity of the formation increases. Synthetic data computed by using the above techniques is used to evaluate the performance of inverse filters based on the Doll Geometric factor for various formation geometries including the thin bed formation model. Currently, various deconvolution filters are being developed using response functions based on propagated geometric factors. The paper will include the results of an evaluation of these filters on various cylindrically symmetric formation geometries.