Transient electromagnetic inversion based on an approximate solution to the forward problem

Abstract

A rapid algorithm for forward one‐dimensional modeling is based on the graphical construction of a multi‐layered apparent resistivity curve using an appropriate combination of two‐layered curves. A collection of two‐layered curves is calculated only once for fixed geoelectrical parameters and saved for future use; an arbitrary two‐layered curve within the wide range of the geoelectrical parameters is then obtained by simple interpolation. This method reduces computation time over other fast algorithms by at least one order of magnitude; in addition, it does not produce any significant computation errors in the late stage as do most other methods. A maximum relative error of about 10 to 15 percent may occur at a few points (usually two to three) in the vicinity of the intersection of the two‐layered curves. In most cases, however, this error does not affect the inversion since the relative contributions of these points to an objective function are small. The application of such a rapid forward algorithm allows one to attack the equivalence problem. For this purpose, several starting search points are randomly distributed within a feasible range in the parameter space. The inversion is then begun with the initial guesses for the parameters; several if not all of the minima of the objective function are found within the specified parameter range. To reduce ambiguity of the interpretation, all reasonable solutions are then correlated with available a priori geologic and/or geophysical information. Application of the above technique to real data shows the ability of the algorithm to detect equivalence and, thus, render the interpretation more objective. Both forward and inverse programs have been installed on a portable desktop computer (an IBM-PC compatible). The programs are easy to use and allow interpretation to be carried out in the field.