Straightforward inversion of vertical electrical sounding data

Abstract

A straightforward inversion scheme (SIS) has been developed to interpret vertical electrical sounding data. This scheme does not require quasi-linearization of the inverse resistivity problem and thereby dispenses with the iterative process and the necessity of guessing the number of layers and their resistivities and thicknesses. The entire solution domain is divided into uniform thickness layers, whose scale must be judiciously selected for the desired resolution. The apparent resistivity formula can now be posed as an underdetermined matrix equation whose minimum norm solution is downward continued to obtain the reflection coefficients which, in turn, yield the vertical resistivity distribution. A recurrence relation has been developed especially for this purpose. In general, when data are expected to be noisy, a regressed minimum norm solution is used. Exhaustive tests of the algorithm have established its numerical efficiency. Results of six typical synthetic models, representing diverse geological conditions, as well as results of two field examples are included to demonstrate this claim.