Three-dimensional resistivity inversion using alpha centers

Abstract The method of alpha centers represents a class of solutions to the three-dimensional (3-D) dc conduction equation based on certain nonlinear substitutions for electric potential and earth conductivity. A solution is obtained which is sufficiently fast to make the inversion of 3-D resistivity data practical. The inversion routine results in a conductivity distribution defined by alpha centers which simultaneously fits the data from several parallel or perpendicular dipole-dipole profiles.To illustrate the characteristics of this modeling approach, we apply the inversion algorithm to three theoretical and four field data sets. The four field data sets represent samples from massive sulfide and geothermal environments. The technique, when applied to theoretical data from prismatic bodies, gives fairly good estimates of the positions of conductive inhomogeneities but poor estimates of their actual conductivities.The entire inversion algorithm requires less than 15,000 words of computer memory, thus making it tractable for small computers. We envision two major applications. The first is for in-field data interpretation to site drilling locations or to guide further exploration. The second is for obtaining a good initial guess for more sophisticated and costly multidimensional inversion schemes.