Approximate inversion of high‐frequency electromagnetic soundings using complex image theory

Abstract

Electromagnetic (EM) soundings in an intermediate range between quasi‐static and radar frequencies (e.g., 30 kHz – 300 MHz) were studied with an approximate inversion method for shallow‐layered earth models using complex image theory. The half‐space image theory formulas for calculating forward soundings for any dipole source are easily extended to accommodate a multilayered earth, and only involve elementary complex functions. Approximate inversion using the modified image formulas is compared with more exact numerical integration inversion for horizontal‐layered models to yield the conductivity, thickness, and dielectric permittivity of each layer. A nonlinear least‐squares algorithm was used to obtain parameter and linear parameter error estimates. The results, using known exact forward models and one field data case, indicate that approximate image inversion is more than an order‐of‐magnitude faster than numerical integration inversion. However, approximate inversion could not always resolve deeper layer parameters as well as with exact inversion. Accuracy of both methods, however, depends on the frequency range used. Nevertheless, approximate inversion can be a useful quick reconnaissance tool, and could easily be written for on‐site personal computers.