Inversion of the geophysical inverse problem for n layers with nonuniqueness reduced to n cases

Abstract

A new method is described for reducing nonuniqueness in the geophysical inverse problem for n layers to n cases, provided the ratio of characteristic impedances of sequential layers is of the order of unity and upper and lower layer boundary conditions are known. The method is based on impedance concepts which allow application to a number of different electromagnetic or acoustic experimental methods. Using transformations, the method reduces the nonlinear problem to a linear one as an eigenvalue formulation without approximation. This preserves the nonlinear nature of the problem and increases the significance of the results. Experimental results are given for several electromagnetic applications where the complex permittivity ε = ε′ − iε″ is determined for shallow (35 m) stratified geosections. The frequency range is dictated by multiples of the electrical or acoustic “quarter‐wave” thickness of the layers and, in the particular electromagnetic (EM) studies made, it has been 1 to 8 MHz. Application to ocean bottom sub‐layering is also proposed, arising from the feasibility of experiments under a conductive lake to which mathematical equivalence is shown.