Application of the modified image method to inversion of synthetic active electromagnetic bathymetric data

Abstract

A modified image method is used to invert synthetic active electromagnetic data generated from shallow ocean models by means of the exact Sommerfeld theory. The modified image method offers approximate solutions to the Sommerfeld problem: the response of a layered structure of ohmic conductors to an active electromagnetic source. The image plane for the active electromagnetic source is assumed to be at a complex depth given by [Formula: see text], where [Formula: see text] is the skin depth of the first layer and [Formula: see text] is the multilayer correction factor. Two ad hoc correction factors have been introduced into the modified image method. They bring the image field [Formula: see text] of the single image at a complex depth into very good agreement with the secondary field [Formula: see text] of the exact Sommerfeld theory of a two‐layer bathymetric model. We demonstrate that these correction factors can be calculated from synthetic data. This allows for an accurate, algebraic, and fast inversion of active electromagnetic data in terms of the parameters of a two‐layer model: the conductivities of the sea and sea bottom, and the depth and ohmic skin depth of the sea. The β factor, which takes into account the departure of the primary active electromagnetic field from a plane wave form at the air‐sea interface, is incorporated into the complex two‐layer correction function [Formula: see text]. A rescaling factor F brings [Formula: see text] into good agreement with [Formula: see text] in the depth regime where the β correction factor is ineffective, i.e., where the first layer depth is greater than two skin depths.