Three-dimensional inversion of DCR data incorporating structural similarity constraint

Abstract

The three-dimensional inversion of direct current resistivity data is an ill-posed problem, which should to be regularized to obtain a physically meaningful parameter distribution. This is usually realized by introducing additional stabilizing model objective functionals to the optimization problem or constraining the model parameters. The constraints may be defined relative to a reference model which prevents the divergence of parameters from the given reference model. A half-space of homogeneous resistivity, results of a previous survey (i.e. time lapse) or simply a vector of zeros may be assigned as the reference model. The reference model must be defined in accordance with the physical parameter, subject to the study (resistivity in our case). However, high-resolution geophysical images of subsurface, provided by a different method (e.g. ground penetrating radar) could also be used to define a reference model using appropriate tools. In this study, a method is proposed to carry out a three-dimensional constrained inversion of direct current resistivity data using a reference model derived from ground penetrating radar method. We have converted depth slices of radar data volume and the three-dimensional resistivity model into grayscale images to make them comparable on a common basis. An image quality assessment tool, namely the structural similarity index is used to evaluate the similarity/difference of the calculated model parameters with respect to the radar slices belonging to same depth. The method is tested on two different data sets acquired during archaeogeophysical investigations. The constrained inversion of direct current resistivity data revealed the buried anthropogenic structures more clearly, which verifies the use of the proposed methodology.