2-D nonlinear joint inversion of VLF and VLF-R data using simulated annealing

Abstract

Two-dimensional (2-D) individual and joint inversions of very low frequency (VLF) data (the real and imaginary anomalies), and jointly with VLF-R data (the apparent resistivity and phase) using very fast simulated annealing (VFSA) as a tool in global inversion are considered in this paper. Synthetic responses from two different models, which represent typical subsurface structures in the shield areas, were studied. Various models achieved after 10 VFSA runs were used to compute the mean model and the corresponding covariance and correlation matrices which were then used to estimate the uncertainties in the mean model parameters and correlations between the model parameters. An individual inversion of either real or imaginary anomalies cannot yield a model that would fit both observations. However, the joint inversion of the real and imaginary data sets will yield a model, which fits both observations. The models obtained either by the individual or by joint inversion of VLF data do not show good agreement with the VLF-R observations. Generally, the models obtained from VLF inversions show better agreement with the apparent resistivity than with the phase data. Conversely, the joint inversion of the apparent resistivity and phase data yields models which give good agreement with the real and imaginary anomalies. The results obtained after the joint inversion of all the VLF and VLF-R data give good agreement with all the data sets. Individual inversion of any response cannot yield a reliable subsurface structure no matter how well a particular observed response is fitted by the computed responses. Field data from three profiles traversing different geological structures were also inverted to demonstrate the efficacy of the approach for delineating the geometry and properties of 2-D structures. The VLF-R inversions invariably give superior results in comparison with the VLF inversions. However, the most reliable models are obtained from the joint inversion of both VLF and VLF-R data sets.