Computation of Analytical Derivatives for Airborne TEM Inversion Using a Cole–Cole Parameterization Based on the Current Waveform of the Transmitter

Abstract

Airborne transient electromagnetic (ATEM) technology is a technique often used in mineral exploration and geological mapping. Due to inductive polarization (IP) phenomena, the ATEM response curve often shows a negative response or declines rapidly to the attenuation curve. Traditional resistivity inversion techniques do not explain the IP response of a signal well, so the negative response is usually removed during data processing, resulting in a reduced correctness and authenticity of the findings. In this paper, in the parameter inversion based on the Cole–Cole model, the Jacobian matrix chain analysis method is used to calculate, and the current waveform calculation is also considered in the inversion. The results show that compared with the perturbation method, the analysis technique can greatly reduce the calculation time and improve the inversion efficiency. In the single-point one-dimensional inversion and lateral constraint quasi-two-dimensional inversion, the Cole–Cole four-parameter forward response has strong inversion accuracy, which can successfully invert the actual exploration content and the Cole–Cole four-parameter response. Some measured sounding data in the Qingchengzi survey area of Liaoning Province, China have a negative response to IP, and the resistivity scheme cannot be used alone for inversion, but the real underground resistivity structure can be obtained through the method studied in this paper, and good exploration results can be obtained.

Parallel Inversion of 3D Airborne Transient Electromagnetic Data Using an Approximate Jacobi Matrix

“…When calculating the Jacobian matrix, we use the adjoint forward method to obtain the derivative of the induced electromotive force with respect to resistivity; however, in the IP parameter inversion, we require the Jacobian matrix of the induced electromotive force with respect to multiple IP parameters. As a result, using the Cole-Cole model expression and the derivative chain solution rule, we develop the partial derivative expression appropriate for IP parameter inversion [36]:…”