Development of a new rapid inversion scheme for Total Field Magnetometric Resistivity (TFMMR) data

Abstract

A large number of geophysical inversion methods have been published, but there are no published efficient technique applied to either of MMR or TFMMR data. One of the important aspect of inverting TFMMR data is its dependence on all three components of the anomalous magnetic field. In the case of inverting TFMMR data using gradient methods, we propose a preprocessing reduction of data to the pole to overcome the problems of the effect of the geomagnetic field direction and dependency of the TFMMR data on all three components. By doing this, we invert the data only using the sensitivity of the vertical anomalous magnetic field. After formulating the expressions for computing the Frechet derivatives for the anomalous vertical component on a homogeneous half space model, the Marquart-Levenberg method (damped least squares method) incorporating the quasi-Newton approximation for updating the Jacobian matrix in successive iterations is employed. As the most time consuming task in inversion process is to calculate the Frechet derivatives, therefore employing such scheme will considerably reduce the computing time and improve the stability of the inversion. An analytical solution for calculating the Frechet derivatives in wavenumber domain for all mesh nodes component for a homogeneous half space model is developed first. Next for recovering 2-D models, every 4 by 3 element in the x and z directions respectively constitute a resistivity block. This block parametrisation allows for recovering the sharp resistivity contrasts which occur in mineral exploration prospecting or shallow surface experiments. Assuming a linear variation of transformed electric potential and its gradient over the boundary of the elements, we may derive the discretised form of derivative equations. The efficiency and accuracy of the proposed scheme is demonstrated using a set of synthetic data from a double vertical dike model.