A Computer Code for Aerial Magnetic Soundings of Layered Media

Abstract

An iterative algorithm is described to solve the inverse problem of stratified media using magnetic field data collected in aerial surveys. An airborne antenna sends downwards magnetic fields at several frequencies, and an airborne antenna detects the secondary magnetic fields. The input data for the inversion algorithm are the complex ratios between the secondary and primary magnetic fields at different frequencies. The algorithm selects one value for each unknown in ranges where the solution is likely to lie. Complex residuals between experimental and estimated data are computed. A cost function is defined as the summation of the absolute values of the real parts of the residuals added to the summation of the absolute values of the imaginary parts of the residuals. A value of the cost function is computed for the selected set of values of the unknowns. All such procedures are repeated for other sets of values of the unknowns. Such sets span the ranges of values where the solution is deemed to lie. The solution in the first iteration is the set of values of the unknowns that relates to the minimum computed value of the cost function. In each subsequent iteration, a minimization of the cost function is performed around the solution estimated in the immediately preceding iteration. The final solution relates to the minimum value of the cost function over all the iterations. The inverse problem is solved without recourse to either analytical or numerical computation of derivatives. This provides stability and simplicity to the algorithm. The MATLAB code of the algorithm is set forth. The code is assessed using field data from two aerial magnetic surveys.