A fast 3-D inversion for airborne EM data using pre-conditioned stochastic gradient descent

Abstract

SUMMARY Airborne electromagnetic (AEM) exploration produces large amounts of data due to its high sampling rate, so that the 3-D inversions take extremely big computation and time consumption. We present a fast 3-D inversion framework for large-scale AEM explorations using a pre-conditioned stochastic gradient descent combined with Gauss–Newton (PSG-GN) method. We adopt a compressed sensing (CS) in the 3-D forward modelling, in which a random undersampling is used to reduce the calculation, while the responses for all survey stations are obtained via a reconstruction technique. For our 3-D AEM inversions, a method of combining the stochastic gradient descent with Gauss–Newton (SG-GN) that requires only a small data set in each iteration instead of the conventional full-batch data (complete original data) inversion have been investigated. To further speed up the 3-D inversion, we develop a pre-conditioner considering the random sampling rate and gradient noise to achieve a fast convergence. We use two synthetic models to test the accuracy, convergence and efficiency of our algorithm. The results show that the conventional inversion with full-batch data and the PSG-GN method can both converge quickly, but our method can enhance the inversion efficiency up to 78 per cent. Finally, we invert a field data set acquired from a massive sulfide deposit in Ireland and obtain the results that agree well with the known geologies.