Linearized Bayesian estimation of magnetization and depth to magnetic bottom from satellite data

Abstract

SUMMARY Estimating the depth to magnetic bottom (DTB) from magnetic data is one of the most important and difficult potential field inversion problems. Since DTB can often be linked to the Curie isotherm depth of magnetite (∼580 °C), it could provide crucial constraints on heat flow, even in remote or inaccessible areas. Spectral methods are the most popular approach to estimate DTB, but their reliability has been challenged on many grounds. In contrast, space-domain methods have received relatively little attention, even though they might avoid some of the limitations of spectral methods. Furthermore, many DTB estimation methods are to some extent ad hoc, which makes uncertainty estimation and effective communication of the results difficult. In this work, we develop a Bayesian approach to estimate susceptibility and DTB from magnetic data. We describe the subsurface in terms of tesseroids and use a two-step inversion procedure that consists of a Monte Carlo Markov Chain hyperparameter optimization and a linearized inversion. This way, the uncertainties due to unknown hyperparameter are rigorously propagated to the final maps of susceptibility and DTB. Additionally, pointwise constraints based on heat flow measurements can be easily included into the inversion. Synthetic tests are used to determine the accuracy and reliability of the new algorithm. We find that heat flow constraints are necessary to achieve reliable results, although already a small number of points is sufficient. Finally, we apply the algorithm to the Australian continent and demonstrate applicability to real data.