Magnetization clustering inversion — Part 1: Building an automated numerical optimization algorithm

Abstract

Magnetic data are among the most widely used geoscientific data for studying the earth interior in the oil and mining industries. However, interpreting magnetic data has been traditionally challenged by the presence of remanence. Recently, a new inversion algorithm, called magnetization clustering inversion (MCI), was developed by combining the classical Tikhonov regularized inversion with fuzzy [Formula: see text]-means clustering, an unsupervised machine-learning algorithm. This method has proven to be an effective tool for interpreting magnetic data complicated by remanence through synthetic and field data tests. However, the MCI algorithm in previous work requires users to specify the values of the weighting parameters for both smoothness regularization and clustering terms in the objective function. In practice, this entails many iterations of trial and error, and it consequently hinders the effective use of this inversion algorithm for iterative hypothesis testing and timely decision making. We have developed an automated strategy for determining the two weighting parameter values. Our algorithm of automatic search for optimal weighting parameters is based on an understanding of their roles and the complex interplay between them during an inversion. Our search algorithm works by alternately searching for one weighting parameter, whereas the other is fixed. A series of synthetic examples confirms the effectiveness of this automated optimization strategy. We also applied the automated inversion algorithm to a field data set from the Carajás Mineral Province in Brazil. The recovered magnetic anomalous features are highly consistent with known geology.