Development of Study of Inversion Analyses Using ABIC in Seismology

Abstract

Inversion analyses play a central role in solid earth sciences, since observable quantities are very limited for the earth’s interior. Classical least squares method does not work well in these fields, since observed data are commonly inaccurate and/or insufficient. Least squares methods with additional conditions, such as damping or smoothing, have been widely used, but the weight of damping or smoothing have to be manually adjusted, if we do not take in a probabilistic point of view. In 1980, H. Akaike proposed a Bayesian Information Criterion (ABIC), where smoothness constraint is regarded as prior information that is combined with information from observed data by Bayes’ rule, and then the optimal weight between the information from observed data and prior constraint is objectively determined by minimizing ABIC. ABIC had been introduced to geophysics by several studies. Among them, Yabuki and Matsu’urea (1992) has been the most influential. The inverse method developed by them has been widely applied to various problems in seismology and geodesy. Recently, it has become clear that the inverse method must be further developed beyond the framework given by Yabuki and Matsu’ura (1992). Generalization has been performed in dealing with prior constraints, hyperparameters, and observed data.