Efficient Bayesian model selection strategy for tsunami source inversion

Abstract

Bayesian model selection (BMS) allows for quantification of consistency between data information content and model assumptions. In many geophysical inverse problems, such as, finite fault or tsunami waveform inversion, a particular model discretization or parametrization is typically assumed a priori and, thus, inferences are tied to it. Trans-dimensional (TransD) inversions, which have been relatively recently introduced to geophysical problems, permit to relax such a parametrization assumptions by estimating the degree of data support to parametrizations with different number of parameters, in a parsimonious fashion. The TransD posterior is normally estimated by employing sampling techniques and, thus, for large problems can be computationally demanding. In this work, we develop a BMS strategy that also addresses the problem of finding the data support to different parametrizations but that avoids expensive sampling schemes. We apply our approach to recover the tsunami source following the great Tohoku earthquake (2011, Mw = 9.1). In our method, different parametrizations are compared by computing the their Bayesian evidence. Since the tsunami forward problem is linear (for stations sufficiently far from the coast), we can employ analytical expressions for the Bayesian evidence by assuming Gaussian likelihood and prior. This also implies that tsunami waveform predictions can be computed as a superposition of the propagation of elementary tsunami source functions. We, independently, employ two types of elementary functions. One type is of global support, that is, functions are defined over the whole tsunami source domain. In the other type, functions are defined over portions of such a domain. For both cases, we present inversion simulations for a realistic station distribution. We show that a correlated, non-stationary data covariance matrix can be reasonably recovered from a iterative non-parametric approach. Finally, we apply these methods to measured tsunami data from 16 stations, obtaining consistent source models. Our results are in excellent agreement with a previous TransD study of the Tohoku tsunami source. Since many geophysical problems can be, at least partially, formulated as linear, these approaches can be of help when speeding-up inversions is required.