Probabilistic point source inversion of strong-motion data in 3-D media using pattern recognition: A case study for the 2008 M w 5.4 Chino Hills earthquake

Despite the ever increasing availability of computational power, real-time source inversions based on physical modeling of wave propagation in realistic media remain challenging. We investigate how a nonlinear Bayesian approach based on pattern recognition and synthetic 3-D Green's functions can be used to rapidly invert strong-motion data for point source parameters by means of a case study for a fault system in the Los Angeles Basin. The probabilistic inverse mapping is represented in compact form by a neural network which yields probability distributions over source parameters. It can therefore be evaluated rapidly and with very moderate CPU and memory requirements. We present a simulated real-time inversion of data for the 2008 Mw 5.4 Chino Hills event. Initial estimates of epicentral location and magnitude are available ∼14 s after origin time. The estimate can be refined as more data arrive: by ∼40 s, fault strike and source depth can also be determined with relatively high certainty

A framework for fast probabilistic centroid-moment-tensor determination-inversion of regional static displacement measurements

The determination of earthquake source parameters is an important task in seismology. For many applications, it is also valuable to understand the uncertainties associated with these determinations, and this is particularly true in the context of earthquake early warning (EEW) and hazard mitigation. In this paper, we develop a framework for probabilistic moment tensor point source inversions in near real time. Our methodology allows us to find an approximation to p(m|d), the conditional probability of source models (m) given observations (d). This is obtained by smoothly interpolating a set of random prior samples, using Mixture Density Networks (MDNs)—a class of neural networks which output the parameters of a Gaussian mixture model. By combining multiple networks as ‘committees’, we are able to obtain a significant improvement in performance over that of a single MDN. Once a committee has been constructed, new observations can be inverted within milliseconds on a standard desktop computer. The method is therefore well suited for use in situations such as EEW, where inversions must be performed routinely and rapidly for a fixed station geometry. To demonstrate the method, we invert regional static GPS displacement data for the 2010 MW 7.2 El Mayor Cucapah earthquake in Baja California to obtain estimates of magnitude, centroid location and depth and focal mechanism. We investigate the extent to which we can constrain moment tensor point sources with static displacement observations under realistic conditions. Our inversion results agree well with published point source solutions for this event, once the uncertainty bounds of each are taken into account

Solving probabilistic inverse problems rapidly with prior samples

Owing to the increasing availability of computational resources, in recent years the probabilistic solution of non-linear, geophysical inverse problems by means of sampling methods has become increasingly feasible. Nevertheless, we still face situations in which a Monte Carlo approach is not practical. This is particularly true in cases where the evaluation of the forward problem is computationally intensive or where inversions have to be carried out repeatedly or in a timely manner, as in natural hazards monitoring tasks such as earthquake early warning. Here, we present an alternative to Monte Carlo sampling, in which inferences are entirely based on a set of prior samples—that is, samples that have been obtained independent of a particular observed datum. This has the advantage that the computationally expensive sampling stage becomes separated from the inversion stage, and the set of prior samples—once obtained—can be reused for repeated evaluations of the inverse mapping without additional computational effort. This property is useful if the problem is such that repeated inversions of independent data have to be carried out. We formulate the inverse problem in a Bayesian framework and present a practical way to make posterior inferences based on a set of prior samples. We compare the prior sampling based approach to a Markov Chain Monte Carlo approach that samples from the posterior probability distribution. We show results for both a toy example, and a realistic seismological source parameter estimation problem. We find that the posterior uncertainty estimates obtained based on prior sampling can be considered conservative estimates of the uncertainties obtained by directly sampling from the posterior distribution