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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

SUMMARY Displacement time-series recorded by Global Positioning System (GPS) receivers are a new type of near-field waveform observation of the seismic source. We have developed an inversion method which enables the recovery of an earthquake's mechanism and centroid coordinates from such data. Our approach is identical to that of the 'classical' Centroid-Moment Tensor (CMT) algorithm, except that we forward model the seismic wavefield using a method that is amenable to the efficient computation of synthetic GPS seismograms and their partial derivatives. We demonstrate the validity of our approach by calculating CMT solutions using 1 Hz GPS data for two recent earthquakes in Japan. These results are in good agreement with independently determined source models of these events. With wider availability of data, we envisage the CMT algorithm providing a tool for the systematic inversion of GPS waveforms, as is already the case for teleseismic data. Furthermore, this general inversion method could equally be applied to other near-field earthquake observations such as those made using accelerometers. [ABSTRACT FROM AUTHOR]

The ability to handle large amounts of data automatically is essential for any major tomographic inversion. As part of this process, it is necessary to differentiate between high-quality seismograms, and those that are unusable due to noise or other errors. This quality assessment is traditionally made visually; however, the sheer quantity of data in a modern tomographic data set makes this approach unfeasible. It is therefore necessary to develop techniques for automating this quality assessment process. We demonstrate that a simple neural network, trained to recognize the frequency-domain characteristics of high- and low-quality data, can successfully distinguish the two classes in unseen data. We demonstrate that the resulting clean data sets are of sufficient quality to allow full-waveform determination of event focal mechanisms and hypocentral parameters. The process we outline allows the rapid creation of a high-quality data set for seismic tomography. Depending on application, this may be suitable for use without further refinement. In some circumstances, a further visual inspection may remain desirable to ensure the data set is noise-free; however, a significant benefit will still derive from the reduction in number of traces to be examined. This will enable full-waveform inversion using significantly larger data sets than has hitherto been possible. The selection strategy relies only on measurements made from the seismogram, and on rough estimates of hypocentral location—the final data set does not depend on any a priori assumptions regarding earth structure or wave propagation. Our focus has been on data selection for seismic tomography, but the approach is general and may find application across a wide range of seismic investigations. An automated system is of interest wherever large data sets must be handled, or where time is of the essence—such as in earthquake hazard assessment. [ABSTRACT FROM AUTHOR]

To perform seismic tomography, accurate determinations of event locations and focal mechanisms are required. These are usually obtained prior to tomographic inversion; often, little attention is paid to the earth model used for their determination. We show that an imprint of this model is found in the model recovered after tomographic inversion. To reduce this problem, it is important to recalculate earthquake source parameters as the inversion proceeds; synthetic tests suggest that this yields a better correspondence between recovered and true models. However, alternate source and structure inversions lead to a slow rate of convergence, and significant errors remain. We therefore propose combining source and structure inversion into a single inverse problem, and present an efficient algorithm to do this. We demonstrate that this reduces the number of iterations required to achieve a given accuracy; in our experiments, we observe a fourfold improvement on alternate inversions. We focus on full-waveform inversions for both source and structure, although the methods presented are general and should be applicable to other techniques. [ABSTRACT FROM AUTHOR]