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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]

SUMMARY What makes a seismogram look like a seismogram? Seismic data sets generally contain waveforms sharing some set of visual characteristics and features-indeed, seismologists routinely exploit this when performing quality control 'by hand'. Understanding and harnessing these characteristics offers the prospect of a deeper understanding of seismic waveforms, and opens up many potential new techniques for processing and working with data. In addition, the fact that certain features are shared between waveforms suggests that it may be possible to transform the data away from the time domain, and represent the same information using fewer parameters. If so, this would be a significant step towards making fully non-linear tomographic inversions computationally tractable. Hinton & Salakhutdinov showed that a particular class of neural network, termed 'autoencoder networks', may be used to find lower-dimensional encodings of complex binary data sets. Here, we adapt their work to the continuous case to allow the use of autoencoders for seismic waveforms, and offer a demonstration in which we compress 512-point waveforms to 32-element encodings. We also demonstrate that the mapping from data to encoding space, and its inverse, are well behaved, as required for many applications. Finally, we sketch a number of potential applications of the technique, which we hope will be of practical interest across all seismological disciplines, and beyond. [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]