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How do body-wave traveltimes constrain the Earth's radial (1-D) seismic structure? Existing 1-D seismological models underpin 3-D seismic tomography and earthquake location algorithms. It is therefore crucial to assess the quality of such 1-D models, yet quantifying uncertainties in seismological models is challenging and thus often ignored. Ideally, quality assessment should be an integral part of the inverse method. Our aim in this study is twofold: (i) we show how to solve a general Bayesian non-linear inverse problem and quantify model uncertainties, and (ii) we investigate the constraint on spherically symmetric P-wave velocity (VP) structure provided by body-wave traveltimes from the EHB bulletin (phases Pn, P, PP and PKP). Our approach is based on artificial neural networks, which are very common in pattern recognition problems and can be used to approximate an arbitrary function. We use a Mixture Density Network to obtain 1-D marginal posterior probability density functions (pdfs), which provide a quantitative description of our knowledge on the individual Earth parameters. No linearization or model damping is required, which allows us to infer a model which is constrained purely by the data.We present 1-D marginal posterior pdfs for the 22 VP parameters and seven discontinuity depths in our model. P-wave velocities in the inner core, outer core and lower mantle are resolved well, with standard deviations of ∼0.2 to 1 per cent with respect to the mean of the posterior pdfs. The maximum likelihoods of VP are in general similar to the corresponding ak135 values, which lie within one or two standard deviations from the posterior means, thus providing an independent validation of ak135 in this part of the radial model. Conversely, the data contain little or no information on P-wave velocity in the D′′ layer, the upper mantle and the homogeneous crustal layers. Further, the data do not constrain the depth of the discontinuities in our model. Using additional phases available in the ISC bulletin, such as PcP, PKKP and the converted phases SP and ScP, may enhance the resolvability of these parameters. Finally, we show how the method can be extended to obtain a posterior pdf for a multidimensional model space. This enables us to investigate correlations between model parameters. [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]