{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T07:04:57Z","timestamp":1772262297447,"version":"3.50.1"},"reference-count":107,"publisher":"Copernicus GmbH","issue":"7","license":[{"start":{"date-parts":[[2021,7,29]],"date-time":"2021-07-29T00:00:00Z","timestamp":1627516800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Solid Earth"],"abstract":"<jats:p>Abstract. We present a series of new open-source deep-learning algorithms to accelerate Bayesian full-waveform point source inversion of microseismic\nevents. Inferring the joint posterior probability distribution of moment tensor components and source location is key for rigorous uncertainty\nquantification. However, the inference process requires forward modelling of microseismic traces for each set of parameters explored by the sampling\nalgorithm, which makes the inference very computationally intensive. In this paper we focus on accelerating this process by training deep-learning\nmodels to learn the mapping between source location and seismic traces for a given 3D heterogeneous velocity model and a fixed isotropic moment\ntensor for the sources. These trained emulators replace the expensive solution of the elastic wave equation in the inference process. We compare our results with a previous study that used emulators based on Gaussian processes to invert microseismic events. For fairness of\ncomparison, we train our emulators on the same microseismic traces and using the same geophysical setting. We show that all of our models provide\nmore accurate predictions, \u223c\u2009100 times faster predictions than the method based on Gaussian processes, and a \ud835\udcaa(105) speed-up\nfactor over a pseudo-spectral method for waveform generation. For example, a 2\u2009s long synthetic trace can be generated in \u223c\u200910 ms on a\ncommon laptop processor, instead of \u223c\u20091\u2009h using a pseudo-spectral method on a high-profile graphics processing unit card. We also\nshow that our inference results are in excellent agreement with those obtained from traditional location methods based on travel time estimates. The\nspeed, accuracy, and scalability of our open-source deep-learning models pave the way for extensions of these emulators to generic source mechanisms\nand application to joint Bayesian inversion of moment tensor components and source location using full waveforms.<\/jats:p>","DOI":"10.5194\/se-12-1683-2021","type":"journal-article","created":{"date-parts":[[2021,7,29]],"date-time":"2021-07-29T04:22:37Z","timestamp":1627532557000},"page":"1683-1705","source":"Crossref","is-referenced-by-count":11,"title":["Accelerating Bayesian microseismic event location with deep learning"],"prefix":"10.5194","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5698-0990","authenticated-orcid":false,"given":"Alessio","family":"Spurio Mancini","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9836-2661","authenticated-orcid":false,"given":"Davide","family":"Piras","sequence":"additional","affiliation":[]},{"given":"Ana Margarida Godinho","family":"Ferreira","sequence":"additional","affiliation":[]},{"given":"Michael Paul","family":"Hobson","sequence":"additional","affiliation":[]},{"given":"Benjamin","family":"Joachimi","sequence":"additional","affiliation":[]}],"member":"3145","published-online":{"date-parts":[[2021,7,29]]},"reference":[{"key":"ref1","unstructured":"Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.\u00a0S., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Man\u00e9, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Vi\u00e9gas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., and Zheng, X.:\nTensorFlow: Large-Scale Machine Learning on Heterogeneous Systems,\navailable at: https:\/\/www.tensorflow.org\/ (last access: 20 July 2021),\nsoftware available from tensorflow.org, 2015.\u2002a"},{"key":"ref2","unstructured":"Arjovsky, M., Chintala, S., and Bottou, L.:\nWasserstein GAN,\narXiv [preprint], arXiv:1701.07875, 2017.\u2002a, b, c, d"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"Arridge, S., Maass, P., Ozan, O., and Sch\u00f6nlieb, C.-B.:\nSolving inverse problems using data-driven models,\nActa Numer.,\n28, 1\u2013174, https:\/\/doi.org\/10.1017\/S0962492919000059, 2019.\u2002a","DOI":"10.1017\/S0962492919000059"},{"key":"ref4","doi-asserted-by":"crossref","unstructured":"Auld, T., Bridges, M., Hobson, M., and Gull, S.:\nFast cosmological parameter estimation using neural networks,\nMon. 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