We present a series of new open-source deep-learning algorithms to accelerate Bayesian full-waveform point source inversion of microseismic events. Inferring the joint posterior probability distribution of moment tensor components and source location is key for rigorous uncertainty quantification. However, the inference process requires forward modelling of microseismic traces for each set of parameters explored by the sampling algorithm, which makes the inference very computationally intensive. In this paper we focus on accelerating this process by training deep-learning models to learn the mapping between source location and seismic traces for a given 3D heterogeneous velocity model and a fixed isotropic moment tensor 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 comparison, we train our emulators on the same microseismic traces and using the same geophysical setting. We show that all of our models provide more accurate predictions, ∼ 100 times faster predictions than the method based on Gaussian processes, and a 𝒪(10⁵) speed-up factor over a pseudo-spectral method for waveform generation. For example, a 2 s long synthetic trace can be generated in ∼ 10 ms on a common laptop processor, instead of ∼ 1 h using a pseudo-spectral method on a high-profile graphics processing unit card. We also show that our inference results are in excellent agreement with those obtained from traditional location methods based on travel time estimates. The speed, accuracy, and scalability of our open-source deep-learning models pave the way for extensions of these emulators to generic source mechanisms and application to joint Bayesian inversion of moment tensor components and source location using full waveforms.

中文翻译：

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通过深度学习加速贝叶斯微震事件定位

我们提出了一系列新的开源深度学习算法来加速微地震事件的贝叶斯全波形点源反演。推断矩张量分量和源位置的联合后验概率分布是严格不确定性量化的关键。然而，推理过程需要对采样算法探索的每组参数的微震轨迹进行前向建模，这使得推理的计算量非常大。在本文中，我们专注于通过训练深度学习模型来加速这一过程，以学习给定 3D 异构速度模型的震源位置和地震道之间的映射以及震源的固定各向同性矩张量。这些训练有素的模拟器在推理过程中取代了昂贵的弹性波动方程解决方案。我们将我们的结果与之前使用基于高斯过程的模拟器来反演微震事件的研究进行比较。为了公平起见，我们在相同的微地震轨迹上并使用相同的地球物理设置训练我们的模拟器。我们表明我们所有的模型都提供了更准确的预测，∼  100 倍的预测速度比基于高斯过程的方法快，并且比用于波形生成的伪谱方法有一个𝒪(10 ⁵ )加速因子。例如， 在普通笔记本电脑处理器上，可以在~ 10 ms 内生成2  s长的合成轨迹，而不是~  1  h在高配置图形处理单元卡上使用伪光谱方法。我们还表明，我们的推理结果与基于旅行时间估计的传统定位方法获得的结果非常一致。我们开源深度学习模型的速度、准确性和可扩展性为将这些仿真器扩展到通用源机制和应用到使用完整波形的矩张量分量和源位置的联合贝叶斯反演铺平了道路。