S U M M A R Y We present an accelerated full-waveform inversion based on dynamic mini-batch optimization, which naturally exploits redundancies in observed data from different sources. The method rests on the selection of quasi-random subsets (mini-batches) of sources, used to approximate the misfit and the gradient of the complete data set. The size of the mini-batch is dynamically controlled by the desired quality of the gradient approximation. Within each mini-batch, redundancy is minimized by selecting sources with the largest angular differences between their respective gradients, and spatial coverage is maximized by selecting candidate events with Mitchell’s best-candidate algorithm. Information from sources not included in a specific minibatch is incorporated into each gradient calculation through a quasi-Newton approximation of the Hessian, and a consistent misfit measure is achieved through the inclusion of a control group of sources. By design, the dynamic mini-batch approach has several main advantages: (1) The use of mini-batches with adaptive size ensures that an optimally small number of sources is used in each iteration, thus potentially leading to significant computational savings; (2) curvature information is accumulated and exploited during the inversion, using a randomized quasiNewton method; (3) new data can be incorporated without the need to re-invert the complete data set, thereby enabling an evolutionary mode of full-waveform inversion. We illustrate our method using synthetic and real-data inversions for upper-mantle structure beneath the African Plate. In these specific examples, the dynamic mini-batch approach requires around 20 per cent of the computational resources in order to achieve data and model misfits that are comparable to those achieved by a standard full-waveform inversion where all sources are used in each iteration.

中文翻译：

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使用动态小批量加速全波形反演

总结我们提出了一种基于动态小批量优化的加速全波形反演，它自然地利用了来自不同来源的观察数据的冗余。该方法依赖于源的准随机子集（小批量）的选择，用于估计完整数据集的失配和梯度。小批量的大小由所需的梯度近似质量动态控制。在每个小批量中，通过选择各自梯度之间角度差异最大的源来最小化冗余，并通过使用 Mitchell 的最佳候选算法选择候选事件来最大化空间覆盖。来自未包含在特定小批量中的来源的信息通过 Hessian 的准牛顿近似纳入每个梯度计算，并且通过包含一个控制组源来实现一致的失配度量。通过设计，动态小批量方法有几个主要优点：（1）使用具有自适应大小的小批量确保在每次迭代中使用最佳数量的源，从而潜在地节省大量计算；(2) 在反演过程中积累和利用曲率信息，使用随机拟牛顿法；(3) 无需重新反演完整数据集即可合并新数据，从而实现全波形反演的演化模式。我们使用非洲板块下上地幔结构的合成和真实数据反演来说明我们的方法。在这些具体的例子中，