SUMMARY

We present a new approach to full-waveform inversion (FWI) that enables the assimilation of data sets that expand over time without the need to reinvert all data. This evolutionary inversion rests on a reinterpretation of stochastic Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS), which randomly exploits redundancies to achieve convergence without ever considering the data set as a whole. Specifically for seismological applications, we consider a dynamic mini-batch stochastic L-BFGS, where the size of mini-batches adapts to the number of sources needed to approximate the complete gradient. As an illustration we present an evolutionary FWI for upper-mantle structure beneath Africa. Starting from a 1-D model and data recorded until 1995, we sequentially add contemporary data into an ongoing inversion, showing how (i) new events can be added without compromising convergence, (ii) a consistent measure of misfit can be maintained and (iii) the model evolves over times as a function of data coverage. Though applied retrospectively in this example, our method constitutes a possible approach to the continuous assimilation of seismic data volumes that often tend to grow exponentially.

中文翻译：

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演化全波形反演

概要

我们提出了一种全波形反转（FWI）的新方法，该方法可以吸收随时间扩展的数据集，而无需重新反转所有数据。这种进化反演基于对随机受限内存Broyden-Fletcher-Goldfarb-Shanno（L-BFGS）的重新解释，该随机研究利用冗余来实现收敛，而无需考虑整个数据集。专门针对地震学应用，我们考虑了动态小批量随机L-BFGS，其中小批量的大小适合于逼近完整梯度所需​​的震源数量。作为说明，我们介绍了非洲下方上地幔结构的演化FWI。从一维模型开始，直到1995年记录数据，我们依次将当代数据添加到正在进行的反演中，展示了（i）如何添加新事件而又不影响收敛性；（ii）可以保持一致的失配度量；以及（iii）模型随数据覆盖率的变化而发展。尽管在本示例中进行了回顾性应用，但我们的方法构成了对地震数据量进行连续同化的可能方法，这些地震数据量往往呈指数增长。