Abstract
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.
Highlights
Seismic tomography has come a long way since its early applications (e.g. Aki & Lee 1976; Dziewonski et al 1977)
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
Summary
Seismic tomography has come a long way since its early applications (e.g. Aki & Lee 1976; Dziewonski et al 1977). While FWI may eliminate most simplifications of wave physics and thereby improve resolution, it comes with significant computational cost because each iterative model update requires forward and adjoint simulations, at a cost scaling with frequency to the power of 4 (Virieux & Operto 2009; Pirli 2017). Earth models should ideally update regularly to incorporate this new wealth of information For ray tomography, such evolutionary approaches were pioneered by Debayle et al (2016) at global scale and Tong et al (2017) at regional scale. These authors expand their data set sequentially and reinvert the larger data set to obtain an update. While evolutionary inversion would be desirable for FWI, periodic reinversions of a growing data set are computationally out of scale
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