Data-adaptive global full-waveform inversion

We present a novel approach to global-scale full-waveform inversion (FWI) that can reduce computational cost by over an order of magnitude, compared to previously published methods, without sacrificing physical and mathematical rigour. This is based on data-adaptation, and thereby application-oriented specialization, on two complementary levels. On the simulation level, we exploit the approximate azimuthal symmetry of seismic wavefields by implementing wavefield-adapted meshes and discrete adjoints, thereby lowering numerical simulation cost. On the measurement level, we use a quasi-stochastic approach where variable mini-batches of data are used during an iterative misfit minimization in order to promote a parsimonious exploitation of data. In addition to the methodological developments, we present an inversion of long-period (100-200 s) seismic waveforms from 1179 earthquakes for 3-D whole-mantle structure. The computational cost of the 72 iterations in the inversion approximately equals one third of a single iteration using an FWI approach with widely used cubed-sphere-based meshes and non-stochastic gradient optimization. The resulting LOng-Wavelength earth model (LOWE) constitutes the first global FWI constructed entirely from a spherically symmetric initial mantle structure. While mostly serving as a showcase for the method, LOWE contains a wealth of regional-scale structures that compare well to earlier tomographic images. Being conservatively smooth and based on minimal assumptions, it may therefore serve as starting model for future inversions at shorter period or smaller scales.