Multiscale full waveform inversion

We develop and apply a full waveform inversion method that incorporates seismic data on a wide range of spatio-temporal scales, thereby constraining the details of both crustal and uppermantle structure. This is intended to further our understanding of crust-mantle interactions that shape the nature of plate tectonics, and to be a step towards improved tomographic models of strongly scale-dependent earth properties, such as attenuation and anisotropy. The inversion for detailed regional earth structure consistently embedded within a largescale model requires locally refined numerical meshes that allow us to (1) model regional wave propagation at high frequencies, and (2) capture the inferred fine-scale heterogeneities. The smallest local grid spacing sets the upper bound of the largest possible time step used to iteratively advance the seismic wave field. This limitation leads to extreme computational costs in the presence of fine-scale structure, and it inhibits the construction of full waveform tomographic models that describe earth structure on multiple scales. To reduce computational requirements to a feasible level, we design amultigrid approach based on the decomposition of amultiscale earth model with widely varying grid spacings into a family of single-scalemodels where the grid spacing is approximately uniform. Each of the single-scale models contains a tractable number of grid points, which ensures computational efficiency. The multi-to-singlescale decomposition is the foundation of iterative, gradient-based optimization schemes that simultaneously and consistently invert data on all scales for one multi-scale model. We demonstrate the applicability of our method in a full waveform inversion for Eurasia, with a special focus on Anatolia where coverage is particularly dense. Continental-scale structure is constrained by complete seismic waveforms in the 30-200 s period range. In addition to the well-known structural elements of the Eurasian mantle, our model reveals a variety of subtle features, such as the Armorican Massif, the Rhine Graben and the Massif Central. Anatolia is covered by waveforms with 8-200 s period, meaning that the details of both crustal and mantle structure are resolved consistently. The final model contains numerous previously undiscovered structures, including the extension-related updoming of lower-crustal material beneath the Menderes Massif in western Anatolia. Furthermore, the final model for the Anatolian region confirms estimates of crustal depth from receiver function analysis, and it accurately explains cross-correlations of ambient seismic noise at 10 s period that have not been used in the tomographic inversion. This provides strong independent evidence that detailed 3-D structure is well resolved.