Modelling earthquakes and earth,s interior based upon exascale simulations of seismic wave propagation

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We propose to use modern numerical methods and computers to improve images of earthquakes and Earth's interior based upon forward and inverse simulations of seismic wave propagation. The simulations are based upon a spectral-element method and account for heterogeneity in the crust and mantle, topography, anisotropy, attenuation, fluid-solid interactions, self-gravitation, rotation, and the oceans. On future exascale machines we will able to reach frequencies well below 1 Hz in global simulations. Our objective is to go beyond classical traveltime tomography, and to use information contained in entire seismic waveforms. By drawing connections between seismic tomography, adjoint methods popular in climate and ocean dynamics, and time-reversal imaging, we have demonstrated that one iteration in tomographic inversions may be performed based upon just two numerical simulations for each earthquake: one calculation for the current model and a second adjoint calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources. This has finally opened the door to solving the 3D inverse problem, namely the problem of using the remaining differences between the data and the