Harnessing high-performance computers and accurate numerical methods to better constrain physical properties of Earth's interior is becoming one of the most important research topics in structural and exploration seismology. We use spectralelement and adjoint methods to iteratively improve 3D subsurface images ranging from continental to exploration scales. The spectral-element method, a high-order finite-element method with the advantage of a diagonal mass matrix, is used to accurately calculate three-component synthetic seismograms in a complex 3D Earth model. An adjoint method is used to numerically compute Frechet derivatives of a misfit function based on the interaction between the wavefield for a reference Earth model and a wavefield obtained by using time-reversed differences between data and synthetics at all receivers as simultaneous sources. In combination with gradient-based optimization methods, such as a preconditioned conjugate gradient method, we are able to iteratively improve 3D images of Earth's interior and gradually minimize discrepancies between observed and simulated seismograms. Various misfit functions may be chosen to quantify these discrepancies, such as crosscorrelation traveltime differences, frequency-dependent phase and amplitude anomalies as well as full-waveform differences. Various physical properties of the Earth are constrained based on this method, such as elastic wavespeeds, radial anisotropy, shear attenuation and impedance contrasts. We apply this method to study seismic inverse problems at various scales, from continental-scale seismic tomography to exploration-scale full-waveform inversion. Two examples are utilized to illustrate the applications of this method, namely, 1) application of adjoint tomography in improving 3D elastic wavespeeds of the European crust and upper mantle, and 2) application of the impedance gradient in elastic reverse-time migration for a 2D salt dome model.


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