# Studies in seismic scattering

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## Abstract

Modem methods of seismic data analysis are tending to inversion through model fitting, i.e., actually finding the best model of the Earth's subsurface which would produce the amplitude and phase variation in the observed data. An understanding of seismic scattering is fundamental to this form of data analysis. This dissertation involves the study of seismic scattering and its use in the inverse problem, applying full waveform inversion ideas in novel situations. The terminology and methodology of inverse theory may sometimes hide what is going on, and may make it difficult to connect the results with those from more familiar techniques. In Chapter 1 I show that, with the appropriate choice for the model parameters, the first iteration of the nonlinear least-squares seismic waveform inversion algorithm reduces to classical results from linear filter theory. I use the idea of the adjoint of the Frechet derivative linear operator in Chapter 2 to understand smoothing in the waveform inversion, which manifests itself as a new sensitivity function incorporating the smoothing information. This gives us physical intuition into the wave equation based inverse problem. My mathematical analysis is general; however, using sensitivity functions for the paraxial equation in ray centered coordinates, I show a specific application to full waveform imaging in a tomographic experiment where only phase information (travel-time data) is normally used. I consider an inversion of teleseismic data from some deep earthquakes in Chapter 3. I use the phase and amplitude variation in the seismic signals in an imaging technique derived from inverse theory and digital signal analysis, interpreting the coherent energy in the coda of the first arrival as due to scattering from upper mantle discontinuities. Applying an inversion through iterative forward modeling, I measure the depth variation of the spinel-perovskite upper mantle phase transition within the subduction zone region. This measurement allows me to characterize the variation of the transition with respect to pressure and temperature. My results are consistent with convection in a model of a chemically homogeneous mantle, where the presence of the phase transition at around 670 km depth disrupts the full mantle convection patterns.