Studying global discontinuities using full waveforms

Seismology aims at obtaining accurate tomographic images of the Earth’s interior by simulating models to create waveforms that fit recorded seismograms. The resolution of an acquired image greatly depends on the accuracy of the numerical tool used for modelling and the quality of observed data. Using a state-of-the art numerical wave propagation software, I study the structure of global discontinuities. I develop an iterative optimisation methodology for modelling the waveforms by minimising the misfit caused by the existence of topographic structure on discontinuities. Given that the disconti- nuity structure has mainly been studied in a ray theoretical framework, I only use synthetics in order to assess the reliability of conventional methods and to develop a novel approach based on full waveforms and non-linear min- imisation. My study also focuses on the sensitivity of waveforms related to discontinuity structure. Analyses of their exact sensitivity pave the way towards a better comprehension of real data and improvement of the inversion methodologies. To that extent, a new inversion method is proposed which relies on the iterative optimisation of boundary and structural models, with special focus on the structure of global discontinuities using boundary Fréchet derivatives for the first time in an inversion problem.
Successive steps for the iterative optimisation of the model are: choose a starting model and select a misfit function to calculate the discrepancies between observed and synthetic data. The objective function is the most important step in the inversion. By computing the derivative of this function, employing time-reversal and adjoint methods, one creates a model update which should minimise the previous misfit. Adjoint methods rely on the inter- action between "forward" and "adjoint" wavefields, propagating from source to receivers and vice versa. This process is iterated until the global misfit value sufficiently reduces. In this thesis, it is shown that this novel approach for imaging discontinuities improves the inference of internal discontinuity structure and provides an integrated method for global seismology. The pro- posed full waveform methodology outperforms ray theory to a great extent and should be used in real data applications.