Seismic Waveform Inversion: Bump functional, parameterization analysis and imaging ahead of a tunnel-boring machine

During a seismic experiment, mechanical waves are usually generated by various manmade sources. These waves propagate in the subsurface and are recorded at receivers. Modern seismic exploration methods analyze them to infer the mechanical properties of the subsurface; this is commonly referred as quantitative imaging. These properties assist in the determination of the subsurface rock type and structure. Exploration methods are not only useful while looking for the deposits such as crude oil, natural gas and minerals but also for near-surface geotechnical investigation. A motive of this thesis is to adopt these methods to image the subsurface ahead of a tunnel-boring machine for hazard assessment during excavation. Full-waveform inversion (FWI) is a gradient-based optimization problem that is employed in seismic exploration for quantitative imaging of the recorded waves. During FWI, seismic waves are simulated in a computer by using certain physical laws that govern the wave propagation. After inversion, output subsurface properties simulate waves that fit the recorded waves in a least-squares sense. In other words, the gradient-based optimization aims to find the minimum of the least-squares misfit between the simulated and the recorded waves. Finding such a minimum is not straight forward due to the existence of multiple local minima when using the least-squares objective. As a result, it might often happen that the optimizer converges to local minima, where the simulated waves only partially explain the recorded waves. The presence of local minima is associated to the strong non-linear dependence of the recorded waves on the subsurface properties. In this thesis, we attempt to overcome this difficulty. We propose a new measure of misfit between the recorded and the simulated waves. This measure compares the waveforms in a simplified form after taking the absolute value and blurring. We show that the new misfit measure suffers less from the local-minima problem. For robust inversion, we use a multi-objective inversion scheme, where the new measure is used as an auxiliary objective to pull the trapped solution out of the least-squares local minimum whenever necessary. In multi-parameter FWI, more than one kind of subsurface properties are simultaneously estimated. When only the first-order derivatives of the misfit are used during minimization, different choices of subsurface parameterization are not equivalent; they can be interpreted as different preconditioners. Therefore, the choice of parametrization will affect the rate of convergence in multi-parameter FWI and the best choice of parameterization is the one with the highest rate. In this thesis, we also analyse various choices of subsurface parameterization in search of the best one. It is well known that the local-minima problem in FWI can easily be resolved by reliably generating and recording low-frequency waves in the subsurface. Recently, a seismic source capable of generating such low frequencies is developed based on linear synchronous motors technology. Finally, we demonstrated a shear-wave seismic ground prediction system using these sources to enable imaging ahead of a tunnel boring machine (TBM).