Seismic waveform inversion is a method with very ambitious goals. It attempts to obtain Earth's model parameters from seismic data in one encompassing and comprehensive process. This thesis, however, is concerned with acoustic waveform inversion in the frequency-domain with emphasis on areas with complex near surface.
We give an overview of seismic inversion and the method on which waveform inversion is based, seismic migration. We review waveform inversion from a theoretical point of view and attempt to coherently put together the different theories and conclusions reached by some authors in the literature. We derive the formula of the gradient of the misfit function for waveform inversion and, in one derivation, we explicitly invoke the well known linearization, the Born approximation, and therefore we show how it is related to seismic migration. We, also, compare and contrast waveform inversion with seismic migration, in general, Kirchhoff migration and true amplitude inversion, in particular; in addition to traveltime tomography.
Since the near surface is highly heterogeneous, we examine the effect of heterogeneity on waveform inversion and whether it can perform in an acceptable manner to relatively high frequency, almost 25 Hz. We then apply waveform inversion to a realistic model representative of challenging near surface environments, like those in the Middle East. Waveform inversion was able to give very high resolution models that can resolve the issues associated with long-wavelength statics. We then examine if waveform inversion can indeed resolve the challenging problem of first arrival shingling. We show that it can indeed resolve this long standing problem.
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