Spatial variability in seismic depth tomography
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The location of a reflector or medium in the subsurface is correlated with the high wavenumbers or high frequencies in the velocity field. Indeed, the determination of the high frequencies of the velocity field both normally and laterally is the key step for improving seimic data and then get a better insight of the position of a reflector in the subsurface. This project focus on the velocity data processing part involved in seismic tomography. We describe, compare and implement several highpass operators based on finite-difference and the Hamming window in order to filter a seismic velocity dataset. In fact, we study their behaviour in the frequency domain by examining their spectrums. The main contribution of this project is to construct two dimensional anisotropic operators by rotating a one dimensional operator based on linear interpolation. We test all the operators on a synthetic seismic velocity dataset and compare the results obtained between the isotropic filtering method and the anisotropic filtering method. We show that anisotropic filters can be useful in certain geological circumstances. Finally we attempt to scale the different operators in order to fully incorporate them in the seismic tomography inversion problem by using a Bayesian method. We show that it is possible to decide the strength of the constraint in which we want to filter the seismic dataset by using a regularization parameter.