Application of wavelet transforms to seismic data processing and inversion.

摘要

The goal of this thesis is to use wavelet transforms as tools to analyze simultaneously the time (or location) and frequency (or scale) variant characteristics of seismic data and then to apply these information to two important geophysical problems: noise filtering and travel time inversion.; In the noise filtering problem, the discrete non-orthogonal wavelet transform is used to analyze the time-variant characteristics of signal and noise. This information can be used to filter noise in the transformed domain. This approach is applied to ground roll attenuation for field seismic data according to the localised characteristics.; Geophysical inverse problems are, in general, non-linear, underdetermined and ill-posed. An initial model and some prior information describing the model is needed to find the model perturbation that minimizes an objective function. Traditionally, the perturbation is assumed to be an independent Gaussian or a correlated but stationary process, an assumption which is not physically correct according to the analyses of well logs. Indeed, analysis of logs described in this thesis suggests that log data can be decomposed into (a) a fractal process, usually non-stationary, with wavelet coefficients which follow a power law, and (b) some non-fractal structures including a large scale trend and some spiky details. The inverse problem can be solved using the wavelet transform in two steps. First, I solve an overdetermined problem to invert the large scale trend, then, I solve for a model with fractal constraints.; Another important application of the wavelet transform in inverse problems is to reduce the effects of the noise in the input data. Since the noise effect varies with scale, the regularization can be done accordingly. Wavelet transform constrained inversions are tested using 1-D and 2-D synthetic examples.