Wavelet Approaches to Seismic Data Analysis

There have been extensive applications of wavelets to petroleum seismic data. In this dissertation, we focus on developing and testing new wavelets approaches to seismic data compression, microseismic first arrival picking, seismic event picking, and seismic reflectivity inversion.

First, we developed new methodologies for seismic data compression based on wavelets. We started with applying matching pursuit to obtain a sparse representation of seismic signals on a dictionary, so we only need to store and transmit the sparse representation. The dictionaries tested initially are Symlets. To improve the performance of compression further, we proposed the new idea of using subspace matching pursuit to obtain perfect reconstruction for a phase-rotated signal. We obtained better fidelity than matching pursuit, but the convergence is slowed down due to the incompleteness of the dictionary. Finally we proposed using matching pursuit with a combination of Symlets dictionary and subspace dictionary, thereby obtaining the best quality with the same compression ratio.

Second, we report a new method of automatic first break detection of P-waves and S-waves. Our method is based on a time-frequency analysis of the seismic trace using minimum uncertainty wavelets, in particular in the minimum-phase form. We have tested our method on both lab data with various signal-to-noise ratio (S/N or SNR) and on field data.

Third, we explored methods of automatic seismic event picking. It is known that no single automatic seismic event indicator works for all data; therefore, we explored two indicators based on the minimum uncertainty wavelets and on an energy ratio. Thresholding was applied to pick seismic events. We have tested the methods with both synthetic data and offshore field data.

Finally, we proposed new seismic sparse inversion methods based on complex basis pursuit (CBP) and a modified complex basis pursuit (MCBP). In practice, constant phase wavelets are used for seismic inversion algorithms, for example, the basis pursuit (BP). If the phase of the estimated wavelet is wrong, this will surely cause an error in reflectivity. We can obtain more accurate reflectivity even though the estimated wavelet has biased phase by using CBP and MCBP rather than BP.