AVO inversion is a well established seismic exploration methodology to predict the earth's elastic parameters and thus rock and fluid properties. This thesis introduces a series of theoretical improvements to the AVO inverse problem. These include, a practical methodology to perform three-term AVO inversion instead of the industry standard of performing two-term AVO inversion. Two-term AVO inversion constrains the inversion either implicitly by truncating a term, or explicitly through some empirical relationship, thus introducing bias into the estimate. Using probabilistic constraints based on local geologic information, the three-term inversion can be constrained so as to give stable estimates, but with minimal bias. To help the explorationist understand the reliability of these estimates, a series of quality controls are developed and verified.
In order to estimate reliable density reflectivity, long offsets are required. NMO stretch and offset-dependent tuning introduce problematic distortions at these offsets. Two methods are investigated to address these issues. First, stretch-free NMO is investigated as a way to precondition the data. Secondly, an AVO waveform inversion which incorporates into the forward model NMO stretch and offset-dependent tuning is considered.
Both the AVO inversion and AVO waveform inversion are developed using a Bayesian framework. Gaussian and long-tailed distributions are explored for the likelihood and a priori probability distributions. The optimization problem results in non-linear solutions. The AVO inversion is solved using Newton-Raphson while the AVO waveform inversion is solved using conjugate gradient. In each case, the methodology is demonstrated on synthetic and real data examples.
The synthetic example shows that the AVO waveform inversion provides the most accurate estimates in the presence of NMO stretch and tuning. Preconditioning the data with stretch-free NMO improves the results of the AVO inversion, but not as much as the AVO waveform inversion results. For real seismic data the AVO waveform inversion also provided the best results of the methods tested. An example is shown where both the AVO inversion and AVO waveform inversion are able to estimate density reflectivity that differentiate commercial from noncommercial gas.
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