Regularization of the AVO inverse problem by means of a ...

5.1 Introduction
CHAPTER 5
Three-term AVO Inversion
Three-term AVO inversion uses three-term approximations on Zoeppritz equation as a for-
ward model. It is the most favored inversion method for two main basic reasons. First,
the three-term approximations like Aki and Richards’s are considered as the best approxi-
mation to the exact reflection coefficient (Rpp). In addition, the three term approximation
allows to retrieve one more model parameter i.e direct density information which is useful
parameter to characterize physical property of rocks (subsurface geology). Including the
third term provides information which can be used to separate gas sands from wet sands,
tight sands, and shales or to study gas saturation (Kabir et al., 2006; Sun et al., 2005; Li,
2005). However, as pointed out in the introduction part of chapter 4, using three-term
approximations as inversion model is more ill-conditioned than a two-term approximation.
This suggests that more attention should be given to stabilizing the inversion although both
cases need regularization in order to make the solution more stable. Following a similar pro-
cedure given in the previous chapter, the three term AVO regularizations are constructed
via Bayesian approach. This chapter is mainly to address a new way of regularizing the
three-term AVO inversion using Trivariate Cauchy probability distribution in comparison
with other two possible regularization methods. This is demonstrated by both synthetic
and real data examples.
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