A comparison of approximations for the converted-wave reflection

Maria Silvia Donati, Nicolas Williams Martin

AVO analysis for converted waves has been restricted mainly to model AVO responses as a function of offset, varying some horizon characteristics, such as thickness and VP/VS ratio. To generalize, facilitate, and make comparable to P-P AVO analysis, the converted wave reflection coefficient, RPS(), given by Aki and Richards (1980), has been simplified through different approaches. Each approximation has associated different levels of error, which depends on how the original terms in RPS() are manipulated.

The best approximation, named R1PS, is valid for incidence angles between 0 and 90 degrees, but some terms do not provide any additional information about the elastic properties. In contrast, R5PS approach shows an error lower than 10 percent, for incidence angles between 0 and 50 degrees, and resembles Shuey's P-P quadratic approach. In this case, R5PS shows a more suitable expression to be inverted for elastic parameters through least squares fit.

The R5PS approach will provide inverted elastic parameters sections, such as: (i) a rigidity relative contrast and (ii) a S-wave velocity reflectivity (Smith and Gidlow, 1987). These sections could be potentially used to discriminate and recognize possible gas/oil zones, in conjunction with P-P AVO analysis.