A comparison of approximations for the converted-wave reflection

Maria Donati and Nicolas W. 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 V P /V S ratio. To generalize, facilitate, and make comparable to P-P AVO analysis, the converted wave reflection coefficient, R PS (θ), 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 R PS (θ) are manipulated.

The best approximation, named R 1 PS , 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, R 5 PS 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, R 5 PS shows a more suitable expression to be inverted for elastic parameters through least squares fit.

The R 5 PS 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.

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