Estimation and accounting for the modeling error in probabilistic linearized amplitude variation with offset inversion

A linearized form of Zoeppritz equations combined with the convolution model is widely used in inversion of amplitude variation with offset (AVO) seismic data. This is shown to introduce a "modeling error," compared with using the full Zoeppritz equations, whose magnitude depends on the degree of subsurface heterogeneity. Then, we evaluate a methodology for quantifying this modeling error through a probability distribution. First, a sample of the unknown probability density describing the modeling error is generated. Then, we determine how this sample can be described by a correlated Gaussian probability distribution. Finally, we develop how such modeling errors affect the linearized AVO inversion results. If not accounted for (which is most often the case), the modeling errors can introduce significant artifacts in the inversion results, if the signal-to-noise ratio is less than 2, as is the case for most AVO data obtained today. However, if accounted for, such artifacts can be avoided. The methodology can easily be adapted and applied to most linear AVO inversion methods, by allowing the use of the inferred modeling error as a correlated Gaussian noise model.