Two-step (Analytical + geostatistical) pre-stack seismic inversion for elastic properties estimation and litho-fluid facies classification

We infer the P-wave velocity, S-wave velocity, density, and the litho-fluid classes through a two cascade estimation steps. First, we analytically invert each seismic gather independently using a linear 1D convolutional forward operator and assuming a Gaussian-mixture prior. This step is computationally fast because no hard or lateral constraints are imposed to the recovered solution. The outcomes provided by the analytical inversion are used as auxiliary variables for a geostatistical simulation that generates the initial ensemble of models for the subsequent stage of geostatistical inversion in which the estimated models are generated and iteratively updated according to a more realistic non-parametric prior, while spatial and hard constraints are now imposed to the solution. This second step determines the model update from the match between observed and predicted seismic gathers that are computed through a 1D convolutional operator based on the full Zoeppritz equations. Synthetic inversions are used to validate the method and demonstrate that starting the second inversion step from an ensemble of models that already quite accurately reproduce the observed data allows for a fast retrieval of a subsurface model that honours the non-parametric prior, the hard constraints, and the spatial continuity patterns as coded by the variogram model.