Petrophysical Inversion Using Adaptive Ensemble-Based Optimization Method

We present a new inverse problem approach to address the complex issue of using reversing a Petro-Elastic Model (PEM) to estimate petrophysical properties from elastic ones. This approach samples the solution space of this non-linear non-convex quadratic problem, as encountered in the inversion of petrophysical properties, through an ensemble-based model.

A prior ensemble constructed from a prior model of petrophysical properties is used to sample the uncertainty of the parameters before entering the inversion process. Each petrophysical sample of the ensemble is then updated in order to reduce the value of an objective function expressing the mismatch between the elastic response given by the PEM and the elastic attributes. The first derivative matrix is adaptively estimated from sub-ensembles of petrophysical parameters and their corresponding forward model responses. The final ensemble provides an estimation of the uncertainty on the petrophysical parameters (including fluids) after the inversion process.

We apply this technique to a turbidite field in order to update existing petrophysical models with realizations from a stochastic acoustic seismic inversion. Despite not using dynamic data directly, we show that the updated models match real production data better than the initial models.