Adaptive Ensemble-based Petrophysical Inversion for Seismically Constrained Static Model Building

Seismic inversion produces a limited number of elastic variables (up to 3) however, the subsurface model is often described using a much larger number of variables such as porosity, clay content, fluids content, pressure etc. Through the use of a Petro-Elastic Model (PEM), it is possible to link the petrophysical properties to the elastic ones, but this forward model is not easily reversible as a given combination of elastic attributes (P -Impedance, Vp/Vs ratio...) can result from many possible combinations of petrophysical properties. Our adaptive ensemble optimization approach addresses this issue by sampling the solution space of this non-linear non-convex quadratic inverse problem 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 to reduce the mismatch between the elastic response given by the PEM and the elastic attributes. This update is given by a Gauss-Newton like approach where 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 after the inversion process. We apply this technique on an on-shore clastic gas field in Pakistan, as part of an integrated multi-disciplinary workflow to obtain a robust, high-resolution static model integrating geology, sedimentology, petrophysics and seismic data. Stochastic modelling techniques are used to create three scenarios of varying levels of seismic influence, for a more rigorous uncertainty analysis.