Stochastic nonlinear inversion of seismic data for the estimation of petroelastic properties using the ensemble smoother and data reparameterization

We have developed a new stochastic nonlinear inversion method for seismic reservoir characterization studies to jointly estimate elastic and petrophysical properties and to quantify their uncertainty. Our method aims to estimate multiple reservoir realizations of the entire set of reservoir properties, including seismic velocities, density, porosity, mineralogy, and saturation, by iteratively updating the initial ensemble of models based on the mismatch between their seismic response and the measured seismic data. The initial models are generated using geostatistical methods and the geophysical forward operators include rock-physics relations and a seismic forward model. The optimization is achieved using an iterative ensemble-based algorithm, namely, the ensemble smoother with multiple data assimilation, in which each iteration is based on a Bayesian updating step. The advantages of the proposed method are that it can be applied to nonlinear inverse problems and it can provide an ensemble of solutions from which we can quantify the uncertainty of the model properties of interest. To reduce the computational cost of the inversion, we perform the optimization in a lower dimensional data space reparameterized by singular value decomposition. The proposed methodology is validated on a synthetic case in which the set of petroelastic properties is recovered with satisfactory accuracy. Then, we applied the inversion method to a real seismic data set from the Norne field in the Norwegian Sea.