Rock-physics-guided petrophysical seismic AVA inversion using the Levenberg-Marquardt algorithm

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Seismic petrophysical inversion aims to predict petrophysical properties, such as porosity, lithology, and fluid saturation, given a set of seismic measurements by combining inversemethods with AVO and rock physics models. Stochastic optimization methods are often used; however, their applicability to real cases is limited by the large computational costs due to the size of the data and the required number of iterations. We propose a deterministic approach based on the Gauss-Newton inversion using the Levenberg-Marquardt algorithm. This nonlinear optimization algorithm calculates the Hessian matrix using the sum of outer products of the gradients. The novelty of the work is the analytical calculation of the Jacobian matrix of the seismic and rock physics models. In the proposed implementation, the partial derivatives of the seismic properties with respect to the petrophysical properties are expressed in a closed form. In our implementation, we test the inversion with a seismic AVO convolutional model combined with the soft sand model; however, the proposed inversion method can be extended to any geophysical model. The proposed method has been tested and validated on a simulated synthetic dataset based on field data measured offshore Norway. The results prove that the proposed method is robust and efficient in predicting petrophysical properties from seismic data.