Seismic petrophysical inversion aims to predict petrophysical properties, such as porosity, lithology, and fluid saturation, given a set of seismic measurements by combining inverse methods with amplitude-variation-with-offset (AVO) and rock-physics models. Stochastic optimization methods are often used; however, their applicability to real cases is limited by large computational costs due to the size of the data and the required number of iterations. We develop 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 the 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 our 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, our inversion method can be extended to any geophysical model. Our method has been tested and validated on a simulated synthetic data set based on field data measured offshore Norway. The results prove that our method is robust and efficient in predicting petrophysical properties from seismic data.

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