Introducing one, two, and three term inversion algorithms to estimate the input parameters for the rock physics modelling using well logs

Rock physics models are extensively used in reservoir geophysics and quantitative seismic interpretations. To ensure the accuracy of the final estimations, the proper approximation of the input parameters is vital. Among these inputs are mineral elastic moduli, pore aspect ratio, and porosity. In this research, the algorithm proposed by Jalini and Falahat in 2021 is revisited to develop four new algorithms. These algorithms, along with the original method are then employed in a carbonate gas reservoir. First, the improved Jalini–Falahat model is introduced. In this algorithm, Jalini and Falahat’s model is modified using a combination of the finite difference method and Broyden’s numerical approximation of Jacobian. This version of the algorithm estimates the mineral elastic moduli and pore aspect ratio eight times faster than the original method and will be useful in large data sets. To evaluate the results, the approximations are utilized to recalculate compressional and shear velocity ( \({V}_{P}\) $V_P$ and \({V}_{S}\) $V_S$ ) logs. The mean relative error for this method is in the similar range as the original one (less than \({10}^{-3}\) ${10}^{-3}$ % for \({V}_{P}\) $V_P$ and 2.97% for \({V}_{S}\) $V_S$ ). Secondly, the two-parameter inversion method is presented, in which both \({V}_{P}\) $V_P$ and \({V}_{S}\) $V_S$ are used in the estimation of mineral elastic moduli and pore aspect ratio. Employing compressional and shear velocities in this procedure includes both lithology and fluid effects, which improves the estimation of elastic moduli and aspect ratio in highly porous zones and reduces the mean relative error of \({V}_{S}\) $V_S$ to \(6\times {10}^{-6}\) $6\times {10}^{-6}$ %. As the next step, the full inversion method is introduced. Here, the porosity values are estimated along with the mineral elastic moduli and pore aspect ratio, both in the absence of density data (the full inversion) and its presence (the three-parameter full inversion). The mean absolute errors between the estimated values of porosity and the measured logs are less than 1% (0.98% and 0.3%, respectively), which ensures the accuracy of the method.