A Pareto Multi‐Objective Optimization Approach for Anisotropic Shale Models. Issue 7 (16th July 2021) - Zidan, A.; Li, Y. E.; Cheng, A.
Abstract: When the elastic parameters of rocks such as shales vary with the propagation direction of a passing seismic wave that rock is called anisotropic. Modern seismic data are typically acquired over a wide azimuth range using long offsets. For such data, optimum imaging and subsequent quantitative amplitude interpretation requires taking subsurface anisotropy adequately into account during execution of the quantitative interpretation workflow. Here, we present a multi‐objective approach to find an optimal solution using both well logs and seismic data. We include minimization of a seismic match objective function as a constraint to narrow the uncertainty distribution around model parameters and to ensure that the model is consistent with seismic as well as well log data. Consequently, the resulting anisotropy model can be used for both well logs and seismic data analysis. First, the Hudson‐Cheng crack model is used to obtain rock matrices properties and aspect ratio of a set of ellipsoidal cracks. Then, we obtain a set of non‐dominated solutions, which minimizes the rock physics model multi‐parameter objective function and the Amplitude‐Versus‐Offset objective function. The approach is applied to field data with one vertical well log and pre‐stack migrated seismic data. In spite of the low signal‐to‐noise ratio of the seismic data, the overall results are consistent with the rock physics model and fit the seismic amplitude variations, particularly for the confidently interpretable mid‐to‐far angles of incidence. Furthermore, we extend the approach to predict seismic anisotropy away from well calibration, to map the occurrence of high‐quality organic‐rich shales. Plain Language Summary: Anisotropy is defined as the change in elastic properties with propagation direction. In case of highly anisotropic rock layers, that is, shale rocks, isotropic models fail to predict the effective moduli of the medium, and subsequently leading to false lithology and fluid predictions. Since we cannot directly measure elastic anisotropy from well logs, rock physics models are built to estimate the effective moduli of the medium, and subsequently the elastic anisotropy. In this study, we propose a multi‐objective approach that uses well log and seismic data to obtain the effective moduli of a vertical transverse isotropy medium, in which ellipsoidal thin cracks are added to an isotropic background. The proposed workflow is applied to a field well log data set, consisting of shale, siltstone, and mudstone rock layers. The resulting anisotropy parameters are in good agreement with the well logs and seismic data, which can be used to map the high‐quality shale‐gas zones across the seismic array. Key Points: A multi‐objective genetic algorithm is proposed to estimate seismic anisotropy that fits both log data and seismic amplitudes The additional seismic amplitude constraints greatly reduce the uncertainties in the anisotropy parameters Predicted seismic anisotropy away from well log location has the potential to indicate resource volume and rock brittleness