Facies-Constrained Kriging Interpolation Method for Parameter Modeling

In seismic exploration, establishing a reliable parameter model (such as velocity, density, impedance) is crucial for seismic migration imaging and reservoir characterization. The interpolation of well data to obtain a complete spatial model is an important aspect of parameter modeling. However, in practical applications, well data are often sparse and irregularly distributed, which complicates the accurate construction of subsurface parameter models. The Kriging method is an effective interpolation method based on discrete well data, but its theoretical assumptions do not meet the practical requirements in seismic exploration, resulting in low modeling accuracy. This article introduces seismic facies information into the Kriging method and proposes a novel parameter modeling method named the facies-constrained Kriging (FC-Kriging) method. The FC-Kriging method modifies the Euclidean distance metric used in Kriging so that the distance between two points depends not only on their spatial coordinates but also on their associated facies categories. The proposed method is a multi-information fusion method that integrates facies information based on well data, enabling good interpolation results even with a limited number of wells. The parameter modeling results based on the FC-Kriging method are more consistent with geological logic, exhibiting clearer boundary features and higher resolution. Furthermore, the FC-Kriging method does not introduce additional computational complexity, making it convenient to implement in a 3D situation. The FC-Kriging method is applied to the 2D Sigsbee model, the 3D Standford V reservoir model and F3 block field data. The results demonstrate its accuracy and effectiveness.