Regionalized multiple-point statistical simulation for calibrating process-based geologic models to seismic data

Abstract

Calibrating process-based geologic models to seismic data is critical and has been challenging for decades. The traditional approach to data calibration involves tuning the model input parameters by trial-and-error or through an automated inverse procedure. This can improve the model calibration to data but can hardly reach a fully satisfactory result. We adopt a multiple-point statistics (MPS) approach where a process-based geologic model is used as a training image for statistical pattern recognition. First, we define a rock-physics model from the process-based geologic model and derive its seismic attributes through seismic forward modeling. Then, we use the process-based model and its seismic attributes as coupled training images for geologic pattern recognition and regeneration under seismic data constraints. The method differs from the conventional MPS method in several ways: (1) the training image is a process-based geologic model of the reservoir of interest, thus defined on the same grid of the reservoir model; (2) the training image is generally nonstationary but there is no need to partition the nonstationary training image into pseudostationary ones; (3) the geologic facies and seismic constraint are related through seismic forward modeling instead of statistical inference, thus there is no need to convert seismic data to facies proportion or probability; (4) multiple-point statistics are based on Bayes’ law and Gaussian kernel approximation of conditional probability instead of a somehow arbitrary probability combination scheme or a heuristic rule; and (5) the method does not involve an iterative optimization procedure. Therefore, it also differs from the neural-network-based machine-learning approach, where the data conditioning is achieved through an iterative optimization procedure. These differences make our method advantageous for calibrating process-based geologic models. The two examples with synthetic data illustrate the effectiveness of the method. The first one is derived from a satellite image of a river delta, and the second one from the Stanford VI reservoir model.