Methods based on multiple-point statistics (MPS) have been routinely used to characterize complex geological formations in the last decade. These methods use the available static data (for example, measured conductivities) for conditioning. Integrating dynamic data (for example, measured transient piezometric head data) into the same framework is challenging because of the complex non-linear relationship between the dynamic response and geology. The Ensemble PATtern (EnPAT) search method was recently developed as a promising technique to handle this problem. In this approach, a pattern is postulated to be composed of both parameter and state variables, and then, parameter values are sequentially (point-wise) simulated by directly sampling the matched pattern from an ensemble of training images of both geologic parameters and state variables. As a consequence, the updated ensemble of realizations of the geological parameters preserve curvilinear structures (i.e., non-multiGaussanity) as well as the complex relationship between static and dynamic data. Moreover, the uncertainty of flow and transport predictions can be assessed using the updated ensemble of geological models. In this work, we further modify the EnPAT method by introducing the pilot-point concept into the algorithm. More specifically, the parameter values at a set of randomly selected pilot point locations are simulated by the pattern searching procedure, and then a faster MPS method is used to complete the simulation by conditioning to the previously simulated pilot point values. This pilot point guided MPS implementation results in lower computational cost and more accurate inference of the parameter field. In addition, in some situations where there is sparsity of measured geologic static data, the EnPAT algorithm is extended to work only with the dynamic data. We employed a synthetic example to demonstrate the effectiveness of pilot points in the implementation of EnPAT, and also the capability of dynamic data to identify complex geologic structures when measured conductivity data are not available.
All Science Journal Classification (ASJC) codes
- Water Science and Technology