Locality-based 3-D multiple-point statistics reconstruction using 2-D geological cross sections

Abstract

Abstract. Multiple-point statistics (MPS) has shown promise in representing complicated subsurface structures. For a practical three-dimensional (3-D) application, however, one of the critical issues is the difficulty in obtaining a credible 3-D training image. However, bidimensional (2-D) training images are often available because established workflows exist to derive 2-D sections from scattered boreholes and/or other samples. In this work, we propose a locality-based MPS approach to reconstruct 3-D geological models on the basis of such 2-D cross sections (3DRCS), making 3-D training images unnecessary. Only several local training subsections closer to the central uninformed node are used in the MPS simulation. The main advantages of this partitioned search strategy are the high computational efficiency and a relaxation of the stationarity assumption. We embed this strategy into a standard MPS framework. Two probability aggregation formulas and their combinations are used to assemble the probability density functions (PDFs) from different subsections. Moreover, a novel strategy is adopted to capture more stable PDFs, where the distances between patterns and flexible neighborhoods are integrated on multiple grids. A series of sensitivity analyses demonstrate the stability of the proposed approach. Several hydrogeological 3-D application examples illustrate the applicability of the 3DRCS approach in reproducing complex geological features. The results, in comparison with previous MPS methods, show better performance in portraying anisotropy characteristics and in CPU cost.

Extended GOSIM: MPS‐Driven Simulation of 3D Geological Structure Using 2D Cross‐Sections

“…The 3DRCS algorithm (Chen et al., 2018) can build 3D geological structures that are similar to this example. Therefore, we calculated 10 simulation results by the 3DRCS algorithm, of which the best result is shown in Figure 22.…”

An enhanced dual IDW method for high-quality geospatial interpolation

“…In future work, the author plans to empower DIDW with enough capabilities in accounting for complex spatial dependency 42 – 44 and finding more efficient means to seek appropriate LVEs.…”

Entropy Evaluation Method for Sandstone Uranium Reservoir Characteristics Based on Convex Hull Search

“…Multiplicative methods include Bordley [38] and Tau models and log-linear pooling [39] (based on odd ratios). These two formulas have been proven to be equivalent for cases with only two attributes, but the latter has better performance for non-binary events [40]. In the field of geosciences, the concurrency of events is more emphasized; that is, two or more events act simultaneously and output a final result.…”