Choosing between Gaussian and MPS simulation: the role of data information content—a case study using uncertain interpretation data points

Abstract

Integration of geophysical data with information such as from boreholes and expert domain knowledge is often performed as cognitive or explicit geological modeling when generating deterministic geological models of the subsurface. However, such cognitive geological models lack the ability to express the uncertainty of layer boundaries. To remedy the shortcomings of this strategy we propose a novel stochastic methodology combining the efforts of probabilistic data integration and cognitive modeling. We treat geological interpretation points from the cognitive model as uncertain “soft” data. These data are then combined with analogous geology in a probabilistic model. We test two ways of combining and sampling from such a probabilistic model. Firstly, a high-entropy setup based on Gaussian distributions simulation. Secondly, lower entropy (and conceivable more realistic) geological solutions are obtained from multiple-point geostatistics (MPS). We apply both ways of solving the problem at a study site near Horsens, Denmark, where airborne transient electromagnetic measurements, seismic data, and borehole information are available and interpreted in cognitive modeling. We explain the complete framework for integrating the uncertain interpretations in geostatistical simulation. Results show that both the Gaussian simulation and multiple-point geostatistical approach allows satisfactory simulations of uncertain geological interpretations and are consistent with prior geological knowledge. Our results suggest that the number of uncertain data points and their information content play a pivotal role in selecting the most appropriate simulation method for the given framework. MPS simulations allow connectivity in scenarios with few data points due to the low entropy of the model. When the number of soft data increases, Gaussian simulation is less prone to produce simulation artifacts, faster to apply, and could be considered preferential to using MPS simulation.

Introducing INPOX: a method for informed point extraction from geological 2D surfaces exemplified on the Danish national hydrostratigraphic model

“…If some geologically relevant points are available from for example borehole information, it is trivial to include these in the draw by setting the draw probability in the PM to 1. Madsen et al (2021b) suggest using the gradient as a measure to calculate the points that are most relevant for describing the surface. As was the case for the Laplacians, the user would look for areas with a steep gradient.…”

“…Agrawal et al 2006;Boissonnat & Oudot 2006;Harker & O'Leary 2015). However, to our knowledge no method or algorithm is currently available that considers the spatial properties of the surface when sampling points from a (geological) surface, although Hansen (2021) and Madsen et al (2021b) showed that information content differs between points. Thus, the selection of points matters in terms of recreating the essential features of the surface.…”

“…To manipulate the basis probability, a series of probability functions (f 1 (L), f 2 (L), f 3 (L),…) can be introduced that either increases or decreases the basis probability depending on the Laplacian. Madsen et al (2021b) and Enemark et al (2023) argue that major changes in the elevation of a geological surface in manual interpretation models are related to geologically relevant features. This is argued since variations in elevation mainly arise due to active choices made by the interpreter, for example, when mapping rivers, buried valleys and faults.…”

3D multiple-point geostatistical simulation of joint subsurface redox and geological architectures

“…These realizations are generated using stochastic modeling that accounts for the spatial dependency between the model parameters. We choose MPS simulation over, e.g., a two-point geostatistical approach because it is generally more capable of producing realizations with geological realism in terms of correlation and coherency of geological features (Journel and Zhang, 2006;Madsen et al, 2021;Mariethoz and Caers, 2015). Effectively reproducing coherent layers is key for successful subsequent hydrological modeling.…”

Enhancing Estimation Accuracy of Nonstationary Hydrogeological Fields via Geodesic Kernel-based Gaussian Process Regression

“…Both MPS and SGAN methods typically rely on training images as a source of nonstationary spatial statistical information. As noted in literature (Mariethoz, 2018;Madsen et al, 2021), these methods are most effective in when there is a severe scarcity or abundance of information present; however, they may not perform optimally in cases where an intermediate level of geological detail from secondary information such as geophysical data is available, which is the issue addressed in this study.…”