Multiple-point statistical simulation for hydrogeological models: 3-D training image development and conditioning strategies

Abstract

Abstract. Most studies on the application of geostatistical simulations based on multiple-point statistics (MPS) to hydrogeological modelling focus on relatively fine-scale models and concentrate on the estimation of facies-level structural uncertainty. Much less attention is paid to the use of input data and optimal construction of training images. For instance, even though the training image should capture a set of spatial geological characteristics to guide the simulations, the majority of the research still relies on 2-D or quasi-3-D training images. In the present study, we demonstrate a novel strategy for 3-D MPS modelling characterized by (i) realistic 3-D training images and (ii) an effective workflow for incorporating a diverse group of geological and geophysical data sets. The study covers an area of 2810 km 2 in the southern part of Denmark. MPS simulations are performed on a subset of the geological succession (the lower to middle Miocene sediments) which is characterized by relatively uniform structures and dominated by sand and clay. The simulated domain is large and each of the geostatistical realizations contains approximately 45 million voxels with size 100 m × 100 m × 5 m. Data used for the modelling include water well logs, high-resolution seismic data, and a previously published 3-D geological model. We apply a series of different strategies for the simulations based on data quality, and develop a novel method to effectively create observed spatial trends. The training image is constructed as a relatively small 3-D voxel model covering an area of 90 km 2 . We use an iterative training image development strategy and find that even slight modifications in the training image create significant changes in simulations. Thus, this study shows how to include both the geological environment and the type and quality of input information in order to achieve optimal results from MPS modelling. We present a practical workflow to build the training image and effectively handle different types of input information to perform large-scale geostatistical modelling.

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

“…Two-point geostatistics (Pyrcz and Deutsch, 2014;Ritzi, 2000) and object-based methods (Deutsch and Tran, 2002;Maharaja, 2008;Pyrcz et al, 2009) are not effective at reproducing anisotropic features and connectivity patterns properly (Heinz et al, 2003;Klise et al, 2009;Knudby and Carrera, 2005;Vassena et al, 2010) due to the lack of high-order statistics and the difficulty in parameterization. To overcome the abovementioned limitations, multiple-point statistics (MPS) was developed over recent years and has shown prospects in modeling subsurface anisotropic structures, such as porous media, hydrofacies, reservoirs and other sedimentary structures (Dell Arciprete et al, 2012;Hajizadeh et al, 2011;Hu and Chugunova, 2008;Oriani et al, 2014;Pirot et al, 2015;Wu et al, 2006).…”

Response to Reviewer #1

“…5 No matter which MPS algorithm is used, a suitable training image is the fundamental requirement. Although such algorithms are gaining popularity in hydrogeological applications (Hermans et al, 2015;He et al, 2014;Høyer et al, 2017;Hu and Chugunova, 2008;Huysmans et al, 2014;Jha et al, 2014;Mahmud et al, 2015), they still suffer from one vital limitation: the lack of training images, especially for 3-D situations. Object-based or process-based techniques are one possibility to build 3-D training images (de Marsily et al, 2005;de Vries et al, 2009;Feyen and Caers, 2004;Maharaja, 10 2008;Pyrcz et al, 2009).…”

Response to Reviewer #3

“…No matter which MPS algorithm is used, a suitable training image is the fundamental requirement. Although such algorithms are gaining popularity in hydrogeological applications (Hermans et al, 2015;He et al, 2014;Høyer et al, 2017;Hu and Chugunova, 2008;Huysmans et al, 2014;Jha et al, 2014;Mahmud et al, 2015), they still suffer from one vital limitation: the lack of training images, especially for 3-D situations. Object-based or process-based techniques are one possibility to build 3-D training images (de Marsily et al, 2005;de Vries et al, 2009;Feyen and Caers, 2004;Maharaja, 2008;Pyrcz et al, 2009).…”