Transition probability‐based stochastic geological modeling using airborne geophysical data and borehole data

Abstract

Geological heterogeneity is a very important factor to consider when developing geological models for hydrological purposes. Using statistically based stochastic geological simulations, the spatial heterogeneity in such models can be accounted for. However, various types of uncertainties are associated with both the geostatistical method and the observation data. In the present study, TProGS is used as the geostatistical modeling tool to simulate structural heterogeneity for glacial deposits in a head water catchment in Denmark. The focus is on how the observation data uncertainty can be incorporated in the stochastic simulation process. The study uses two types of observation data: borehole data and airborne geophysical data. It is commonly acknowledged that the density of the borehole data is usually too sparse to characterize the horizontal heterogeneity. The use of geophysical data gives an unprecedented opportunity to obtain high-resolution information and thus to identify geostatistical properties more accurately especially in the horizontal direction. However, since such data are not a direct measurement of the lithology, larger uncertainty of point estimates can be expected as compared to the use of borehole data. We have proposed a histogram probability matching method in order to link the information on resistivity to hydrofacies, while considering the data uncertainty at the same time. Transition probabilities and Markov Chain models are established using the transformed geophysical data. It is shown that such transformation is in fact practical; however, the cutoff value for dividing the resistivity data into facies is difficult to determine. The simulated geological realizations indicate significant differences of spatial structure depending on the type of conditioning data selected. It is to our knowledge the first time that grid-to-grid airborne geophysical data including the data uncertainty are used in conditional geostatistical simulations in TProGS. Therefore, it provides valuable insights regarding the advantages and challenges of using such comprehensive data.

Challenges in conditioning a stochastic geological model of a heterogeneous glacial aquifer to a comprehensive soft data set

“…The descriptions in the borehole reports are converted to a categorical binary (sand/clay) system at 5 cm vertical discretization. Further, each borehole's uncertainty is validated according to the method of He et al (2014). The uncertainty assessment allows for definition of individual trust scores and thus the definition of how much each borehole should constrain the conditional simulation in the form of soft data.…”

“…This supports the use of geophysical data only for the lateral model of spatial variability and incorporation of the fine descriptions from the borehole data for the vertical model of spatial variability. He et al (2014) developed a method to manually calibrate the cutoff value by comparing borehole with SkyTEM data at different spatial domains with the aim to reduce the deviation in sand proportion between the two data types. It is assumed that the deviation has to be minimized at domains with a high borehole density where the boreholes are assumed to best represent the domain conditions.…”

“…Further, He et al (2014) developed a histogram probability matching (HPM) method that enables a direct translation from resistivity into facies probability. Resistivity is paired with the lithological borehole description at the coinciding cell.…”

Integrating deterministic lithostratigraphic models in stochastic realizations of subsurface heterogeneity. Impact on predictions of lithology, hydraulic heads and groundwater fluxes

“…With the transition probability approach, the spatial structure of geological data is modelled by mathematical functions (i.e., Markov chain models) relating transition probabilities to distance. Although this is a two-point geostatistical method, geological knowledge can be taken into account in the determination of the coefficients of these functions, which can be directly related to interpretable geological properties including proportions of each facies, mean lengths, connectivity, and juxtapositional tendencies (e.g., Carle et al, 1998;Weissmann and Fogg, 1999;Ritzi, 2000;Lee et al, 2007;He et al, 2014a;Bianchi et al, 2015).…”

“…The use of additional "soft" data consisting of indirect observations of geological properties, as well as qualitative and interpretative information (e.g., geophysical surveys or conceptualizations of the depositional system) has been shown to be effective to overcome limitations due to the lack of direct observations (Elfeki et al,1995;Copty and Rubin, 1995;Hyndman and Gorelick, 1996;Liu et al, 2004;Elfeki, 2006;Emery and Robles, 2009;Ye and Khaleel, 2008;Engdal et al, 2010;He et al, 2014a). He et al (2014a), for example, developed a stochastic model of the distribution of sand and clay in glacial deposits based on both soft geophysical data from airborne electromagnetic surveys and hard borehole observations. Validation analysis conducted on a subset of the borehole data showed that soft conditioning (i.e., conditioning to the soft data) significantly improved the accuracy of lithology predictions for the sand units, for which there was a scarcity of direct observations.…”