Geostatistical three-dimensional modeling of the subsurface unconsolidated materials in the Göttingen area

Abstract

Having a plenty of geotechnical records and measurements in Göttingen area, a subsurface three-dimensional model of the unconsolidated sediment classes was required. To avoid the repetition of the long expressions, from this point on, these unconsolidated materials which vary from the loose sediments to the hard rocks has been termed as “soil”, “category”, “soil class” or “soil category”. These sediments which are intermediate between the hard bed-rock and loose sediments (soils) were categorized based on the geotechnical norms of the DIN 18196. In this study, the aim was to evaluate the capabilities of the application of geostatistical estimation and simulation methods in modeling the subsurface heterogeneities, especially about the geotechnical soil classes. Such a heterogeneity modeling is a crucial step in a variety of applications such as geotechnics, mining, petroleum engineering, hydrogeology, and so on. For an accurate modeling of the essential continuous parameters, such as the ore grades, porosity, permeability, and hydraulic conductivity of a porous medium, the precise delineation of the facies or soil category boundaries prior to any modeling step is necessary. The focus of this study is on a three-dimensional modeling and delineation of the unconsolidated materials of the subsurface using the geostatistical methods. The applied geostatistical methods here consisted of the pixel-based conventional and transition-probability Markov chain-based geostatistical methods. After a general statistical evaluation of different parameters, the presence and absence of each category along the sampling boreholes was coded by new parameters called indicators. The indicator of a category in a sampling point is one (1) when the category exists and zero (0) when it is absent. Some intermediate states can also be found. For instance, the indicator of a two categories can be assigned to 0.5 when both the categories probably exist at that location but it is unsure which one exactly presents at that location. Moreover, to increase the stationarity characteristic of the indicator variables, the initial coordinates were transformed into a new system proportional to the top and bottom of the modeled layer as a first modeling step. In the new space, to conduct the conventional geostatistical modeling, the indicator variograms were calculated and modeled for each category in a variety of directions. In this text, for easier reference to the semi-variograms, the term variogram has been applied instead. II Using the indicator kriging, the probability of the occurrence of each category at each modeling node was estimated. Based on the estimated probabilities of the existence of each soil category from the previous stage, the most probable category was assigned to each modeling point then. Moreover, the employed indicator variogram models and indicator kriging estimation parameters were validated and improved. The application of a less number of samples were also tested and suggested for similar cases with a comparable precision in the results. To better reflect the fine variations of the categories, the geostatistical simulation methods were applied, evaluated, and compared together. The employed simulation methods consisted of the sequential indicator simulation (SISIM) and the transition probability Markov chain (TP/MC). The conducted study here suggested that the TP/MC method could generate satisfactory results especially compared to those of the SISIM method. Some reasons were also brought and discussed for the inefficiency of the other facies modeling alternatives for this application (and similar cases). Some attempts for improving the TP/MC method were also conducted and a number of results and suggestions for further researches were summarized here. Based on the achieved results, the application of the TP/MC methods was advised for the similar problems. Besides, some simulation selection, tests, and assessment frameworks were proposed for analogous applications. In addition, some instructions for future studies were made. The proposed framework and possibly the improved version of it could be further completed by creating a guided computer code that would contain all of the proposed steps. The results of this study and probably its follow-up surveys could be of an essential importance in a variety of important applications such as geotechnics, hydrogeology, mining, and hydrocarbon reservoirs.