Recent advances in geomathematics in Croatia: examples from subsurface geological mapping and biostatistics

http://sherpa.ac.uk/romeo/issn/2076-3263/Geomathematics is extremely important in geosciences, particularly in the geology. The key for any geomathematical analysis is the definition of a typical model to be applied for further prognosis, either through deterministic or stochastic approaches. The selection of the appropriate procedure is presented in this paper. Two different geomathematical subfield datasets were used in subsurface geological mapping and palaeontology and different biostatistics applications, representing important geomathematical subfields in the Croatian geology. The different subsurface interpolation methods tested, validated and recommended for application were used to obtain the best possible outcome in reservoir modelling, in the cases with small datasets. Cross- validation may be chosen as the main selection criteria, applied to the Croatian part of the Pannonian Basin System (CPBS). Recent advances in biostatistics applied in palaeontology and case studies from Croatia are also presented, where biometric studies are of significant importance in fossil biota. Data, methods and problems in geosciences are vast subjects, and address a wide spectrum of fundamental science. Because geology includes subsurface and surface geology, and very different datasets regarding variable and number of data, we have chosen here two representative case study groups with original samples from Northern Croatia. Subsurface mapping has been presented on limited petrophysical datasets from the Northern Croatian, Miocene, hydrocarbon reservoirs. Biostatistics have been presented on very different samples, allowing us to achieve paleoenvironmental reconstructions of the size of relevant fossils, such as dinosaurs or other species and their paleoenvironments. All examples highlight examples of the valuable application of geomathematical tools in geology. The results, cautiously validated and correlated with other, non-numerical (indicator, categorical) geological knowledge, are of enormous assistance in creating better geological models.info:eu-repo/semantics/publishedVersio

High-resolution truncated plurigaussian simulations for the characterization of heterogeneous formations

Integrating geological concepts, such as relative positions and proportions of the different lithofacies, is of highest importance in order to render realistic geological patterns. The truncated plurigaussian simulation method provides a way of using both local and conceptual geological information to infer the distributions of the facies and then those of hydraulic parameters. The method (Le Loc'h and Galli 1994) is based on the idea of truncating at least two underlying multi-Gaussian simulations in order to create maps of categorical variable. In this manuscript we show how this technique can be used to assess contaminant migration in highly heterogeneous media. We illustrate its application on the biggest contaminated site of Switzerland. It consists of a contaminant plume located in the lower fresh water Molasse on the western Swiss Plateau. The highly heterogeneous character of this formation calls for efficient stochastic methods in order to characterize transport processes.Comment: 12 pages, 9 figure

Fractal relationships and spatial distribution of ore body modelling

The nature of spatial distributions of geological variables such as ore grades is of primary concern when modelling ore bodies and mineral resources. The aim of any mineral resource evaluation process is to determine the location, extent, volume and average grade of that resource by a trade off between maximum confidence in the results and minimum sampling effort. The principal aim of almost every geostatistical modelling process is to predict the spatial variation of one or more geological variables in order to estimate values of those variables at locations that have not been sampled. From the spatial analysis of these variables, in conjunction with the physical geology of the region of interest, the location, extent and volume, or series of discrete volumes, whose average ore grade exceeds a specific ore grade cut off value determined\u27 by economic parameters can be determined, Of interest are not only the volume and average grade of the material but also the degree of uncertainty associated with each of these. Geostatistics currently provides many methods of assessing spatial variability. Fractal dimensions also give us a measure of spatial variability and have been found to model many natural phenomenon successfully (Mandelbrot 1983, Burrough 1981), but until now fractal modelling techniques have not been able to match the versatility and accuracy of geostatistical methods. Fractal ideas and use of the fractal dimension may in certain cases provide a better understanding of the way in which spatial variability manifests itself in geostatistical situations. This research will propose and investigate a new application of fractal simulation methods to spatial variability and spatial interpolation techniques as they relate to ore body modelling. The results show some advantages over existing techniques of geostatistical simulation

Hydraulic Tomography: 3D Hydraulic Conductivity, Fracture Network, and Connectivity in Mudstone

We present the first demonstration of hydraulic tomography (HT) to estimate the three‐dimensional (3D) hydraulic conductivity (K) distribution of a fractured aquifer at high‐resolution field scale (HRFS), including the fracture network and connectivity through it. We invert drawdown data collected from packer‐isolated borehole intervals during 42 pumping tests in a wellfield at the former Naval Air Warfare Center, West Trenton, New Jersey, in the Newark Basin. Five additional tests were reserved for a quality check of HT results. We used an equivalent porous medium forward model and geostatistical inversion to estimate 3D K at high resolution (K blocks m3), using no strict assumptions about K variability or fracture statistics. The resulting 3D K estimate ranges from approximately 0.1 (highest‐K fractures) to approximately 10−13 m/s (unfractured mudstone). Important estimated features include: (1) a highly fractured zone (HFZ) consisting of a sequence of high‐K bedding‐plane fractures; (2) a low‐K zone that disrupts the HFZ; (3) several secondary fractures of limited extent; and (4) regions of very low‐K rock matrix. The 3D K estimate explains complex drawdown behavior observed in the field. Drawdown tracing and particle tracking simulations reveal a 3D fracture network within the estimated K distribution, and connectivity routes through the network. Model fit is best in the shallower part of the wellfield, with high density of observations and tests. The capabilities of HT demonstrated for 3D fractured aquifer characterization at HRFS may support improved in situ remediation for contaminant source zones, and applications in mining, repository assessment, or geotechnical engineering

Development of Optimal Geostatistical Model for Geotechnical Applications

Evaluation and application of various geo-statistical interpolation techniques (including deterministic and probabilistic methods) to site characterization has received much attention in the recent years (Rouhani 1996, Fenton 1997, Asa et al 2012). However, the existing geo-statistical tools in their original form lack several inbuilt functionalities including hypothesis based normality check for the data; positional outlier separation; automated selection of base variogram and optimal kriging model; and elimination of negative kriging weights. This research addresses these issues, and aims at developing a generalized, public domain, open source and optimal linear geo-statistical model using MATLAB environment that best fits a given set of site specific parameters. The measured data at the random borehole locations were analyzed, and used to generate the prediction and error surfaces of the site parameters at user specified intervals. Normality of the data was statistically tested using Kolmogorov‐Smirnov test at 5 and 10% significance levels. Positional outliers that may adversely affect the simulation were discarded from the analysis using the concept of point density. The best semi-variogram with optimum searching neighbourhood was automated using residual statistics. Negative kriging weights given at the known data locations were successively eliminated in the algorithm. A graphical user interface (GUI) in MATLAB for use with site managers / construction engineers of a region was developed in this wor

Seismic chronostratigraphy for reservoir characterization : modeling and applications

The assumption of the chronostratigraphic significance of seismic reflections serves as a fundamental premise in interpreting stratigraphy from seismic images. This hypothesis proposed in 1977 was initially applied to delineate depositional sequences as the basic interpretive unit, and then to reconstruct Wheeler Diagram and regional sea level curves. After a further comparison against with global eustatic events, these regional curves can further facilitate predicting the age, distribution, and facies of depositional sequence before drilling in a seismic-covered area during petroleum exploration. With a boom in reservoir-level seismic applications, for obtaining significant high frequency sequence (HFS) surfaces as the bounding surfaces in static reservoir model construction, this fundamental assumption was inevitably extended to characterize HFS and even high-frequency cycles (HFC) during seismic reservoir characterization. For an ultimate improvement in constructing reservoir-bounding surfaces, the author targeted at evaluating the validity of this fundamental assumption as applied to high-order seismic stratigraphy. The author conducted the entire project via the forward seismic modeling upon geologic models with known chronostratigraphic relationship. Besides, these input models carefully honor the reservoir geology for meaningful discussions on (1) shallow marine siliciclastic reservoirs in Starfak Field, GoM, (2) shallow-water mixed carbonate/clastic Upper San Andres-Grayburg reservoirs in Permian Basin, and (3) shallow-water carbonate Abo shelf margin-Clear Fork platform in Permian Basin. This study has achieved three-fold contributions. On the aspect of realistic geocellular, property and seismic modeling at the reservoir scale, the author integrated high-resolution sequence stratigraphic framework, published 3D depositional model, intra-facies heterogeneity in 3D modeling to selectively apply advanced geostatistical methods to model hierarchical heterogeneity. Subsequently, the author proposed an evaluation scheme with a defined parameter ('time-correlation error/TCE') to assess HFS-scale reservoir-bounding surfaces. These assessments revealed an interactive influence from (1) stratal geometry, (2) lateral lithofacies variation, (3) lithofacies-sonic velocity relationship in pure- versus mixed-lithology successions, (4) intra-facies heterogeneity, and (5) seismic frequency. Finally, based on these forward modeling results, the author proposed a decision tree to determine valid interpretation strategy in seismic chronostratigraphic correlation in scenarios with geoscientists’ expert knowledge and recommended an attribute-driven volumetric picking scheme to improve published algorithms for scenarios without prior knowledge.Geological Science

Adequate model complexity and data resolution for effective constraint of simulation models by 4D seismic data

4D seismic data bears valuable spatial information about production-related changes in the reservoir. It is a challenging task though to make simulation models honour it. Strict spatial tie of seismic data requires adequate model complexity in order to assimilate details of seismic signature. On the other hand, not all the details in the seismic signal are critical or even relevant to the flow characteristics of the simulation model so that fitting them may compromise the predictive capability of models. So, how complex should be a model to take advantage of information from seismic data and what details should be matched? This work aims to show how choices of parameterisation affect the efficiency of assimilating spatial information from the seismic data. Also, the level of details at which the seismic signal carries useful information for the simulation model is demonstrated in light of the limited detectability of events on the seismic map and modelling errors. The problem of the optimal model complexity is investigated in the context of choosing model parameterisation which allows effective assimilation of spatial information in the seismic map. In this study, a model parameterisation scheme based on deterministic objects derived from seismic interpretation creates bias for model predictions which results in poor fit of historic data. The key to rectifying the bias was found to be increasing the flexibility of parameterisation by either increasing the number of parameters or using a scheme that does not impose prior information incompatible with data such as pilot points in this case. Using the history matching experiments with a combined dataset of production and seismic data, a level of match of the seismic maps is identified which results in an optimal constraint of the simulation models. Better constrained models were identified by quality of their forecasts and closeness of the pressure and saturation state to the truth case. The results indicate that a significant amount of details in the seismic maps is not contributing to the constructive constraint by the seismic data which is caused by two factors. First is that smaller details are a specific response of the system-source of observed data, and as such are not relevant to flow characteristics of the model, and second is that the resolution of the seismic map itself is limited by the seismic bandwidth and noise. The results suggest that the notion of a good match for 4D seismic maps commonly equated to the visually close match is not universally applicable