Mathematical Geosciences

The purpose of this study was to capture the structure of a geological process within a multivariate statistical framework by using geological data generated by that process and, where applicable, by associated processes. It is important to the practitioners of statistical analysis in geology to determine the degree to which the geological process can be captured and explained by multivariate analysis by using sample data (for example, chemical analyses) taken from the geological entity created by that process. The process chosen for study here is the creation of a coal deposit. In this study, the data are chemical analyses expressed in weight percentage and parts per million, and therefore are subject to the affects of the constant sum phenomenon. The data array is the chemical composition of the whole coal. This restriction on the data imposed by the constant sum phenomenon was removed by using the centered logratio (clr) transformation. The use of scatter plots and principal component biplots applied to the raw and centered logratio (clr) transformed data arrays affects the interpretation and comprehension of the geological process of coalification.

Việc đặc trưng hóa các cấu trúc trầm tích bị chôn vùi thông qua việc sử dụng dữ liệu địa chấn là một phần của nhiều dự án địa chất. Sự tiến bộ trong khả năng thu thập và xử lý địa chấn đã cho phép thu thập một lượng dữ liệu ngày càng tăng, tăng cường độ phân giải hình ảnh để các đối tượng trầm tích (cơ thể địa chất) có thể được hình ảnh hóa với độ chính xác cao hơn trong các lớp trầm tích. Tuy nhiên, việc khám phá và giải thích chúng trong các tập dữ liệu lớn có thể là một công việc tốn thời gian. Thực tiễn gần đây đã cho thấy tiềm năng của các phương pháp tự động để hỗ trợ những người giải thích trong nhiệm vụ này. Trong giấy này, một phương pháp nửa giám sát mới được trình bày để xác định các cơ thể địa chất nhiều facies trong dữ liệu địa chấn ba chiều, đồng thời bảo quản sự biến đổi nội tại của chúng và theo dõi độ không chắc chắn của đầu vào. Phương pháp này kết hợp một phương pháp dựa trên dữ liệu phi tuyến tính với một phương pháp học có giám sát mới. Nó yêu cầu một sự phân định trước của các cơ thể địa chất trên một vài hình ảnh địa chấn, cùng với sự tự tin trước vào sự phân định đó. Phương pháp này dựa vào việc học một đại diện dữ liệu phù hợp, và truyền đạt sự tự tin trước đến xác suất sau cho sự phân định cuối cùng. Phương pháp đề xuất đã được áp dụng cho dữ liệu thực ba chiều, cho thấy khả năng lấy lại liên tục và hiệu quả các cơ thể địa chất nhiều facies trong các bể trầm tích chuyển giao khối lượng trong trường hợp này.

Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided.

Geochemical data used in geological interpretation of mine deposits and identification of geological domains often contain outliers. Undertaking statistically sound and robust decision-making about outliers (such as deciding whether observations under consideration belong to a given domain) can be a challenging task. Traditional statistical procedures are often poorly suited to the noisy, intrinsically multivariate and high-dimensional nature of geochemical data. We present herein a novel approach for detecting outliers robustly in large multi-dimensional geochemical data. The approach incorporates a feature selection method that automatically seeks the best subset of chemical ratios that, together with the original chemical variables, best represent the inherent characteristics of the data. The proposed approach robustly distinguishes outliers even at high contamination levels. Experimental results demonstrating the advantages of the proposed feature selection algorithm over previous methods used in outlier detection are shown using data from an iron ore deposit located in the Brockman Iron Formation of Hamersley Province, Western Australia.

Both water level drops and erosion have previously been suggested as causes of fluid overpressures in the subsurface. Quantification of the relevance of these processes to supra-lithostatic fluid pressure formation with a wide selection of input parameters is lacking, and thus desired. The magnitudes and drop times that are required for water level drops to result in supra-lithostatic pore pressures in a variety of situations are calculated. Situations with pore fluids consisting of water, water with dissolved methane, water with a gas hydrate layer and dissolved methane in the underlying sediments, and water with dissolved methane, a gas hydrate layer, and free gas accumulation below the hydrate layer are separately addressed. The overpressure formation from reservoir gas expansion is also simulated. The simulation results demonstrate that high fluid overpressures can develop in a rock as a response to a water level drop without the presence of gas, provided that the rock has a sufficiently low compressibility. The contribution to fluid overpressuring is however dramatically increased if the pore water is saturated with methane prior to the water level drop, and is further amplified by the presence of gas hydrates and free gas accumulations beneath such hydrates. Gas expansion in reservoirs should be expected to significantly increase the fluid overpressures in shallow, sealed pressure compartments that experience erosion or water level drops, even if the water level drop duration exceeds one million years. Enough relationships between the calculated overpressure formation and the main controlling factors are provided in order to enable readers to make inferences about a variety of geological settings. Analyses of simulation results prompt us to suggest that pockmarks are likely to be triggered by gas expansion in vertical fluid migration pathways, that the giant craters at the seabed west of Albatross South in the Barents Sea result from hydrate dissociation, and that overpressure build-up due to gas expansion has contributed to reservoir overpressuring in many eroded basins, including the Hammerfest Basin in the Barents Sea.

This paper aims at providing a flexible and compact volumetric object model capable of representing many sedimentary structures at different scales. Geobodies are defined by a boundary representation; each bounding surface is constructed as a parametric deformable surface. A three-dimensional sedimentary object with a compact parametrization which allows for representing various geometries and provides a curvilinear framework for modeling internal heterogeneities is proposed. This representation is based on non-uniform rational basis splineswhich smoothly interpolate between a set of points. The three-dimensional models of geobodies are generated using a small number of parameters, and hence can be easily modified. This can be done by a point and click user interaction for manual editing or by a Monte-Carlo sampling for stochastic simulation. Each elementary shape is controlled by deformation rules and has connection constraints with associated objects to maintain geometric consistency through editing. The boundary representations of the different sedimentary structures are used to construct hexahedral conformal grids to perform petrophysical property simulations following the particular three-dimensional parametric space of each object. Finally these properties can be upscaled, according to erosion rules, to a global grid that represents the global depositional environment.