The Tau Model for Data Redundancy and Information Combination in Earth Sciences: Theory and Application   总被引：3，自引：0，他引：3  

Sunderrajan Krishnan 《Mathematical Geosciences》2008,40(6):705-727

Many decision-making processes in the Earth sciences require the combination of multiple data originating from diverse sources. These data are often indirect and uncertain, and their combination would call for a probabilistic approach. These data are also partially redundant with each other or with all others taken jointly. This overlap in information arises due to a variety of reasons—because the data arises from the same geology, because they originate from the same location or the same measurement device, etc. The proposed tau model combines partially redundant data, each taking the form of a prior probability for the event being assessed to occur given that single datum. The parameters of that tau model measure the additional contribution brought by any single datum over that of all previously considered data; they are data sequence-dependent and also data value-dependent. Data redundancy depends on the sequence in which the data is considered and also on the data values themselves. However, for a given sequence, averaging the tau model parameters over all possible data values leads to exact analytical expressions and corresponding approximations and inference avenues. Information on multiple-point connectivity of permeability arrives from core data, well-test data and seismic data which are defined over varying supports with complex redundancy between these information sources. In order to compute these tau weights for determining connectivity, one needs a model of data redundancy, here expressed as a vectorial training image (Ti) constructed using a prior conceptual knowledge of geology and the physics of data measurement. From such a vectorial Ti, the tau weights can be computed exactly. Neglecting data redundancy leads to an over-compounding of individual data information and the possible risk of making extreme decisions.  相似文献   

Group Time Delay in the Reflection of P-Polarized Electromagnetic Plane Waves at a Stratigraphic Interface     

Fu-Ping Liu  Rui-Zhong Li  Jin-yao Li  Hui-Guo Chen  Chang-Chun Yang 《Mathematical Geosciences》2008,40(7):813-829

The group time delay (GTD) formulae of quasi-total reflection of inhomogeneous P-polarized electromagnetic waves (P-PEW, whose electric field parallels to the plane of incidence), caused by the Goos–Hänchen effect, is derived by the phase shift of the wave. A numerical example where the frequency equals to 1 GHz is given. The curves of calculating results show that there are three discontinuous points at the critical angle of phase shift vector, the critical angle of attenuation vector and 90^○. When the angle of incidence is equal to one of these three angles, the GTD will become infinite, and the electromagnetic wave will propagate along the interface. The GTD will be very large, when the angle of incidence is close to one of these three angles. The results indicate that there is an important relationship between the two critical angles and the conductivity and permittivity of the two strata, and that the GTD has an important relationship with the angle of incidence. These results can be used to determine the lithology of the strata and to delimit the interfaces of strata more effectively. It is suggested that this research may prove useful in electromagnetic logging analysis and, perhaps, in the design of logging instruments.  相似文献   

Change of Support for Estimating Local Block Grade Distributions     

Xavier Emery 《Mathematical Geosciences》2008,40(6):671-688

An important aspect in mineral resource evaluation is the reduction of variance when post-processing the grade distributions defined on the support (volume) of the available data into distributions defined on the support of the proposed selective mining units. Although the volume-variance relationship is well understood for the estimation of global grade distributions, it is still an unsolved issue for local estimation studies based on non-parametric geostatistical methods, such as indicator kriging, for which the support correction is not inherent to the method. To clarify this relationship, the local change of support problem is examined in the scope of two parametric models (multi-Gaussian and discrete Gaussian models). It is shown that the variance reduction factor between point and block-support local distributions depends on the block being considered and is less than the global variance reduction factor. As a consequence, post-processing the local point-support grade distributions on the basis of the latter systematically understates the importance of the change of support at the local scale and makes selective mining appear more economically attractive than it really is. In the light of these results, a methodology is proposed to post-process the local point-support distributions obtained via non-parametric (indicator) methods into block-support distributions. An application to simulated data indicates that this methodology provides an accurate estimation at the block support when dealing with diffusion-type random fields.  相似文献   

Some Results on the Spatial Breakdown Point of Robust Point Estimates of the Variogram     

R. M. Lark 《Mathematical Geosciences》2008,40(7):729-751

The effect of outliers on estimates of the variogram depends on how they are distributed in space. The ‘spatial breakdown point’ is the largest proportion of observations which can be drawn from some arbitrary contaminating process without destroying a robust variogram estimator, when they are arranged in the most damaging spatial pattern. A numerical method is presented to find the spatial breakdown point for any sample array in two dimensions or more. It is shown by means of some examples that such a numerical approach is needed to determine the spatial breakdown point for two or more dimensions, even on a regular square sample grid, since previous conjectures about the spatial breakdown point in two dimensions do not hold. The ‘average spatial breakdown point’ has been used as a basis for practical guidelines on the intensity of contaminating processes that can be tolerated by robust variogram estimators. It is the largest proportion of contaminating observations in a data set such that the breakdown point of the variance estimator used to obtain point estimates of the variogram is not exceeded by the expected proportion of contaminated pairs of observations over any lag. In this paper the behaviour of the average spatial breakdown point is investigated for cases where the contaminating process is spatially dependent. It is shown that in two dimensions the average spatial breakdown point is 0.25. Finally, the ‘empirical spatial breakdown point’, a tool for the exploratory analysis of spatial data thought to contain outliers, is introduced and demonstrated using data on metal content in the soils of Sheffield, England. The empirical spatial breakdown point of a particular data set can be used to indicate whether the distribution of possible contaminants is likely to undermine a robust variogram estimator.  相似文献   

Stability Analysis and Numerical Simulation of Differential Frost Heave     

Rorik A. Peterson 《Mathematical Geosciences》2008,40(3):277-298

Differential frost heave is often implicated in the formation of patterned ground in regions subject to recurrent freezing and thawing. A linear stability analysis (LSA) indicates that a continuum model of frost heave is linearly unstable under typical natural freezing conditions of silty-clay soils. A two-dimensional non-linear numerical analysis corroborates the frozen time LSA results, and also indicates the importance of non-linear and time-dependent terms that ultimately lead to a preferred mode, which the LSA fails to predict. Instability of the one-dimensional solution occurs at shallow freezing depths and near-zero surface loads when positive perturbations in the ice content at the freezing front lead to a concomitant increase in thermomolecular pressure and upward ice velocity. Differential frost heave can then occur because of the increased heat flux from the perturbed surfaces. A three-dimensional model using random initial surface perturbations indicates that regular surface patterns will evolve with a length scale in the order of 2–4 meters, which corresponds quite closely with naturally-occurring non-sorted patterned ground.  相似文献   

Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments   总被引：7，自引：0，他引：7  

Qiuming Cheng 《Mathematical Geosciences》2008,40(5):503-532

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.  相似文献   

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks   总被引：1，自引：0，他引：1  

Chongbin Zhao  Bruce E. Hobbs  Alison Ord  Shenglin Peng  Liangming Liu 《Mathematical Geosciences》2008,40(2):179-197

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.  相似文献   

Paleozoic granitoid magmatism of the eastern part of the Central Asian Fold Belt and formation of large ore deposits     

N. P. Romanovskii  Yu. F. Malyshev  M. V. Goroshko 《Russian Journal of Pacific Geology》2008,2(2):137-149

Evidence on the Paleozoic granitoids of the eastern part of the Central Asian Fold Belt (CAFB) was analyzed. A tectonic chart of orogenic belts was compiled. Sketch maps were constructed for the geodynamic settings of the formation of Paleozoic granitoids and the extensiveness of their occurrence. Two types of deep controlling structures were distinguished: zones of lithospheric faults and plumes, including the newly recognized Jiamusi-Bureya plume. It was sown that the distribution of large and superlarge Paleozoic ore deposits is related to these structures, primarily to plumes. Sites promising for large and superlarge deposits related to the Paleozoic granitoid magmatism were determined in the Russian Far East.  相似文献   

Long-term seismic noise investigations on Shikotan Island: First results     

Yu. A. Kugaenko  V. A. Saltykov  V. I. Sinitsyn  A. A. Shishkin 《Russian Journal of Pacific Geology》2008,2(3):218-227

In 2003–2004, long-term seismic noise observations were launched on Shikotan Island (Lesser Kuril Range) based on the “Shikotan” dormant regional seismic station. The geological and geophysical data on the registration area are reported. Information about the equipment and its technical specifications is given. The precursors to the strongest local earthquakesthat occurred in the Shikotan Island region in January 2005–March 2007 are identified.  相似文献   

Oxygen isotopes in the Cretaceous-Paleogene granites of Primorye and some problems of their genesis     

G. A. Valui  E. Yu. Moskalenko  A. A. Strizhkova  G. R. Sayadyan 《Russian Journal of Pacific Geology》2008,2(2):150-157

The Cretaceous-Paleogene granites of the Eastern Sikhote Alin volcanic belt (ESAVB) and Late Cretaceous granitoids of the Tatibin Series (Central Sikhote Alin) are subdivided into three groups according to their oxygen isotope composition: group I with δ¹⁸O from +5.5 to +6.5‰, group II with δ¹⁸O from +7.6 to +10.2‰, and group III with less than +4.5‰. Group I rocks are similar in oxygen isotope composition to that of oceanic basalts and can be derived by melting of basaltic crust. Group II (rocks of the Tatibin Series) have higher δ¹⁸O, which suggests that their parental melts were contaminated by sedimentary material. The low ¹⁸O composition of group III rocks can be explained by their derivation from ¹⁸O-depleted rocks or by subsolidus isotopic exchange with low-¹⁸O fluid or meteoric waters. The relatively low δ¹⁸O and ⁸⁷Sr/⁸⁶Sr in the granitoids of Primorye suggest their derivation from rocks with a short-lived crustal history and can result from the following: (1) melting of sedimentary rocks enriched in young volcanic material that was accumulated in the trench along the transform continental margin (granites of the Tatibin Series) and (2) melting of a mixture of abyssal sediments, ocean floor basalts, and upper mantle in the lithospheric plate that subsided beneath the continent in the subduction zone (granites of the ESAVB).  相似文献