Introduction to the index to the Journal of the International Association for Mathematical Geology volumes 1-10, 1969-1978
[No abstract available]
Journal of the International Association for Mathe↗
SEARCH · Search USGS
Results for “Mathematical Geology”
Search indexed USGS publications on groundwater, aquifers, geologic maps, mineral resources and earthquakes. Explore source records by subject and place.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Andrei borisovich vistelius: A dominant figure in 20th century mathematical geology
Andrei Borisovich Vistelius (1915-1995), along with William Christian Krumbein (1902-1979) and John Cedric Griffiths (1912-1992), were dominant figures in the formative and development years of mathematical (or quantitative) geology as a subdiscipline of geology.
Natural Resources Research↗
The geometric signature: Quantifying landslide-terrain types from digital elevation models
Topography of various types and scales can be fingerprinted by computer analysis of altitude matrices (digital elevation models, or DEMs). The critical analytic tool is the geometric signature, a set of measures that describes topographic form well enough to distinguish among geomorphically disparate landscapes. Different surficial processes create topography with diagnostic forms that are recognizable in the field. The geometric signature abstracts those forms from contour maps or their DEMs and expresses them numerically. This multivariate characterization enables once-in-tractable problems to be addressed. The measures that constitute a geometric signature express different but complementary attributes of topographic form. Most parameters used here are statistical estimates of central tendency and dispersion for five major categories of terrain geometry; altitude, altitude variance spectrum, slope between slope reversals, and slope and its curvature at fixed slope lengths. As an experimental application of geometric signatures, two mapped terrain types associated with different processes of shallow landsliding in Marin County, California, were distinguished consistently by a 17-variable description of topography from 21??21 DEMs (30-m grid spacing). The small matrix is a statistical window that can be used to scan large DEMs by computer, thus potentially automating the mapping of contrasting terrain types. The two types in Marin County host either (1) slow slides: earth flows and slump-earth flows, or (2) rapid flows: debris avalanches and debris flows. The signature approach should adapt to terrain taxonomy and mapping in other areas, where conditions differ from those in Central California. ?? 1988 International Association for Mathematical Geology.
Mathematical Geology↗
Use of the truncated shifted Pareto distribution in assessing size distribution of oil and gas fields
The truncated shifted Pareto (TSP) distribution, a variant of the two-parameter Pareto distribution, in which one parameter is added to shift the distribution right and left and the right-hand side is truncated, is used to model size distributions of oil and gas fields for resource assessment. Assumptions about limits to the left-hand and right-hand side reduce the number of parameters to two. The TSP distribution has advantages over the more customary lognormal distribution because it has a simple analytic expression, allowing exact computation of several statistics of interest, has a "J-shape," and has more flexibility in the thickness of the right-hand tail. Oil field sizes from the Minnelusa play in the Powder River Basin, Wyoming and Montana, are used as a case study. Probability plotting procedures allow easy visualization of the fit and help the assessment. ?? 1988 International Association for Mathematical Geology.
Mathematical Geology↗
On-line estimation of nonlinear physical systems
Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared. ?? 1988 International Association for Mathematical Geology.
Mathematical Geology↗
Comparison of structural and least-squares lines for estimating geologic relations
Two different goals in fitting straight lines to data are to estimate a "true" linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating "true" straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal-predicting the dependent variable-OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples. ?? 1990 International Association for Mathematical Geology.
Mathematical Geology↗
Multi-model approach to petroleum resource appraisal using analytic methodologies for probabilistic systems
The geologic appraisal model that is selected for a petroleum resource assessment depends upon purpose of the assessment, basic geologic assumptions of the area, type of available data, time available before deadlines, available human and financial resources, available computer facilities, and, most importantly, the available quantitative methodology with corresponding computer software and any new quantitative methodology that would have to be developed. Therefore, different resource assessment projects usually require different geologic models. Also, more than one geologic model might be needed in a single project for assessing different regions of the study or for cross-checking resource estimates of the area. Some geologic analyses used in the past for petroleum resource appraisal involved play analysis. The corresponding quantitative methodologies of these analyses usually consisted of Monte Carlo simulation techniques. A probabilistic system of petroleum resource appraisal for play analysis has been designed to meet the following requirements: (1) includes a variety of geologic models, (2) uses an analytic methodology instead of Monte Carlo simulation, (3) possesses the capacity to aggregate estimates from many areas that have been assessed by different geologic models, and (4) runs quickly on a microcomputer. Geologic models consist of four basic types: reservoir engineering, volumetric yield, field size, and direct assessment. Several case histories and present studies by the U.S. Geological Survey are discussed. ?? 1988 International Association for Mathematical Geology.
Mathematical Geology↗
Response of selected binomial coefficients to varying degrees of matrix sparseness and to matrices with known data interrelationships
Numerous departures from ideal relationships are revealed by Monte Carlo simulations of widely accepted binomial coefficients. For example, simulations incorporating varying levels of matrix sparseness (presence of zeros indicating lack of data) and computation of expected values reveal that not only are all common coefficients influenced by zero data, but also that some coefficients do not discriminate between sparse or dense matrices (few zero data). Such coefficients computationally merge mutually shared and mutually absent information and do not exploit all the information incorporated within the standard 2 ?? 2 contingency table; therefore, the commonly used formulae for such coefficients are more complicated than the actual range of values produced. Other coefficients do differentiate between mutual presences and absences; however, a number of these coefficients do not demonstrate a linear relationship to matrix sparseness. Finally, simulations using nonrandom matrices with known degrees of row-by-row similarities signify that several coefficients either do not display a reasonable range of values or are nonlinear with respect to known relationships within the data. Analyses with nonrandom matrices yield clues as to the utility of certain coefficients for specific applications. For example, coefficients such as Jaccard, Dice, and Baroni-Urbani and Buser are useful if correction of sparseness is desired, whereas the Russell-Rao coefficient is useful when sparseness correction is not desired. ?? 1989 International Association for Mathematical Geology.
Mathematical Geology↗
Declustering of clustered preferential sampling for histogram and semivariogram inference
Measurements of attributes obtained more as a consequence of business ventures than sampling design frequently result in samplings that are preferential both in location and value, typically in the form of clusters along the pay. Preferential sampling requires preprocessing for the purpose of properly inferring characteristics of the parent population, such as the cumulative distribution and the semivariogram. Consideration of the distance to the nearest neighbor allows preparation of resampled sets that produce comparable results to those from previously proposed methods. Clustered sampling of size 140, taken from an exhaustive sampling, is employed to illustrate this approach. ?? International Association for Mathematical Geology 2007.
Mathematical Geology↗
Physical deposit measures and commercial potential: The case of titanium-bearing heavy-mineral deposits
Physical measures of mineral deposit characteristics, such as grade and tonnage, long have been used in both subjective and analytic models to predict favorability of areas for the occurrence of mineral deposits of particular types. After a deposit has been identified, however, the explorationist must decide whether to continue data collection, begin an economic feasibility study, or abandon the prospect. The decision maker can estimate the probability that a deposit will be commercial by examining physical measures. The amount of sampling data required before such a probability estimate can be considered reliable can be determined. A logit probability model estimated from onshore titanium-bearing heavy-mineral deposit data identifies and quantifies the relative influence of a deposit's physical measures on the chances of the deposit becoming commercial. A principal conclusion that can be drawn from the analysis is that, along with a measure of deposit size, the characteristics most important in predicting commercial potential are grades of the constituent minerals. Total heavy-mineral-bearing sand grade or even total titanium grade (without data on constituent mineral grades) are poor predictors of the deposit's commercial potential. ?? 1988 International Association for Mathematical Geology.
Mathematical Geology↗
Adjusting stream-sediment geochemical maps in the Austrian Bohemian Massif by analysis of variance
The Austrian portion of the Bohemian Massif is a Precambrian terrane composed mostly of highly metamorphosed rocks intruded by a series of granitoids that are petrographically similar. Rocks are exposed poorly and the subtle variations in rock type are difficult to map in the field. A detailed geochemical survey of stream sediments in this region has been conducted and included as part of the Geochemischer Atlas der Republik O??sterreich, and the variations in stream sediment composition may help refine the geological interpretation. In an earlier study, multivariate analysis of variance (MANOVA) was applied to the stream-sediment data in order to minimize unwanted sampling variation and emphasize relationships between stream sediments and rock types in sample catchment areas. The estimated coefficients were used successfully to correct for the sampling effects throughout most of the region, but also introduced an overcorrection in some areas that seems to result from consistent but subtle differences in composition of specific rock types. By expanding the model to include an additional factor reflecting the presence of a major tectonic unit, the Rohrbach block, the overcorrection is removed. This iterative process simultaneously refines both the geochemical map by removing extraneous variation and the geological map by suggesting a more detailed classification of rock types. ?? 1995 International Association for Mathematical Geology.
Mathematical Geology↗
Prospector II: Towards a knowledge base for mineral deposits
What began in the mid-seventies as a research effort in designing an expert system to aid geologists in exploring for hidden mineral deposits has in the late eighties become a full-sized knowledge-based system to aid geologists in conducting regional mineral resource assessments. Prospector II, the successor to Prospector, is interactive-graphics oriented, flexible in its representation of mineral deposit models, and suited to regional mineral resource assessment. In Prospector II, the geologist enters the findings for an area, selects the deposit models or examples of mineral deposits for consideration, and the program compares the findings with the models or the examples selected, noting the similarities, differences, and missing information. The models or the examples selected are ranked according to scores that are based on the comparisons with the findings. Findings can be reassessed and the process repeated if necessary. The results provide the geologist with a rationale for identifying those mineral deposit types that the geology of an area permits. In future, Prospector II can assist in the creation of new models used in regional mineral resource assessment and in striving toward an ultimate classification of mineral deposits. ?? 1994 International Association for Mathematical Geology.
Mathematical Geology↗
Stochastic simulation of spatially correlated geo-processes
In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simu??lation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail. ?? 1987 International Association for Mathematical Geology.
Mathematical Geology↗
An objective replacement method for censored geochemical data
Geochemical data are commonly censored, that is, concentrations for some samples are reported as "less than" or "greater than" some value. Censored data hampers statistical analysis because certain computational techniques used in statistical analysis require a complete set of uncensored data. We show that the simple substitution method for creating an uncensored dataset, e.g., replacement by 3/4 times the detection limit, has serious flaws, and we present an objective method to determine the replacement value. Our basic premise is that the replacement value should equal the mean of the actual values represented by the qualified data. We adapt the maximum likelihood approach (Cohen, 1961) to estimate this mean. This method reproduces the mean and skewness as well or better than a simple substitution method using 3/4 of the lower detection limit or 3/4 of the upper detection limit. For a small proportion of "less than" substitutions, a simple-substitution replacement factor of 0.55 is preferable to 3/4; for a small proportion of "greater than" substitutions, a simple-substitution replacement factor of 1.7 is preferable to 4/3, provided the resulting replacement value does not exceed 100%. For more than 10% replacement, a mean empirical factor may be used. However, empirically determined simple-substitution replacement factors usually vary among different data sets and are less reliable with more replacements. Therefore, a maximum likelihood method is superior in general. Theoretical and empirical analyses show that true replacement factors for "less thans" decrease in magnitude with more replacements and larger standard deviation; those for "greater thans" increase in magnitude with more replacements and larger standard deviation. In contrast to any simple substitution method, the maximum likelihood method reproduces these variations. Using the maximum likelihood method for replacing "less thans" in our sample data set, correlation coefficients were reasonably accurately estimated in 90% of the cases for as much as 40% replacement and in 60% of the cases for 80% replacement. These results suggest that censored data can be utilized more than is commonly realized. ?? 1993 International Association for Mathematical Geology.
Mathematical Geology↗
Observed oil and gas field size distributions: A consequence of the discovery process and prices of oil and gas
If observed oil and gas field size distributions are obtained by random samplings, the fitted distributions should approximate that of the parent population of oil and gas fields. However, empirical evidence strongly suggests that larger fields tend to be discovered earlier in the discovery process than they would be by random sampling. Economic factors also can limit the number of small fields that are developed and reported. This paper examines observed size distributions in state and federal waters of offshore Texas. Results of the analysis demonstrate how the shape of the observable size distributions change with significant hydrocarbon price changes. Comparison of state and federal observed size distributions in the offshore area shows how production cost differences also affect the shape of the observed size distribution. Methods for modifying the discovery rate estimation procedures when economic factors significantly affect the discovery sequence are presented. A primary conclusion of the analysis is that, because hydrocarbon price changes can significantly affect the observed discovery size distribution, one should not be confident about inferring the form and specific parameters of the parent field size distribution from the observed distributions. ?? 1988 International Association for Mathematical Geology.
Mathematical Geology↗
Knowledge-based geographic information systems (KBGIS): New analytic and data management tools
In its simplest form, a geographic information system (GIS) may be viewed as a data base management system in which most of the data are spatially indexed, and upon which sets of procedures operate to answer queries about spatial entities represented in the data base. Utilization of artificial intelligence (AI) techniques can enhance greatly the capabilities of a GIS, particularly in handling very large, diverse data bases involved in the earth sciences. A KBGIS has been developed by the U.S. Geological Survey which incorporates AI techniques such as learning, expert systems, new data representation, and more. The system, which will be developed further and applied, is a prototype of the next generation of GIS's, an intelligent GIS, as well as an example of a general-purpose intelligent data handling system. The paper provides a description of KBGIS and its application, as well as the AI techniques involved. ?? 1988 International Association for Mathematical Geology.
Mathematical Geology↗
Cyclostratigraphic calibration of cretaceous magnetic polarity events (Cismon, Southern Alps, Italy)
In an introductory section the problems of constructing a geologic time scale and the role of magnetic reversals and Milankovitch cycles in geochronology are outlined. Results of a detailed cyclostratigraphic and magnetostratigraphic study of the Valanginian/Hauterivian part of the pelagic limestone section at Cismon in the Southern Alps are presented and used in conjunction to estimate the duration of magnetic subchrons between CM10N and CM8. The new estimates are shorter than in most published time scales by a factor of two to three. More research along these lines may make a revision of the Early Cretaceous time scale necessary. ?? 1994 International Association for Mathematical Geology.
Mathematical Geology↗
Prediction of hydrocarbons in sedimentary basins
To estimate the undiscovered hydrocarbon potential of sedimentary basins, quantitative play assessments specific for each location in a region may be obtained using geostatistical methods combined with the theory of classification of geological objects, a methodology referred to as regionalization. The technique relies on process modeling and measured borehole data as well as probabilistic methods to exploit the relationship between geology (the "predictor") and known hydrocarbon productivity (the "target") to define prospective stratigraphic intervals within a basin. It is demonstrated in case studies from the oil-producing region of the western Kansas Pennsylvanian Shelf and the gas-bearing Rotliegend sediments of the Northeast German Basin. ?? 1993 International Association for Mathematical Geology.
Mathematical Geology↗