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Results for “Journal of the International Association for Mathematical Geology”

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At least 19 recordsLinked to original sources
USGS1973

A semiobjective method for condensing classifications

A simple, semiobjective method is described to reduce the number of groups in a classification to an arbitrary level without losing contact with the geologic information contained in the evolving groups. The method, operated in a stepwise or cyclic manner, employs some of the commonly used numerical techniques, but avoids strict adherence to them to obtain geologically more meaningful results. The method is illustrated in a facies study of the upper Paleozoic rocks of southeastern Utah. ?? 1973 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1977

Estimation of the probability of success in petroleum exploration

A probabilistic model for oil exploration can be developed by assessing the conditional relationship between perceived geologic variables and the subsequent discovery of petroleum. Such a model includes two probabilistic components, the first reflecting the association between a geologic condition (structural closure, for example) and the occurrence of oil, and the second reflecting the uncertainty associated with the estimation of geologic variables in areas of limited control. Estimates of the conditional relationship between geologic variables and subsequent production can be found by analyzing the exploration history of a "training area" judged to be geologically similar to the exploration area. The geologic variables are assessed over the training area using an historical subset of the available data, whose density corresponds to the present control density in the exploration area. The success or failure of wells drilled in the training area subsequent to the time corresponding to the historical subset provides empirical estimates of the probability of success conditional upon geology. Uncertainty in perception of geological conditions may be estimated from the distribution of errors made in geologic assessment using the historical subset of control wells. These errors may be expressed as a linear function of distance from available control. Alternatively, the uncertainty may be found by calculating the semivariogram of the geologic variables used in the analysis: the two procedures will yield approximately equivalent results. The empirical probability functions may then be transferred to the exploration area and used to estimate the likelihood of success of specific exploration plays. These estimates will reflect both the conditional relationship between the geological variables used to guide exploration and the uncertainty resulting from lack of control. The technique is illustrated with case histories from the mid-Continent area of the U.S.A. ?? 1977 Plenum Publishing Corp.

Journal of the International Association for Mathe↗
USGS1983

Characteristic analysis-1981: Final program and a possible discovery

The latest ornewest version of thecharacteristicanalysis (NCHARAN)computer program offers the exploration geologist a wide variety of options for integrating regionalized multivariate data. The options include the selection of regional cells for characterizing deposit models, the selection of variables that constitute the models, and the choice of logical combinations of variables that best represent these models. Moreover, the program provides for the display of results which, in turn, makes possible review, reselection, and refinement of a model. Most important, the performance of the above-mentioned steps in an interactive computing mode can result in a timely and meaningful interpretation of the data available to the exploration geologist. The most recent application of characteristic analysis has resulted in the possible discovery of economic sulfide mineralization in the Grong area in central Norway. Exploration data for 27 geophysical, geological, and geochemical variables were used to construct a mineralized and a lithogeochemical model for an area that contained a known massive sulfide deposit. The models were applied to exploration data collected from the Gjersvik area in the Grong mining district and resulted in the identification of two localities of possible mineralization. Detailed field examination revealed the presence of a sulfide vein system and a partially inverted stratigraphic sequence indicating the possible presence of a massive sulfide deposit at depth. ?? 1983 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1983

A procedure to estimate the parent population of the size of oil and gas fields as revealed by a study of economic truncation

An estimation technique has been derived to predict the number of small fields in a geologic play or basin. Historically, many small oil and gas fields went unreported because they were not economical. This led to an underestimation of the number of undiscovered small fields. A study of the distributions of reported oil and gas fields in well-explored areas suggests that the large fields when grouped into log base 2 size classes are geometrically distributed. Further, the number of small fields reported is a function of the cost of exploration and development. Thus, the population field-size distribution is conjectured to be log geometric in form. ?? 1983 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1985

Comparative study of aggregations under different dependency assumptions for assessment of undiscovered recoverable oil resources in the world

The U.S. Geological Survey assessed all significant sedimentary basins in the world for undiscovered conventionally recoverable crude-oil resources. Probabilistic methodology was applied to each basin assessment to produce estimates in the form of probability distributions. Basin probability distributions were computer aggregated to produce resource estimates for the entire world. Aggregation was approximated by a three-parameter lognormal distribution by combining the first three central moments of basin distributions. For purposes of experiment and study, world aggregation was conducted under four different sets of assumptions. The four cases are (1) dependent assessments of all basins, (2) dependent assessments within continental areas, but independent assessments among continental areas, (3) dependent assessments within countries, but independent assessments among countries, and (4) independent assessments of all basins. Mean estimate remained the same in all four cases, but the width of interval estimate formed using the 95th and 5th fractiles decreased with reduced dependency in going from first to fourth case. ?? 1985 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1980

Resource estimation from historical data: Mercury, a test case

A simple technique based on historical records of tonnage and grade of ore produced provides a means for calculating how much of a mineral product will be available in the future at various average grades. Estimates made on this basis are independent of geologic considerations or changing economic and political factors, although they are based on mining history, which was largely determined by these factors. The relatively minor element, mercury, was used for the test case reported here, but the method has been found applicable to forecasts of resources for other mineral products. Mercury resources available in ore in which the average grade is as low as 0.1% are estimated to be 53 ??106kg (1.5 ??106flasks) for the United States and 1551 ??106kg (45 ??106flasks) for the world; this amount is more than adequate to meet predicted demand to the year 2000. The expectable price of mercury in 1978 dollars at this 0.1% grade is projected to be $58.75 per kg ($2,025 per flask), but at a 10% annual inflation rate, it would be more than $12,000 per flask. To satisfy just the projected U.S. demand for mercury by 2000, the price is calculated to be $48.96 per kg ($1,688 per flask) in 1978 dollars at an average annual grade of 0.12%. ?? 1980 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1980

Scaling variables and interpretation of eigenvalues in principal component analysis of geologic data

The dominant feature distinguishing one method of principal components analysis from another is the manner in which the original data are transformed prior to the other computations. The only other distinguishing feature of any importance is whether the eigenvectors of the inner product-moment of the transformed data matrix are taken directly as the Q-mode scores or scaled by the square roots of their associated eigenvalues and called the R-mode loadings. If the eigenvectors are extracted from the product-moment correlation matrix, the variables, in effect, were transformed by column standardization (zero means and unit variances), and the sum of the p-largest eigenvalues divided by the sum of all the eigenvalues indicates the degree to which a model containing p components will account for the total variance in the original data. However, if the data were transformed in any manner other than column standardization, the eigenvalues cannot be used in this manner, but can only be used to determine the degree to which the model will account for the transformed data. Regardless of the type of principal components analysis that is performed-even whether it is R or Q-mode-the goodness-of-fit of the model to the original data is given better by the eigenvalues of the correlation matrix than by those of the matrix that was actually factored. ?? 1980 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1980

A three-dimensional model to predict future oil discoveries in spatially connected multiple plays

A discovery-process model that had been devised previously to estimate the size distribution of oil and gas fields remaining to be discovered in a single producing horizon was adapted to a basin containing spatially connected multiple plays and producing horizons. This model used the concept of the area of influence of wells to estimate search effort. Other variables estimated from the historical drilling and discovery data are the effective basin size and the exploration-drilling efficiency. Data from the Midland Basin are used to illustrate how the model works. ?? 1980 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1979

Pattern drilling exploration: Optimum pattern types and hole spacings when searching for elliptical shaped targets

In this study the selection of the optimum type of drilling pattern to be used when exploring for elliptical shaped targets is examined. The rhombic pattern is optimal when the targets are known to have a preferred orientation. Situations can also be found where a rectangular pattern is as efficient as the rhombic pattern. A triangular or square drilling pattern should be used when the orientations of the targets are unknown. The way in which the optimum hole spacing varies as a function of (1) the cost of drilling, (2) the value of the targets, (3) the shape of the targets, (4) the target occurrence probabilities was determined for several examples. Bayes' rule was used to show how target occurrence probabilities can be revised within a multistage pattern drilling scheme. ?? 1979 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1979

Vector analysis of chemical variation in the lavas of Parícutin volcano, Mexico

Compositional variations in the lavas of Parícutin volcano, Mexico, have been examined by an extended method of Q-mode factor analysis. Each sample composition is treated as a vector projected from an original eight-dimensional space into a vector system of three dimensions. The compositions represented by the vectors after projection are closely similar to the original compositions except for Na2O and Fe2O3. The vectors in the three-dimensional system cluster about three different planes that represent three stages of compositional change in the Parícutin lavas. Because chemical data on the compositions of the minerals in the lavas are presently lacking, interpretations of the mineral phases that may have been involved in fractional crystallization are based on CIPW norm calculations. Changes during the first stage are attributed largely to the fractional crystallization of plagioclase and olivine. Changes during the second stage can be explained by the separation of plagioclase and pyroxene. Changes during the final stage may have resulted mostly from the assimilation of a granitic material, as previously proposed by R. E. Wilcox.

Journal of the International Association for Mathe↗
USGS1985

Lognormal field size distributions as a consequence of economic truncation

The assumption of lognormal (parent) field size distributions has for a long time been applied to resource appraisal and evaluation of exploration strategy by the petroleum industry. However, frequency distributions estimated with observed data and used to justify this hypotheses are conditional. Examination of various observed field size distributions across basins and over time shows that such distributions should be regarded as the end result of an economic filtering process. Commercial discoveries depend on oil and gas prices and field development costs. Some new fields are eliminated due to location, depths, or water depths. This filtering process is called economic truncation. Economic truncation may occur when predictions of a discovery process are passed through an economic appraisal model. We demonstrate that (1) economic resource appraisals, (2) forecasts of levels of petroleum industry activity, and (3) expected benefits of developing and implementing cost reducing technology are sensitive to assumptions made about the nature of that portion of (parent) field size distribution subject to economic truncation. ?? 1985 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1985

Spatial analysis of extension fracture systems: A process modeling approach

Little consensus exists on how best to analyze natural fracture spacings and their sequences. Field measurements and analyses published in geotechnical literature imply fracture processes radically different from those assumed by theoretical structural geologists. The approach adopted in this paper recognizes that disruption of rock layers by layer-parallel extension results in two spacing distributions, one representing layer-fragment lengths and another separation distances between fragments. These two distributions and their sequences reflect mechanics and history of fracture and separation. Such distributions and sequences, represented by a 2 ?? n matrix of lengthsL, can be analyzed using a method that is history sensitive and which yields also a scalar estimate of bulk extension, e (L). The method is illustrated by a series of Monte Carlo experiments representing a variety of fracture-and-separation processes, each with distinct implications for extension history. Resulting distributions of e (L)are process-specific, suggesting that the inverse problem of deducing fracture-and-separation history from final structure may be tractable. ?? 1985 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1985

Resolving controls on epeiric sedimentation using trend surface analysis

An understanding of patterns of regional sedimentation is crucial to identifying trends of perspective petroleum reservoirs. The Upper Pennsylvanian, Missourian Kansas City Group consists of repetitions of widespread carbonate rock and shale. Each of four cyclothems chosen for subsurface study of western Kansas contains transgressive and regressive lithofacies with evidence of extensive subaerial exposure across the entire paleoshelf. Distribution of carbonate facies on the 350+ km-wide shelf was affected strongly by slight changes in structural configuration of the shelf and variations in sea level. Polynomial trend surface models prepared from selected wireline log information for four successive cyclothems assist in resolving regional and local patterns of sedimentation and help to access the effect of subtle structural deformation on sedimentation. Isopachs of marine portions of four cyclothems were fit by fourth-order trend surfaces, optimizing fit by comparing goodness-of-fit and minimizing skewness of residuals using the smallest order surface. Several cyclothems showed simple patterns of regional, basinward thickening with local, strike-elongated anomalies where goodness-of-fit was maximized with increasing order. One cyclothem did not converge to a good fit at small orders nor did distribution of residuals indicate convergence toward zero. Both anomalies reflected a more complex surface. Rather than thickening regionally, the pattern created by this anomalous cyclothem was more irregular. Mapped patterns resemble those of the present-day structural configuration of these horizons suggesting a general persistence in similar epeirogenic deformation. ?? 1985 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1985

Three-dimensional trend mapping from wire-line logs

Mapping of lithofacies and porosities of stratigraphic units is complicated because these properties vary in three dimensions. The method of moments was proposed by Krumbein and Libby (1957) as a technique to aid in resolving this problem. Moments are easily computed from wireline logs and are simple statistics which summarize vertical variation in a log trace. Combinations of moment maps have proved useful in understanding vertical and lateral changes in lithology of sedimentary rock units. Although moments have meaning both as statistical descriptors and as mechanical properties, they also define polynomial curves which approximate lithologic changes as a function of depth. These polynomials can be fitted by least-squares methods, partitioning major trends in rock properties from finescale fluctuations. Analysis of variance yields the degree of fit of any polynomial and measures the proportion of vertical variability expressed by any moment or combination of moments. In addition, polynomial curves can be differentiated to determine depths at which pronounced expressions of facies occur and to determine the locations of boundaries between major lithologic subdivisions. Moments can be estimated at any location in an area by interpolating from log moments at control wells. A matrix algebra operation then converts moment estimates to coefficients of a polynomial function which describes a continuous curve of lithologic variation with depth. If this procedure is applied to a grid of geographic locations, the result is a model of variability in three dimensions. Resolution of the model is determined largely by number of moments used in its generation. The method is illustrated with an analysis of lithofacies in the Simpson Group of south-central Kansas; the three-dimensional model is shown as cross sections and slice maps. In this study, the gamma-ray log is used as a measure of shaliness of the unit. However, the method is general and can be applied, for example, to suites of neutron, density, or sonic logs to produce three-dimensional models of porosity in reservoir rocks. ?? 1985 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1980

Visual classification of very fine-grained sediments: Evaluation through univariate and multivariate statistics

Classifying very fine-grained rocks through fabric elements provides information about depositional environments, but is subject to the biases of visual taxonomy. To evaluate the statistical significance of an empirical classification of very fine-grained rocks, samples from Devonian shales in four cored wells in West Virginia and Virginia were measured for 15 variables: quartz, illite, pyrite and expandable clays determined by X-ray diffraction; total sulfur, organic content, inorganic carbon, matrix density, bulk density, porosity, silt, as well as density, sonic travel time, resistivity, and ??-ray response measured from well logs. The four lithologic types comprised: (1) sharply banded shale, (2) thinly laminated shale, (3) lenticularly laminated shale, and (4) nonbanded shale. Univariate and multivariate analyses of variance showed that the lithologic classification reflects significant differences for the variables measured, difference that can be detected independently of stratigraphic effects. Little-known statistical methods found useful in this work included: the multivariate analysis of variance with more than one effect, simultaneous plotting of samples and variables on canonical variates, and the use of parametric ANOVA and MANOVA on ranked data. ?? 1980 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗