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

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34 records · Page 2Linked to original sources
USGS1979

Modeling and optimizing a gas-water reservoir: Enhanced recovery with waterflooding

Accepted practice dictates that waterflooding of gas reservoirs should commence, if ever, only when the reservoir pressure has declined to the minimum production pressure. Analytical proof of this hypothesis has yet to appear in the literature however. This paper considers a model for a gas-water reservoir with a variable production rate and enhanced recovery with waterflooding and, using an initial dynamic programming approach, confirms the above hypothesis. ?? 1979 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1981

A distribution-free alternative to least-squares regression and its application to Rb/Sr isochron calculations

A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated Sm and is given by the median of the set of n(n - 1)/2 slope estimators, which may be calculated by inserting pairs of points (Xi, Yi)and (Xj, Yj)into the slope formula Si = (Yi - Yj)/(Xi - Xj), 1 ??? i < j ??? n Once Sm is determined, outliers may be detected by calculating the "residuals" given by Ri = Yi - SmXi where 1 ??? i ??? n, and chosing the median Rm. Outliers are defined as points for which |Ri - Rm| > k (median {|Ri - Rm|}). If no outliers are found, the Y-intercept is given by Rm. Confidence limits on Rm and Sm can be found from the sets of Ri and Si, respectively. The distribution-free estimators are compared with the least-squares estimators now in use by utilizing published data. Differences between the least-squares and distribution-free estimates are discussed, as are the drawbacks of the distribution-free techniques. ?? 1981 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1980

Asymmetric measures of association, closed data, and multivariate analysis

The association between constant-sum variables Xiand Xjexpressed as percentages can be calculated as a product-moment correlation between Xiand Xj/(100 - Xi) and a correlation between Xjand Xi/(100 - Xj). An asymmetric, square matrix may be formed from these coefficients, and multivariate analysis performed by two methods: singular value decomposition and canonical decomposition. Either analysis avoids problems in the interpretation of correlation coefficients determined from closed arrays, and provides information about dependencies among the variables beyond that obtained from the usual correlation coefficient between Xiand Xj. Two examples show the canonical decomposition to have the greater usefulness. ?? 1980 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1977

Target intersection probabilities for parallel-line and continuous-grid types of search

The expressions for calculating the probability of intersection of hidden targets of different sizes and shapes for parallel-line and continuous-grid types of search can be formulated by vsing the concept of conditional probability. When the prior probability of the orientation of a widden target is represented by a uniform distribution, the calculated posterior probabilities are identical with the results obtained by the classic methods of probability. For hidden targets of different sizes and shapes, the following generalizations about the probability of intersection can be made: (1) to a first approximation, the probability of intersection of a hidden target is proportional to the ratio of the greatest dimension of the target (viewed in plane projection) to the minimum line spacing of the search pattern; (2) the shape of the hidden target does not greatly affect the probability of the intersection when the largest dimension of the target is small relative to the minimum spacing of the search pattern, (3) the probability of intersecting a target twice for a particular type of search can be used as a lower bound if there is an element of uncertainty of detection for a particular type of tool; (4) the geometry of the search pattern becomes more critical when the largest dimension of the target equals or exceeds the minimum spacing of the search pattern; (5) for elongate targets, the probability of intersection is greater for parallel-line search than for an equivalent continuous square-grid search when the largest dimension of the target is less than the minimum spacing of the search pattern, whereas the opposite is true when the largest dimension exceeds the minimum spacing; (6) the probability of intersection for nonorthogonal continuous-grid search patterns is not greatly different from the probability of intersection for the equivalent orthogonal continuous-grid pattern when the orientation of the target is unknown. The probability of intersection for an elliptically shaped target can be approximated by treating the ellipse as intermediate between a circle and a line. A search conducted along a continuous rectangular grid can be represented as intermediate between a search along parallel lines and along a continuous square grid. On this basis, an upper and lower bound for the probability of intersection of an elliptically shaped target for a continuous rectangular grid can be calculated. Charts have been constructed that permit the values for these probabilities to be obtained graphically. The use of conditional probability allows the explorationist greater flexibility in considering alternate search strategies for locating hidden targets. ?? 1977 Plenum Publishing Corp.

Journal of the International Association for Mathe↗
USGS1971

Reduction of lithologic-log data to numbers for use in the digital computer

The development of a standardized system for conveniently coding lithologic-log data for use in the digital computer has long been needed. The technique suggested involves a reduction of the original written alphanumeric log to a numeric log by use of computer programs. This numeric log can then be retrieved as a written log, interrogated for pertinent information, or analyzed statistically.

Journal of the International Association for Mathe↗
USGS1978

The use of a paired comparison model in ordering stratigraphic events

Data from lowest and highest occurrence events in several stratigraphic sections are analyzed by means of a paired comparison model with ties. The model produces an estimated relative geochronological ordering of these events. This ordering must be compared with actual observations for revision and interpretation.

Journal of the International Association for Mathe↗
USGS1969

Critical review of some multivariate procedures in the analysis of geochemical data

Simulation experiments have been conducted to examine the potential usefulness of R-mode and Q-mode factor methods in the analysis and interpretation of geochemical data. The R-mode factor analysis experiment consisted of constructing a factor model, using the model to generate a correlation matrix, and attempting to recover the model by R-mode techniques. The techniques were successful in determining the number of factors in the model, but the factor loadings could not be estimated even approximately on the basis of mathematical procedures alone. Q-mode factor methods were successful in recovering all of the properties of a model used to generate hypothetical chemical data on olivine samples , but it was necessary to use a correction previously regarded as unimportant.

Journal of the International Association for Mathe↗
USGS1975

Analysis of the rate of wildcat drilling and deposit discovery

The rate at which petroleum deposits were discovered during a 16-yr period (1957–72) was examined in relation to changes in a suite of economic and physical variables. The study area encompasses 11,000 mi 2 and is located on the eastern flank of the Powder River Basin. A two-stage multiple-regression model was used as a basis for this analysis. The variables employed in this model were: (1) the yearly wildcat drilling rate, (2) a measure of the extent of the physical exhaustion of the resource base of the region, (3) a proxy for the discovery expectation of the exploration operators active in the region, (4) an exploration price/cost ratio, and (5) the expected depths of the exploration targets sought. The rate at which wildcat wells were drilled was strongly correlated with the discovery expectation of the exploration operators. Small additional variations in the wildcat drilling rate were explained by the price/cost ratio and target-depth variables. The number of deposits discovered each year was highly dependent on the wildcat drilling rate, but the aggregate quantity of petroleum discovered each year was independent of the wildcat drilling rate. The independence between these last two variables is a consequence of the cyclical behavior of the exploration play mechanism. Although the discovery success ratio declined sharply during the initial phases of the two exploration plays which developed in the study area, a learning effect occurred whereby the discovery success ratio improved steadily with the passage of time during both exploration plays.

Journal of the International Association for Mathe↗