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At least 1,207 records · Page 67Linked to original sources
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

Changes in drilling density and discovery rates through time

An alternative to time sequence evaluation of field size distributions is presented. Oil fields are ranked in relation to level of prior exploration in the vicinity of discovery wells. Field size distribution patterns for discoveries at sequential levels of prior exploration are evaluated independently from the time sequence of discoveries within the region. Interregional comparisons are made in terms of field discoveries at equivalent levels of prior exploration. The study area covers a large region (approximately 78,000 Km2) of central and northwest Kansas. ?? 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↗
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↗
USGS1983

Dual extraction of R-mode and Q-mode factor solutions

It is mathematically possible to extract both R-mode and Q-mode factors simultaneously (RQ-mode factor analysis)by invoking the Eckhart-Young theorem. The resulting factors will be expressed in measures determined by the form of the scalings that have been applied to the original data matrix. Unless the measures for both solutions are meaningful for the problem at hand, the factor results may be misleading or uninterpretable. Correspondence analysis uses a symmetrical scaling of both rows and columns to achieve measures of proportional similarity between objects and variables. In the literature, the resulting similarity is a ??2distance appropriate for analysis of enumerated data, the original application of correspondence analysis. Justification for the use of this measure with interval or ratio data is unconvincing, but a minor modification of the scaling procedure yields the profile similarity, which is an appropriate measure. Symmetrical scaling of rows and columns is unnecessary for RQ-mode factor analysis. If the data are scaled so the minor product W'W is the correlation matrix, the major product WW'is expressed in the Euclidean distances between objects. Therefore, RQ-mode factor analysis can be performed so that the R mode is a principal components solution and the Q mode is a principal coordinates solution. For applications where the magnitudes of differences are important, this approach will yield more interpretable results than will correspondence analysis. ?? 1983 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↗