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Interactive computer programs for petrologic modeling with extended Q-mode factor analysis

An extended form of Q-mode factor analysis may be used if the row-sums of the data matrix are constant and can be helpful especially in developing and testing petrologic-mixing models for igneous systems. The first step is to represent the sample compositions as unit vectors in M-dimensional space and then to project them into space of fewer dimensions (m) as determined to be appropriate from a factor-variance diagram. Compositions thought to be those of possible end-members in the petrologic system then are represented as vectors in the M-dimensional space and projected into the same space as the sample vectors. If these vectors remain close to unity in length after projection, the corresponding compositions can serve as end-member compositions for the model. After m suitable end-member compositions have been identified, each sample composition is expressed as a mixture of the end-members by computation of the composition loadings. The interactive computer programs presented are useful in these procedures because of the trial-and-error nature of the modeling procedures. ?? 1976.

Computers & Geosciences↗

Resource data bases-Resource assessment

The U.S. Geological Survey's Office of Resource Analysis is developing computer methods for the handling of mineral-resources data in order to provide improved means for addressing and manipulating data. These methods include: computerized data files and predictive resource models. Data files contain the raw or disaggregated information on mineral deposits and commodities. One operational data file is CRIB (Computerized Resources Information Bank) which is a general purpose inventory and reference file on metallic and nonmetallic mineral deposits. A computer file on resources should contain detailed information on the following main categories: record identification, name and location, description of deposit, analytical data, and production/reserves. A resource model employs postulates and inferences in conjunction with the data to make predictions about resources-as key variables concerning a mineral commodity are changed. The objective is to estimate the availability of minerals including: geological availability (occurrence models), technological availability (exploration and beneficiation models), and economic availability (economics models). ?? 1976.

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The national coal-resources data system of the U.S. geological survey

The National Coal Resources Data System (NCRDS) was designed by the U.S. Geological Survey (USGS) to meet the increasing demands for rapid retrieval of information on coal location, quantity, quality, and accessibility. An interactive conversational query system devised by the USGS retrieves information from the data bank through a standard computer terminal. The system is being developed in two phases. Phase I, which currently is available on a limited basis, contains published areal resource and chemical data. The primary objective of this phase is to retrieve, calculate, and tabulate coal-resource data by area on a local, regional, or national scale. Factors available for retrieval include: state, county, quadrangle, township, coal field, coal bed, formation, geologic age, source and reliability of data, and coal-bed rank, thickness, overburden, and tonnage, or any combinations of variables. In addition, the chemical data items include individual values for proximate and ultimate analyses, BTU value, and several other physical and chemical tests. Information will be validated and deleted or updated as needed. Phase II is being developed to store, retrieve, and manipulate basic point source coal data (e.g., field observations, drill-hole logs), including geodetic location; bed thickness; depth of burial; moisture; ash; sulfur; major-, minor-, and trace-element content; heat value; and characteristics of overburden, roof rocks, and floor rocks. The computer system may be used to generate interactively structure-contour or isoline maps of the physical and chemical characteristics of a coal bed or to calculate coal resources. ?? 1976.

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RESIN, a FORTRAN IV program for determining the area of influence of samples or drill holes in resource target search

A FORTRAN IV program that calculates the area of influence of drill holes or samples with respect to the size and shape of elliptical or circular resource targets is presented. Program options include determination of the degree to which areas within a region have been explored and estimation of probabilities that points are centers of undiscovered deposits. Errors of recognition can be utilized in the program input. ?? 1976.

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Binorm-a fortran subroutine to calculate the percentiles of a standardized binormal distribution

BINORM is a FORTRAN subroutine for calculating the percentiles of a standardized binormal distribution. By using a linear transformation, the percentiles of a binormal distribution can be obtained. The percentiles of a binormal distribution are useful for plotting purposes, for establishing confidence intervals, and for sampling from a mixed population that consists of two normal distributions. ?? 1977.

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The U.S. geological survey rass-statpac system for management and statistical reduction of geochemical data

RASS is an acronym for Rock Analysis Storage System and STATPAC, for Statistical Package. The RASS and STATPAC computer programs are integrated into the RASS-STATPAC system for the management and statistical reduction of geochemical data. The system, in its present form, has been in use for more than 9 yr by scores of U.S. Geological Survey geologists, geochemists, and other scientists engaged in a broad range of geologic and geochemical investigations. The principal advantage of the system is the flexibility afforded the user both in data searches and retrievals and in the manner of statistical treatment of data. The statistical programs provide for most types of statistical reduction normally used in geochemistry and petrology, but also contain bridges to other program systems for statistical processing and automatic plotting. ?? 1977.

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Graphic analysis of resources by numerical evaluation techniques (Garnet)

An interactive computer program for graphical analysis has been developed by the U.S. Geological Survey. The program embodies five goals, (1) economical use of computer resources, (2) simplicity for user applications, (3) interactive on-line use, (4) minimal core requirements, and (5) portability. It is designed to aid (1) the rapid analysis of point-located data, (2) structural mapping, and (3) estimation of area resources. ?? 1977.

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A method and fortran program for the computerized reconstruction of three-dimensional objects from serial sections

Three-dimensional objects can be reconstructed automatically from sets of serial sections by using a suitable algorithm. For two-phase systems it is sufficient to match phase boundary loops between adjacent sections. When all possible neighboring pairs of sections have been compared in this manner, the bounding surfaces of the object are described by sets of triangular and nonplanar quadrilateral patches. ?? 1977.

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An exploratory drilling exhaustion sequence plot program

The exhaustion sequence plot program computes the conditional area of influence for wells in a specified rectangular region with respect to a fixed-size deposit. The deposit is represented by an ellipse whose size is chosen by the user. The area of influence may be displayed on computer printer plots consisting of a maximum of 10,000 grid points. At each point, a symbol is presented that indicates the probability of that point being exhausted by nearby wells with respect to a fixed-size ellipse. This output gives a pictorial view of the manner in which oil fields are exhausted. In addition, the exhaustion data may be used to estimate the number of deposits remaining in a basin. ?? 1977.

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Range charts and no-space graphs

No-space graphs present one solution to the familiar problem: given data on the occurrence of fossil taxa in separate, well-sampled sections, determine a range chart; that is, a reasonable working hypothesis of the total range in the area in question of each taxon studied. The solution presented here treats only the relative sequence of biostratigraphic events (first and last occurrences of taxa) and does not attempt to determine an amount of spacing between events. Relative to a hypothesized sequence, observed events in any section may be in-place or out-of-place. Out-of-place events may indicate (1) the event in question reflects a taxon that did not fill its entire range (unfilled-range event), or (2) the event in question indicates a need for the revision of the hypothesized sequence. A graph of relative position only (no-space graph) can be used to facilitate the recognition of in-place and out-of-place events by presenting a visual comparison of the observations from each section with the hypothesized sequence. The geometry of the graph as constructed here is such that in-place events will lie along a line series and out-of-place events will lie above or below it. First-occurrence events below the line series and last-occurrence events above the line series indicate unfilled ranges. First-occurrence events above the line series and last-occurrence events below the line series indicate a need for the revision of the hypothesis. Knowing this, the stratigrapher considers alternative positionings of the line series as alternative range hypotheses and seeks the line series that best fits his geologic and paleontologic judgment. No-space graphs are used to revise an initial hypothesis until a final hypothesis is reached. In this final hypothesis every event is found in-place in at least one section, and all events in all sections may be interpreted to represent in-place events or unfilled-range events. No event may indicate a need for further range revision. The application of the no-space graph method requires the assumption of lack of reworking and the assumption that taxa that are present in a single horizon indicate taxa whose ranges overlap. When applied to hypothetical and actual data, the no-space graph technique produces geologically reasonable range charts that compare favorably with results produced by other methods.

Computers & Geosciences↗

Orthogonal mapping: A computer program for quantifying shape differences

Quantitative differences in the shape of two or more objects can be obtained by Orthogonal Mapping provided coincidental or analogous points can be identified on each object. The least-squares difference between each set of analogous points is determined by use of a projective transformation of a set of measured points which involves the rotation, translocation, and scaling of these points relative to a set of fixed points. ?? 1978.

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An algol program for dissimilarity analysis: a divisive-omnithetic clustering technique

Clustering techniques are used properly to generate hypotheses about patterns in data. Of the hierarchical techniques, those which are divisive and omnithetic possess many theoretically optimal properties. One such method, dissimilarity analysis, is implemented here in ALGOL 60, and determined to be competitive computationally with most other methods. ?? 1979.

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Computational methods for a three-dimensional model of the petroleum-discovery process

A discovery-process model devised by Drew, Schuenemeyer, and Root can be used to predict the amount of petroleum to be discovered in a basin from some future level of exploratory effort: the predictions are based on historical drilling and discovery data. Because marginal costs of discovery and production are a function of field size, the model can be used to make estimates of future discoveries within deposit size classes. The modeling approach is a geometric one in which the area searched is a function of the size and shape of the targets being sought. A high correlation is assumed between the surface-projection area of the fields and the volume of petroleum. To predict how much oil remains to be found, the area searched must be computed, and the basin size and discovery efficiency must be estimated. The basin is assumed to be explored randomly rather than by pattern drilling. The model may be used to compute independent estimates of future oil at different depth intervals for a play involving multiple producing horizons. We have written FORTRAN computer programs that are used with Drew, Schuenemeyer, and Root's model to merge the discovery and drilling information and perform the necessary computations to estimate undiscovered petroleum. These program may be modified easily for the estimation of remaining quantities of commodities other than petroleum. ?? 1980.

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Discrim: a computer program using an interactive approach to dissect a mixture of normal or lognormal distributions

DISCRIM is an interactive computer graphics program that dissects mixtures of normal or lognormal distributions. The program was written in an effort to obtain a more satisfactory solution to the dissection problem than that offered by a graphical or numerical approach alone. It combines graphic and analytic techniques using a Tektronix1 terminal in a time-share computing environment. The main program and subroutines were written in the FORTRAN language. ?? 1980.

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Three FORTRAN programs for finite-difference solutions to binary diffusion in one and two phases with composition-and time-dependent diffusion coefficients

Geological examples of binary diffusion are numerous. They are potential indicators of the duration and rates of geological processes. Analytical solutions to the diffusion equations generally do not allow for variable diffusion coefficients, changing boundary conditions, and impingement of diffusion fields. The three programs presented here are based on Crank-Nicholson finite-difference approximations, which can take into account these complicating factors. Program 1 describes the diffusion of a component into an initially homogeneous phase that has a constant surface composition. Specifically it is written for Fe-Mg exchange in olivine at oxygen fugacities appropriate for the lunar crust, but other components, phases, or fugacities may be substituted by changing the values of the diffusion coefficient. Program 2 simulates the growth of exsolution lamellae. Program 3 describes the growth of reaction rims. These two programs are written for pseudobinary Ca-(Mg, Fe) exchange in pyroxenes. In all three programs, the diffusion coefficients and boundary conditions can be varied systematically with time. To enable users to employ widely different numerical values for diffusion coefficients and diffusion distance, the grid spacing in the space dimension and the increment by which the grid spacing in the time dimension is increased at each time step are input constants that can be varied each time the programs are run to yield a solution of the desired accuracy. ?? 1982.

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The graphic cell method: a new look at digitizing geologic maps

The graphic cell method is an alternative method of digitizing areal geologic information. It involves a discrete-point sampling scheme in which the computer establishes a matrix of cells over the map. Each cell and the whole cell is assigned the identity or value of the geologic information that is recognized at its center. Cell size may be changed to suit the needs of the user. The computer program resolves the matrix and identifies potential errors such as multiple assignments. Input includes the digitized boundaries of each geologic formation. This method should eliminate a primary bottleneck in the creation and testing of geomathematical models in such disciplines as resource appraisal. ?? 1982.

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Geotherm: the U.S. geological survey geothermal information system

GEOTHERM is a comprehensive system of public databases and software used to store, locate, and evaluate information on the geology, geochemistry, and hydrology of geothermal systems. Three main databases address the general characteristics of geothermal wells and fields, and the chemical properties of geothermal fluids; the last database is currently the most active. System tasks are divided into four areas: (1) data acquisition and entry, involving data entry via word processors and magnetic tape; (2) quality assurance, including the criteria and standards handbook and front-end data-screening programs; (3) operation, involving database backups and information extraction; and (4) user assistance, preparation of such items as application programs, and a quarterly newsletter. The principal task of GEOTHERM is to provide information and research support for the conduct of national geothermal-resource assessments. The principal users of GEOTHERM are those involved with the Geothermal Research Program of the U.S. Geological Survey. Information in the system is available to the public on request. ?? 1983.

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SAS program for quantitative stratigraphic correlation by principal components

A SAS program is presented which constructs a composite section of stratigraphic events through principal components analysis. The variables in the analysis are stratigraphic sections and the observational units are range limits of taxa. The program standardizes data in each section, extracts eigenvectors, estimates missing range limits, and computes the composite section from scores of events on the first principal component. Provided is an option of several types of diagnostic plots; these help one to determine conservative range limits or unrealistic estimates of missing values. Inspection of the graphs and eigenvalues allow one to evaluate goodness of fit between the composite and measured data. The program is extended easily to the creation of a rank-order composite. ?? 1985.

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