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Results for “Mathematics of Computation”

Search indexed USGS publications on groundwater, aquifers, geologic maps, mineral resources and earthquakes. Explore source records by subject and place.

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At least 73 records · Page 4Linked to original sources
USGS1981

Complete Bouguer map of the Medicine Lake quadrangle, California

A mathematical technique, called kriging, was programmed for a computer to interpolate hydrologic data based on a network of measured values in west-central Kansas. The computer program generated estimated values at the center of each 1-mile section in the Western Kansas Groundwater Management District No. 1 and facilitated contouring of selected values that are needed in the effective management of ground water for irrigation. The kriging technique produced objective and reproducible maps that illustrated hydrologic conditions in the Ogallala aquifer, the principal source of water in west-central Kansas. Maps of the aquifer, which use a 3-year average, included the 1978-80 water-table altitudes, which ranged from about 2,580 to 3,720 feet; the 1978-80 saturated thicknesses, which ranged from about 0 to 250 feet; and the percentage changes in saturated thickness from 1950 to 1978-80, which ranged from about a 50-percent increase to a 100-percent decrease. A map showing errors of estimate also was provided as a measure of reliability for the 1978-80 water-table altitudes. Errors of estimate ranged from 2 to 24 feet. (USGS)

California↗
USGS1982

Hydrologic maps of Ogallala Aquifer, west-central Kansas, 1979-81

A mathematical technique, called kriging, was programmed for a computer to interpolate hydrologic data based on a network of measured values in west-central Kansas. The computer program generated estimated values at the center of each 1-mile section in the Western Kansas Groundwater Management District No. 1 and facilitated contouring of selected hydrologic data that are needed in the effective management of ground water for irrigation. The kriging technique produced various maps that illustrated hydrologic conditions in the Ogallala aquifer, the principal source of water in west-central Kansas. Maps of the aquifer, which use a 3-year average, included the 1979-81 water-table altitudes, which ranged from about 2,580 to 3,720 feet; the 1979-81 saturated thicknesses, which ranged from about 0 to 250 feet; and the percentage changes in saturated thickness from 1950 to 1979-81, which ranged from about a 40-percent increase to a 100-percent decrease. A map showing errors of estimate also was provided as a measure of reliability for the 1979-81 water-table altitudes. Errors of estimate ranged from 2 to 24 feet. (USGS)

Open-File Report↗
USGS1979

One-dimensional steady-state stream water-quality model

A computer program, based on a one-dimensional mathematical model which predicts the stream water-quality response characteristics from waste source inputs, is described and documented. Variables predicted include dissolved oxygen, biochemical oxygen demand, nitrogen forms, total and fecal-coliform bacteria, orthophosphate-phosphorus, and various conservative substances. The model is based primarily on the well known Streeter-Phelps oxygen-sag equation. Special options of the program include the capability of handling nonpoint source waste inputs and anoxic conditions. The model formulation is based on a steady-state assumption which requires constant flow rate of waste and stream discharges and associated parameters. To achieve a problem solution, each reach of a stream system is broken into a given number of subreaches, generally defined by locations of waste or tributary inflow points. All waste constituents are assumed to be completely mixed within any cross section.

Water-Resources Investigations Report↗
USGS1965

A final report on computed magneto-telluric curves for hypothetical models of crustal structure

Several mathematical models were investigated to determine the capa-bilities of the magneto-telluric method for determining the resistivity structure of the earth's crust. The model parameters were based on the crust model proposed by Keller (1963). The mathematical technique used was developed by Cagniard (1953). The investigations indicate that a three-layer model approximation of the crust and mantle is the most detailed model warranted in inter-preting the information provided by the magneto-telluric method about the lower crust. Only the thickness of the lower crust can be determined, and not the resistivity.

Crustal Studies Technical Letters↗
USGS1994

Simulating and mapping spatial complexity using multi-scale techniques

A central problem in spatial analysis is the mapping of data for complex spatial fields using relatively simple data structures, such as those of a conventional GIS. This complexity can be measured using such indices as multi-scale variance, which reflects spatial autocorrelation, and multi-fractal dimension, which characterizes the values of fields. These indices are computed for three spatial processes: Gaussian noise, a simple mathematical function, and data for a random walk. Fractal analysis is then used to produce a vegetation map of the central region of California based on a satellite image. This analysis suggests that real world data lie on a continuum between the simple and the random, and that a major GIS challenge is the scientific representation and understanding of rapidly changing multi-scale fields.

International Journal of Geographical Information ↗
USGS1971

Data file, Continental Margin Program, Atlantic Coast of the United States: vol. 2 sample collection and analytical data

The purpose of the data file presented below is twofold: the first purpose is to make available in printed form the basic data relating to the samples collected as part of the joint U.S. Geological Survey - Woods Hole Oceanographic Institution program of study of the Atlantic continental margin of the United States; the second purpose is to maintain these data in a form that is easily retrievable by modern computer methods. With the data in such form, repeate manual transcription for statistical or similar mathematical treatment becomes unnecessary. Manual plotting of information or derivatives from the information may also be eliminated. Not only is handling of data by the computer considerably faster than manual techniques, but a fruitful source of errors, transcription mistakes, is eliminated.

Report↗
USGS1984

A modular three-dimensional finite-difference ground-water flow model

This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts were incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilitates development of additional capabilities because new modules or packages can be added to the program without modifying the existing modules or packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow from external stresses, such as flow to wells, areal recharge, evapotranspiration, flow to drains, and flow through riverbeds, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN '66 and will run without modification on most computers which have a FORTRAN '66 compiler. It will also run, without modification, with most extended FORTRAN '77 compilers and with minor modifications on standard FORTRAN '77 compilers. Documentation presented in this report includes a narrative description, a flow chart, a list of variables, and a program listing for each module.

Open-File Report↗
USGS1988

A modular three-dimensional finite-difference ground-water flow model

This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.

Techniques of Water-Resources Investigations↗
USGS1988

A modular three-dimensional finite-difference fround-water flow model

This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.

Techniques of Water-Resources Investigations↗
USGS2003

Probabilistic assessment methodology for continuous-type petroleum accumulations

The analytic resource assessment method, called ACCESS (Analytic Cell-based Continuous Energy Spreadsheet System), was developed to calculate estimates of petroleum resources for the geologic assessment model, called FORSPAN, in continuous-type petroleum accumulations. The ACCESS method is based upon mathematical equations derived from probability theory in the form of a computer spreadsheet system. ?? 2003 Elsevier B.V. All rights reserved.

International Journal of Coal Geology↗
USGS1975

Water-quality data from oil and gas wells in part of the Permian Basin, southeastern New Mexico and western Texas

Approximately 8,000 chemical analyses of water produced from formations of several geologic ages in south eastern New Mexico and western Texas are tabulated by both geographic location and geologic formation. Empirical and mathematical relationships between (1) the dissolved solids and the measured and computed resistivity of water, the chloride-ion concentration and the density, and (2) the concentration of chloride-ion and the density and the resistivity of water, were established. Resistivities of water computed following a method developed by Moore, Szasz, and Whitney (1966) using the concentration of the six most common constituents dissolved in natural water correlate favorably with the measured resistivities of natural water. The water analyses were obtained chiefly from oil companies and oil-service companies operating in the western part of the Permian basin. The data were associated with the proper well by searching location, operator, and reference number cross indexes prepared from the Permian Basin Well Data System files. The cross indexes were determined to be essential to efficient data processing operations. After preliminary screening for nonrepresentative data, all data were indexed to the Permian Basin Well Data System magnetic tape file scout records by the unique reference number. The data were then coded, punched into tabulating cards, and stored on magnetic tape for computer operations. Data verification steps not normally required when using data received from a laboratory following standardized analytical techniques on samples obtained under standardized and controlled procedures were performed in order to upgrade reliability of the information. Data errors detected included poorly located or identified samples; mistakes including reproducing, or key punching; laboratory errors; inconsistent reporting; and nonrepresentative or contaminated samples.

New Mexico, Texas↗
USGS1994

Estimating the magnitude and frequency of low flows of streams in Massachusetts

The report presents techniques used for estimating 7-day 2-year (7Q2) and 7-day 10-year (7Q10) flows at continuous-record streamflow-gaging stations, partial-record stations, and ungaged sites on streams in Massachusetts. A two-parameter log-normal probability distribution was used to compute low flows at 31 continuous-record stream-flow-gaging stations. Graphical and mathematical techniques were used to estimate low flows at partial-record stations. Regional regression techniques commonly are used to estimate 7Q2 and 7Q10 flows at ungaged stream sites. The development and application of a low-flow regression model is described. The model contains two parameters, mean and standard deviation, computed from separate regression equations that use total drainage area and basin relief as independent variables. The coefficients of determination of the mean and standard deviation regression equations are 0.964 and 0.960, respec- tively; the percentage of standard error of the regression of each equation are 35 and 34, respec- tively. The model is applicable for basins in Massachusetts having a drainage area of 5 to 150 square miles, a slope of less than 4 percent, and an area of stratified drift greater than 4 percent of the total drainage area. A computer program is presented that can be used to compute 7Q2 and 7Q10 flows and the 95-percent intervals of confidence and prediction for a given basin.

Water-Resources Investigations Report↗
USGS1982

Hydrologic maps of the High Plains aquifer, January 1981, southwestern Kansas

The U.S. Geological Survey furnishes maps depicting saturated thickness of the High Plains aquifer to the Southwest Kansas Groundwater Management District No. 3 through a continuing cooperative agreement. The Groundwater Management District uses the maps to calculated a planned depletion rate of 40 percent of the saturated thickness of the aquifer in 25 years for a 13-county area. Because the information contained on the maps is used in management decisions, the Groundwater Management District is concerned with the accuracy, reliability, and consistency of the hydrologic information that the maps show. A mathematical technique, called kriging, has been used in the form of a computer program to interpolate hydrologic data based on a network of measured values (Karlinger and Skrivan, 1980). The technique has been applied to geohydrologic data in west-central Kansas with good results (Dunlap and Spinazola, 1981). The program calculates the values at the center of each 1-mile section in a predefined region and facilitates contouring of selected values. The kriging technique was used to produce the hydrologic maps in this report.

Kansas↗
USGS1998

Computer programs for describing the recession of ground-water discharge and for estimating mean ground-water recharge and discharge from streamflow records-update

The computer programs included in this report can be used to develop a mathematical expression for recession of ground-water discharge and estimate mean ground-water recharge and discharge. The programs are intended for analysis of the daily streamflow record of a basin where one can reasonably assume that all, or nearly all, ground water discharges to the stream except for that which is lost to riparian evapotranspiration, and where regulation and diversion of flow can be considered to be negligible. The program RECESS determines the master reces-sion curve of streamflow recession during times when all flow can be considered to be ground-water discharge and when the profile of the ground-water-head distribution is nearly stable. The method uses a repetitive interactive procedure for selecting several periods of continuous recession, and it allows for nonlinearity in the relation between time and the logarithm of flow. The program RORA uses the recession-curve displacement method to estimate the recharge for each peak in the streamflow record. The method is based on the change in the total potential ground-water discharge that is caused by an event. Program RORA is applied to a long period of record to obtain an estimate of the mean rate of ground-water recharge. The program PART uses streamflow partitioning to estimate a daily record of base flow under the streamflow record. The method designates base flow to be equal to streamflow on days that fit a requirement of antecedent recession, linearly interpolates base flow for other days, and is applied to a long period of record to obtain an estimate of the mean rate of ground-water discharge. The results of programs RORA and PART correlate well with each other and compare reasonably with results of the corresponding manual method.

Water-Resources Investigations Report↗
USGS1989

Thermal maturity of the Anadarko Basin

Levels of thermal maturity are estimated for Paleozoic strata in five areas of the central Anadarko basin for times between the Paleozoic and the present, and depths of the oil window are plotted as a function of geologic time. Mean surface temperature assumed here for calculating Lopatin's time-temperature index of thermal maturity (TTl) in the central Anadarko basin declines from 80°F (27°C) to 60°F (16°C) from early Paleozoic time to the present. Shallow-water carbonates and lower paleolatitudes suggest warmer climates in the Paleozoic for this area. The geothermal gradient is assumed to equal 4.0°F/100 ft (7.3°C/100 m) in the Late Cambrian and to decay over a 100-m.y. period to the present regional gradient of 1.3°F/100 ft (2.4°C/100 m). Initial basin formation was caused by crustal thinning. Accumulation of thick Pennsylvanian sediments in a foreland-style basin dominated by vertical lithospheric flexure represents a second major period of subsidence. An elevated geothermal gradient during this time is not assumed for TTl calculations, because mathematical models suggest time-invariant heat flows in such basins. TTl computations based on these assumptions indicate that oil could have been generated in the ancestral Anadarko basin >350 m.y. ago. By the end of the Pennsylvanian, significant volumes of kerogen were in the oil window (and perhaps beyond), and significant volumes have remained in the oil window up to the present day. These circumstances may partially explain the unusual richness of the Anadarko basin as a Paleozoic hydrocarbon province.

Oklahoma↗
USGS1981

Mathematical model of gamma-ray spectrometry borehole logging for quantitative analysis

A technique for analyzing gamma-ray spectral-logging data has been developed, in which a digital computer is used to calculate the effects of gamma-ray attentuation in a borehole environment. The computer model allows for the calculation of the effects of lithology, porosity, density, and the thickness of a horizontal layer of uniformly distributed radioactive material surrounding a centralized probe in a cylindrical borehole. The computer program also contains parameters for the calculation of the effects of well casing, drilling fluid, probe housing, and losses through the sodium-iodide crystal. Errors associated with the commonly used mathematical assumption of a point detector are eliminated in this model. (USGS)

Open-File Report↗
USGS1992

The hydrodynamics of the Big Horn basin: A study of the role of faults

A three-dimensional mathematical model simulates virgin groundwater flow in the Big Horn basin, Wyoming. The computed results are compared to two published interpretations of the Tensleep Sandstone virgin potentiometric surface; both of these interpretations, Bredehoeft and Bennett, and Haun, were made from the same data set. The published maps are quite different. Bredehoeft and Bennett ignored the faults; Haun treated the faults as horizontal barriers to flow. The hydraulic head at depth over much of the Big Horn basin is near the land surface elevation, a condition usually defined as hydrostatic. This condition indicates a high, regional-scale, vertical conductivity for the sediments in the basin. Our hypothesis to explain the high conductivity is that the faults act as vertical conduits for fluid flow. These same faults can act as either horizontal barriers to flow or nonbarriers, depending upon whether the fault zones are more permeable or less permeable than the adjoining aquifers. A three-dimensional simulation of fluid flow in the basin indicates that either of the potentiometric interpretations, that of Bredehoeft and Bennett or that of Haun, can be reproduced. The results depend upon whether the fault zones are lateral barriers to flow. In the case where the faults are lateral barriers, the basin is broken into compartments with much of the areal head loss occurring across the fault zones.

Montana, Wyoming↗
USGS2004

The value of long-term monitoring in the development of ground-water-flow models

As environmental issues have come to the forefront of public concern, so has the awareness of the importance of ground water in the overall water cycle and as a source of the Nation’s drinking water. Heightened interest has spawned a host of scientific enterprises (Taylor and Alley, 2001). Some activities are directed toward collection of water-level data and related information to monitor the physical and chemical state of the resource. Other activities are directed at interpretive studies undertaken, for example, to optimize the location of new water-supply wells or to protect rivers and lakes fed by ground water. An important type of interpretive study is the computer ground-water-flow model that inte- grates field data in a mathematical framework. Long-term, systematic collection of hydro- logic data is crucial to the construction and testing of ground-water models so that they can reproduce the evolution of flow systems and forecast future conditions.

Wisconsin↗