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Results for “Mathematics and Computers in Simulation”

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 19 recordsLinked to original sources
USGS2003

Tag loss can bias Jolly-Seber capture-recapture estimates

We identified cases where the Jolly-Seber estimator of population size is biased under tag loss and tag-induced mortality by examining the mathematical arguments and performing computer simulations. We found that, except under certain tag-loss models and high sample sizes, the population size estimators (uncorrected for tag loss) are severely biased high when tag loss or tag-induced mortality occurs. Our findings verify that this misconception about effects of tag loss and tag-induced mortality could have serious consequences for field biologists interested in population size. Reiterating common sense, we encourage those engaged in capture-recapture studies to be careful and humane when handling animals during tagging, to use tags with high retention rates, to double-tag animals when possible, and to strive for the highest capture probabilities possible.

Wildlife Society Bulletin↗
USGS1987

The space transformation in the simulation of multidimensional random fields

Space transformations are proposed as a mathematically meaningful and practically comprehensive approach to simulate multidimensional random fields. Within this context the turning bands method of simulation is reconsidered and improved in both the space and frequency domains.

Mathematics and Computers in Simulation↗
USGS1977

Computer simulation of two-dimensional unsteady flows in estuaries and embayments by the method of characteristics : Basic theory and the formulation of the numerical method

Two-dimensional unsteady flows of homogeneous density in estuaries and embayments can be described by hyperbolic, quasi-linear partial differential equations involving three dependent and three independent variables. A linear combination of these equations leads to a parametric equation of characteristic form, which consists of two parts: total differentiation along the bicharacteristics and partial differentiation in space. For its numerical solution, the specified-time-interval scheme has been used. The unknown, partial space-derivative terms can be eliminated first by suitable combinations of difference equations, converted from the corresponding differential forms and written along four selected bicharacteristics and a streamline. Other unknowns are thus made solvable from the known variables on the current time plane. The computation is carried to the second-order accuracy by using trapezoidal rule of integration. Means to handle complex boundary conditions are developed for practical application. Computer programs have been written and a mathematical model has been constructed for flow simulation. The favorable computer outputs suggest further exploration and development of model worthwhile. (Woodard-USGS)

Water-Resources Investigations Report↗
USGS1982

An electric-analog simulation of elliptic partial differential equations using finite element theory

Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct.

Mathematics and Computers in Simulation↗
USGS1997

Identification of internal flow dynamics in two experimental catchments

Identification of the internal flow dynamics in catchments is difficult because of the lack of information in precipitation -stream discharge time series alone. Two experimental catchments, Hydrohill and Nandadish, near Nanjing in China, have been set up to monitor internal flows reaching the catchment stream at various depths, from the surface runoff to the bedrock. With analysis of the precipitation against these internal discharges, it is possible to quantify the time constants and volumes associated with various flowpaths in both catchments.

Nanjing↗
USGS1983

Projected effects of proposed chloride-control projects on shallow ground water– Preliminary results for the Wichita River basin, Texas

The U.S. Army Corps of Engineers' plan to control the natural chloride pollution in the Wichita River basin includes the construction of Truscott Brine Lake on a tributary of the North Wichita River. In connection with the proposed brine lake, the U.S. Geological Survey was requested to: (1) Define the existing ground-water conditions in the shallow fresh-water system of the project area; and (2) project the post-construction effects of the proposed lake on the fresh-water aquifer, especially in relation to hydraulic-head changes but also with respect to possible changes in the chemical quality of the ground water. The fresh-water aquifer in the project area is a shallow water-table system with relatively fresh water (generally a calcium sulfate type) that contains approximately 500 to 5,000 milligrams per liter of dissolved solids. The aquifer consists of Permian rocks with very small values of hydraulic conductivity and overlies a brine system (sodium chloride type) that is even less permeable. A thin transition zone separates the fresh-water aquifer and the brine system. Small quantities of infiltration from precipitation throughout the area's watershed constitute the recharge to the aquifer. Discharge from the aquifer consists of the small base flow along creeks; well discharge is negligible. Two-dimensional mathematical computer models were developed for aquifer simulation of: (1) Steady-state conditions in a fresh-water system and (2) transient conditions in a brine- fresh-water system where the density effects of the brine are considered. The main results 'of projecting the effects of the proposed Truscott Brine Lake on the fresh-water aquifer are: (1) Hydraulic head rises of 5 to 40 feet would be confined to areas near the proposed dam and along the lake shoreline, and (2) migration of salt water downstream from the dam generally would be limited to less than 1 mile and apparently would not reach equilibrium during the 100-year duration of the project. The modeling efforts did not include possible effects related to hydrodynamic dispersion in the brine- fresh-water system. Possible changes in the hydraulic conductivity of the aquifer, due to physical and chemical interactions in the brine and fresh-water environments, also were not considered.

Texas↗
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↗
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↗
USGS1988

A simple approach to nonlinear estimation of physical systems

Recursive algorithms for estimating the states of nonlinear physical systems are developed. This requires some key hypotheses regarding the structure of the underlying processes. Members of this class of random processes have several desirable properties for the nonlinear estimation of random signals. An assumption is made about the form of the estimator, which may then take account of a wide range of applications. Under the above assumption, the estimation algorithm is mathematically suboptimal but effective and computationally attractive. It may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. To link theory with practice, some numerical results for a simulated system are presented, in which the responses from the proposed and the extended Kalman algorithms are compared.

Mathematical and Computer Modelling↗
USGS1977

Simulation studies of flow and sediment transport using a mathematical model, Atchafalaya River Basin, Louisiana

Simulation studies were made of flow and sediment transport for the Atchafalaya River basin, Louisiana using a mathematical model calibrated and supplied by the Hydrologic Engineering Center and the New Orleans District, U.S. Army Corps of Engineers. The study results are based on three, 50-year computer simulations for the following alternatives: (1) no-action alternative, (2) channelization with a center-channel flow area of 80,000 sq ft, and (3) channelization with a center-channel flow area of 100,000 sq ft. Analyses of the simulated data base for depth-frequency, inundated-area, floodway cross-section and water-surface profile relationships were made for 10 flow rates. The analyses indicate a general trend of aggradation in the lower part of the floodway with a consequent trend toward increasing the inundated area, especially at higher flood flows.

Louisiana↗
USGS2020

The community code verification exercise for simulating sequences of earthquakes and aseismic slip (SEAS)

Numerical simulations of sequences of earthquakes and aseismic slip (SEAS) have made great progress over past decades to address important questions in earthquake physics. However, significant challenges in SEAS modeling remain in resolving multiscale interactions between earthquake nucleation, dynamic rupture, and aseismic slip, and understanding physical factors controlling observables such as seismicity and ground deformation. The increasing complexity of SEAS modeling calls for extensive efforts to verify codes and advance these simulations with rigor, reproducibility, and broadened impact. In 2018, we initiated a community code-verification exercise for SEAS simulations, supported by the Southern California Earthquake Center. Here, we report the findings from our first two benchmark problems (BP1 and BP2), designed to verify different computational methods in solving a mathematically well-defined, basic faulting problem. We consider a 2D antiplane problem, with a 1D planar vertical strike-slip fault obeying rate-and-state friction, embedded in a 2D homogeneous, linear elastic halfspace. Sequences of quasi-dynamic earthquakes with periodic occurrences (BP1) or bimodal sizes (BP2) and their interactions with aseismic slip are simulated. The comparison of results from 11 groups using different numerical methods show excellent agreements in long-term and coseismic fault behavior. In BP1, we found that truncated domain boundaries influence interseismic stressing, earthquake recurrence, and coseismic rupture, and that model agreement is only achieved with sufficiently large domain sizes. In BP2, we found that complexity of fault behavior depends on how well physical length scales related to spontaneous nucleation and rupture propagation are resolved. Poor numerical resolution can result in artificial complexity, impacting simulation results that are of potential interest for characterizing seismic hazard such as earthquake size distributions, moment release, and recurrence times. These results inform the development of more advanced SEAS models, contributing to our further understanding of earthquake system dynamics.

Seismological Research Letters↗
USGS2005

MODFLOW-2005 : the U.S. Geological Survey modular ground-water model--the ground-water flow process

This report presents MODFLOW-2005, which is a new version of the finite-difference ground-water model commonly called MODFLOW. Ground-water flow is simulated using a block-centered finite-difference approach. Layers can be simulated as confined or unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and rivers, also can be simulated. The report includes detailed explanations of physical and mathematical concepts on which the model is based, an explanation of how those concepts are incorporated in the modular structure of the computer program, instructions for using the model, and details of the computer code. The modular structure consists of a MAIN Program and a series of highly independent subroutines. The subroutines are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system that is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving the set of simultaneous equations resulting from the finite-difference method. Several solution methods are incorporated, including the Preconditioned Conjugate-Gradient method. The division of the program into packages permits the user to examine specific hydrologic features of the model independently. This also facilitates 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 also are designed to permit maximum flexibility. The program is designed to allow other capabilities, such as transport and optimization, to be incorporated, but this report is limited to describing the ground-water flow capability. The program is written in Fortran 90 and will run without modification on most computers that have a Fortran 90 compiler.

Techniques and Methods↗
USGS1987

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

Water-Resources Investigations Report↗
USGS1987

Stochastic simulation of spatially correlated geo-processes

In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simu??lation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail. ?? 1987 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1985

Documentation of a Regional Aquifer Simulation Model, RAQSIM, and a description of support programs applied in the Twin Platte-Middle Republican Study Area, Nebraska

RAQSIM, a generalized flow model of a groundwater system using finite-element methods, is documented to explain how it works and to demonstrate that it gives valid results. Three support programs that are used to compute recharge and discharge data required as input to RAQSIM are described. RAQSIM was developed to solve transient, two-dimensional, regional groundwater flow problems with isotropic or anisotropic conductance. The model can also simulate radially-symmetric flow to a well and steady-state flow. The mathematical basis, program structure, data input and output procedures, organization of data sets, and program features and options of RAQSIM are discussed. An example , containing listings of data and results and illustrating RAQSIM 's capabilities, is discussed in detail. Two test problems also are discussed comparing RAQSIM 's results with analytical procedures. The first support program described, the PET Program, uses solar radiation and other climatic data in the Jensen-Haise method to compute potential evapotranspiration. The second support program, the Soil-Water Program, uses output from the PET Program, soil characteristics, and the ratio of potential to actual evapotranspiration for each crop to compute infiltration, storage, and removal of water from the soil zone. The third program, the Recharge-Discharge Program, uses output from the Soil-Water Program together with other data to compute recharge and discharge from the groundwater flow system. For each support program, a program listing and examples of the data and results for the Twin Platte-Middle Republican study are provided. In addition, a brief discussion on how each program operates and on procedures for running and modifying these programs are presented. (Author 's abstract)

Nebraska↗