Workshop on Deposit Modeling
[No abstract available]
Journal of the International Association for Mathe↗
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Workshop on the Delphi Method
[No abstract available]
Journal of the International Association for Mathe↗
Singularity and Nonnormality in the Classification of Compositional Data
Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore-Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.
Mathematical Geology↗
Harmonic Analysis of Sedimentary Cyclic Sequences in Kansas, Midcontinent, USA
Several stratigraphic sequences in the Upper Carboniferous (Pennsylvanian) in Kansas (Midcontinent, USA) were analyzed quantitatively for periodic repetitions. The sequences were coded by lithologic type into strings of datasets. The strings then were analyzed by an adaptation of a one-dimensional Fourier transform analysis and examined for evidence of periodicity. The method was tested using different states in coding to determine the robustness of the method and data. The most persistent response is in multiples of 8-10 ft (2.5-3.0 m) and probably is dependent on the depositional thickness of the original lithologic units. Other cyclicities occurred in multiples of the basic frequency of 8-10 with persistent ones at 22 and 30 feet (6.5-9.0 m) and large ones at 80 and 160 feet (25-50 m). These levels of thickness relate well to the basic cyclothem and megacyclothem as measured on outcrop. We propose that this approach is a suitable one for analyzing cyclic events in the stratigraphic record.
Mathematical Geology↗
Bibliography of borehole geophysics as applied to ground-water hydrology
Most of the references on borehole geophysics that are relevant to ground-water hydrology are contained in this bibliography, but it does not include every reference that is available under each subject heading; the literature is much too extensive to compile a complete listing. Some of the references may appear under more than one subject heading because the references commonly relate to more than one main topic. Many articles have been cross-referenced in order to assist the reader in locating an article. For example, the article entitled, 'Application of the acoustic televiewer to the characterization of hydraulic fractures in geothermal wells' is listed under both 'Acoustic televiewer,' and 'Geothermal'. The bibliography is intended to lead the reader to other articles on borehole-geophysical logging and related subjects, because each article cited also will have a list of references, which may be more specialized, covering many subjects with related applications, such as physics, mathematics, chemistry, geology, electronics, acoustics, hydrology, and surface geophysics. However, not all of these related subject headings could be included in this bibliography.
Circular↗
Flood-frequency analysis for small natural streams in Georgia
Flood information from 104 project basins (0.1 to 20 square miles) and data available from 170 larger basins (20 to 1,500 square miles) are analyzed to provide planners and designers with relations for estimating the magnitude and frequency of flood-peak discharges on small natural streams in Georgia. More than 90 percent of the project activity was directed toward the acquisition and processing of data for more than two thousand rainfall-runoff periods occurring during 1964-74 at the 104 project stations. Storm rainfall data were computed at 5-minute intervals from records of six long-term (about 75 years) National Weather Service Stations. The U.S. Geological Survey mathematical rainfall-runoff model is used to synthesize long-term flood records for about 80 percent of the project stations. Station flood-frequency data are developed, using the log-Pearson Type III distribution with regionalized skew coefficients. Multiple regression analysis is used to define relations between flood-frequency station data for small and large streams and 10 physical and climatological basin characteristics. The analysis indicates the drainage-basin size is the most significant variable. Five regions having distinct flood-peak characteristics are delineated. The developed relations, expressed as equations and nomographs, are considered usable for virtually any site in Georgia where the drainage area is between 0.1 and 20 square miles, and the flow is natural. (Woodard-USGS)
Open-File Report↗
National Research Program of the Water Resources Division, U.S. Geological Survey, fiscal year 1987
The National Research Program (NRP) of the U.S. Geological Survey's Water Resources Division (WRD) had its beginnings in the late 1950's when "core research" was added as a line item to the Congressional budget. Since that time, the NRP has grown to encompass a broad spectrum of scientific investigations. The sciences of hydrology, mathematics, chemistry, physics, biology, geology, and engineering are used to gain a fundamental understanding of the processes that affect the availability, movement, and quality of the Nation's water resources. The knowledge gained and methods developed have great value to WRD's operational program. Results of the investigations conducted by the NRP are applicable not only to the solution of current water problems, but also to future issues, anticipated or unanticipated, that may affect the Nation's water resources.
Open-File Report↗
Modeling hazardous mass flows Geoflows09: Mathematical and computational aspects of modeling hazardous geophysical mass flows; Seattle, Washington, 9–11 March 2009
A recent workshop at the University of Washington focused on mathematical and computational aspects of modeling the dynamics of dense, gravity-driven mass movements such as rock avalanches and debris flows. About 30 participants came from seven countries and brought diverse backgrounds in geophysics; geology; physics; applied and computational mathematics; and civil, mechanical, and geotechnical engineering. The workshop was cosponsored by the U.S. Geological Survey Volcano Hazards Program, by the U.S. National Science Foundation through a Vertical Integration of Research and Education (VIGRE) in the Mathematical Sciences grant to the University of Washington, and by the Pacific Institute for the Mathematical Sciences. It began with a day of lectures open to the academic community at large and concluded with 2 days of focused discussions and collaborative work among the participants.
Eos, Earth and Space Science News↗
Water Resources Research October 1, 1979 - September 30, 1980: Summary statements of research activities by the Water Resources Division
Research in the WRD had its beginnings in the late 1950's when the "core research" line item was added to the Congressional budget. Since this time the Federal program has grown from a "basic sciences" program to one that includes a broad spectrum of basic and applied scientific investigations. Water resources research in WRD includes the study of water in all its phases and uses the basic sciences of mathematics, chemistry, physics, biology, geology and engineering to gain a fundamental understanding of the processes that affect the movement of water and its chemical constituents through hydrologic systems. The basic knowledge and methodologies derived from water resources research are applicable not only to the solution of current problems associated with the Nation's water resources, but also to anticipated hydrologic issues.
Report↗
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↗
The new camera calibration system at the US Geological Survey
Modern computerized photogrammetric instruments are capable of utilizing both radial and decentering camera calibration parameters which can increase plotting accuracy over that of older analog instrumentation technology from previous decades. Also, recent design improvements in aerial cameras have minimized distortions and increased the resolving power of camera systems, which should improve the performance of the overall photogrammetric process. In concert with these improvements, the Geological Survey has adopted the rigorous mathematical model for camera calibration developed by Duane Brown. An explanation of the Geological Survey's calibration facility and the additional calibration parameters now being provided in the USGS calibration certificate are reviewed. -Author
Photogrammetric Engineering and Remote Sensing↗
National Research Program of the Water Resources Division, U.S. Geological Survey: Fiscal Year 1988
The National Research Program (NRP) of the US Geological Survey 's Water Resources Division (WRD) had its beginnings in the late 1950 's when ' core research ' was added as a line item to the Congressional budget. Since that time, the NRP has grown to encompass a broad spectrum of scientific investigations. The sciences of hydrology, mathematics, chemistry, physics, ecology, biology, geology, and engineering are used to gain a fundamental understanding of the processes that affect the availability, movement, and quality of the Nation 's water resources. The NRP is located principally in Reston, VA, Denver, CO, and Menlo Park , CA. The NRP is subdivided into six disciplines as follows: (1) Ecology; (2) Geomorphology and Sediment Transport; (3) Groundwater Chemistry; (4) Groundwater Hydrology; (5) Surface Water Chemistry; and (6) Surface Water Hydrology. The report provides current information about the NRP on an annual basis. Organized by the six research disciplines, the volume contains a summary of the problem, objective, approach, and progress for each project that was active during fiscal year 1988.
Open-File Report↗
National Research Program of the Water Resources Division, U. S. Geological Survey, Fiscal Year 1989
The National Research Program (NRP) of the U.S. Geological Survey's Water Resources Division (WRD) had its beginnings in the late 1950's when "core research" was added as a line item to the Congressional budget. Since that time, the NRP has grown to encompass a broad spectrum of scientific investigations. The sciences of hydrology, mathematics, chemistry, physics, ecology, biology, geology, and engineering are used to gain a fundamental understanding of the processes that affect the availability, movement, and quality of the Nation's water resources. The knowledge gained and methods developed have great value to WRD's operational program. Results of the investigations conducted by the NRP are applicable not only to the solution of current water problems but also to future issues, anticipated or unanticipated, that may affect the Nation's water resources.
Open-File Report↗
A database and probabilistic assessment methodology for carbon dioxide enhanced oil recovery and associated carbon dioxide retention in the United States
The U.S. Geological Survey (USGS) has developed an assessment methodology for estimating the potential incremental technically recoverable oil resources resulting from carbon dioxide-enhanced oil recovery (CO 2 -EOR) in reservoirs with appropriate depth, pressure, and oil composition. The methodology also includes a procedure for estimating the CO 2 that remains in the reservoir after the CO 2 -EOR process is complete. The methodology relies on a reservoir-level database that incorporates commercially available geologic and engineering data. The mathematical calculations of this assessment methodology were tested and produced realistic results for the Permian Basin Horseshoe Atoll, Upper Pennsylvanian-Wolfcampian Play (Texas, USA). The USGS plans to use the new methodology to conduct an assessment of technically recoverable hydrocarbons and associated CO 2 sequestration resulting from CO 2 -EOR in the United States.
Energy Procedia↗
Simulation of ground-water flow in coastal southern New Jersey
An increasing trend of shallow ground-water withdrawal over the first part of this century on the Cape May Peninsula of New Jersey has resulted in the intrusion of saltwater into the aquifers that comprise the shallow ground-water system. The U.S. Geological Survey has developed a mathematical model of the flow system that simulates the flow regime at the freshwater-saltwater interface in the aquifers. The steady-state hydraulic-head distribution and interface position simulated by the model are in good agreement with those observed.
Conference Paper↗
The inverse problem of refraction travel times, part I: Types of Geophysical Nonuniqueness through Minimization
In a set of two papers we study the inverse problem of refraction travel times. The purpose of this work is to use the study as a basis for development of more sophisticated methods for finding more reliable solutions to the inverse problem of refraction travel times, which is known to be nonunique. The first paper, "Types of Geophysical Nonuniqueness through Minimization," emphasizes the existence of different forms of nonuniqueness in the realm of inverse geophysical problems. Each type of nonuniqueness requires a different type and amount of a priori information to acquire a reliable solution. Based on such coupling, a nonuniqueness classification is designed. Therefore, since most inverse geophysical problems are nonunique, each inverse problem must be studied to define what type of nonuniqueness it belongs to and thus determine what type of a priori information is necessary to find a realistic solution. The second paper, "Quantifying Refraction Nonuniqueness Using a Three-layer Model," serves as an example of such an approach. However, its main purpose is to provide a better understanding of the inverse refraction problem by studying the type of nonuniqueness it possesses. An approach for obtaining a realistic solution to the inverse refraction problem is planned to be offered in a third paper that is in preparation. The main goal of this paper is to redefine the existing generalized notion of nonuniqueness and a priori information by offering a classified, discriminate structure. Nonuniqueness is often encountered when trying to solve inverse problems. However, possible nonuniqueness diversity is typically neglected and nonuniqueness is regarded as a whole, as an unpleasant "black box" and is approached in the same manner by applying smoothing constraints, damping constraints with respect to the solution increment and, rarely, damping constraints with respect to some sparse reference information about the true parameters. In practice, when solving geophysical problems different types of nonuniqueness exist, and thus there are different ways to solve the problems. Nonuniqueness is usually regarded as due to data error, assuming the true geology is acceptably approximated by simple mathematical models. Compounding the nonlinear problems, geophysical applications routinely exhibit exact-data nonuniqueness even for models with very few parameters adding to the nonuniqueness due to data error. While nonuniqueness variations have been defined earlier, they have not been linked to specific use of a priori information necessary to resolve each case. Four types of nonuniqueness, typical for minimization problems are defined with the corresponding methods for inclusion of a priori information to find a realistic solution without resorting to a non-discriminative approach. The above-developed stand-alone classification is expected to be helpful when solving any geophysical inverse problems. ?? Birkha??user Verlag, Basel, 2005.
Pure and Applied Geophysics↗
Use of PRD1 bacteriophage in groundwater viral transport, inactivation, and attachment studies
PRD1, an icosahedra-shaped, 62 nm (diameter), double-stranded DNA bacteriophage with an internal membrane, has emerged as an important model virus for studying the manner in which microorganisms are transported through a variety of groundwater environments. The popularity of this phage for use in transport studies involving geologic media is due, in part, to its relative stability over a range of temperatures and low degree of attachment in aquifer sediments. Laboratory and field investigations employing PRD1 are leading to a better understanding of viral attachment and transport behaviors in saturated geologic media and to improved methods for describing mathematically subsurface microbial transport at environmentally significant field scales. Radioisotopic labeling of PRD1 is facilitating additional information about the nature of viral interactions with solid surfaces in geologic media, the importance of iron oxide surfaces, and allowing differentiation between inactivation and attachment in field-scale tracer tests.
FEMS Microbiology Ecology↗
Selected topics of fluid mechanics
The fundamental equations of fluid mechanics are specific expressions of the principles of motion which are ascribed to Isaac Newton. Thus, the equations which form the framework of applied fluid mechanics or hydraulics are, in addition to the equation of continuity, the Newtonian equations of energy and momentum. These basic relationships are also the foundations of river hydraulics. The fundamental equations are developed in this report with sufficient rigor to support critical examinations of their applicability to most problems met by hydraulic engineers of the Water Resources Division of the United States Geological Survey. Physical concepts are emphasized, and mathematical procedures are the simplest consistent with the specific requirements of the derivations. In lieu of numerical examples, analogies, and alternative procedures, this treatment stresses a brief methodical exposition of the essential principles. An important objective of this report is to prepare the user to read the literature of the science. Thus, it begins With a basic vocabulary of technical symbols, terms, and concepts. Throughout, emphasis is placed on the language of modern fluid mechanics as it pertains to hydraulic engineering. The basic differential and integral equations of simple fluid motion are derived, and these equations are, in turn, used to describe the essential characteristics of hydrostatics and piezometry. The one-dimensional equations of continuity and motion are defined and are used to derive the general discharge equation. The flow net is described as a means of demonstrating significant characteristics of two-dimensional irrotational flow patterns. A typical flow net is examined in detail. The influence of fluid viscosity is described as an obstacle to the derivation of general, integral equations of motion. It is observed that the part played by viscosity is one which is usually dependent on experimental evaluation. It follows that the dimensionless ratios known as the Euler, Froude, Reynolds, Weber, and Cauchy numbers are defined as essential tools for interpreting and using experimental data. The derivations of the energy and momentum equations are treated in detail. One-dimensional equations for steady nonuniform flow are developed, and the restrictions applicable to the equations are emphasized. Conditions of uniform and gradually varied flow are discussed, and the origin of the Chezy equation is examined in relation to both the energy and the momentum equations. The inadequacy of all uniform-flow equations as a means of describing gradually varied flow is explained. Thus, one of the definitive problems of river hydraulics is analyzed in the light of present knowledge. This report is the outgrowth of a series of short schools conducted during the spring and summer of 1953 for engineers of the Surface Water Branch, Water Resources Division, U. S. Geological Survey. The topics considered are essentially the same as the topics selected for inclusion in the schools. However, in order that they might serve better as a guide and outline for informal study, the arrangement of the writer's original lecture notes has been considerably altered. The purpose of the report, like the purpose of the schools which inspired it, is to build a simple but strong framework of the fundamentals of fluid mechanics. It is believed that this framework is capable of supporting a detailed analysis of most of the practical problems met by the engineers of the Geological Survey. It is hoped that the least accomplishment of this work will be to inspire the reader with the confidence and desire to read more of the recent and current technical literature of modern fluid mechanics.
Water Supply Paper↗