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Results for “Mathematical Geology”

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 109 records · Page 6Linked to original sources
USGS2002

Spatial digital database for the geology of the San Pedro River Basin in Cochise, Gila, Graham, Pima, and Pinal Counties, Arizona

This spatial digital database for the geology of the San Pedro River Basin in southeastern Arizona was compiled from three maps by Dickinson (1993, 1998, 2000). Mylar originals of the map sheets were scanned, and the resultant images were rectified to a mathematically-generated set of latitude and longitude registration points. Geologic linework was digitized from the rectified images on screen using ArcView (ver. 3.2), and the resultant shapefiles were converted to ArcInfo (ver. 7.2) coverages. Lines and polygons were then attributed; and the files were merged omtp a single ArcInfo database (quib24k). This digital spatial database is one of many being created by the U.S. Geological Survey as an ongoing effort to provide geologic information in a geographic information system (GIS) for use in spatial analysis. This database can be queried in many ways to produce a variety of geologic maps. Digital base map data files (topography, roads, towns, rivers and lakes, etc.) are not included: they may be obtained from a variety of commercial and government sources. This database is not meant to be used or displayed at any scale larger than 1:24,000 (for example, 1:12,000). The map area is located in southeastern Arizona. This report describes the map units, the methods used to convert the geologic map data into a digital format, and the ArcInfo GIS file structures and relationships; and it explains how to download the digital files from the U.S. Geological Survey public access World Wide Web site on the Internet. See figures 2 and 3 for page-size versions of the map compilation.

Arizona↗
USGS1999

Oxygen isotopes of dissolved sulfate as a tool to distinguish natural and mining-related dissolved constituents

Natural and mining-related dissolved-constituent concentrations need to be distinguished in a watershed affected by abandoned mines to prioritize subbasins for remediation and to assist with the establishment of water-quality standards. The oxygen isotopes of dissolved sulfate can be used to distinguish between natural and mining-related sources of dissolved constituents. Several methods employing the oxygen isotopes of dissolved sulfate can be used to determine the relative amounts of natural and mining related dissolved constituents in water: (1) the isotope-dilution equation for simple mixing zones (two sources and one receiving stream); (2) the isotope mass-balance equation for streams receiving dissolved sulfate from multiple geologic sources; and (3) graphical relations and the mathematical solution of simultaneous equations in a watershed approach. Using the different methods for data collected during low flow, about 71 to 75 percent of the dissolved-constituent concentrations are from natural sources in selected subbasins of the upper Animas watershed.

Open File Report↗
USGS1983

Hydrologic and geologic aspects of waste management and disposal; a bibliography of publications by U.S. Geological Survey authors, 1950-81

References to more than 550 reports, articles, and maps are listed alphabetically by author and are indexed by subject. The subject index includes geographic-area terms. Citations from 69 series are included; series are listed separately. The publications listed report the results of U.S. Geological Survey research and field projects throughout the Nation concerning earth-science aspects of waste management and disposal. They include organic, inorganic, and radioactive wastes and related topics such as mathematical models of solute transport. Most of the references are to (1) Geological Survey report series such as Water-Supply Papers, Professional Papers, Bulletins, Circulars, Water-Resources Investigations, and Open-File Reports, (2) technical journals of professional organizations, or (3) reports by other Federal and State agencies.

Circular↗
USGS2000

Methods for estimating low-flow statistics for Massachusetts streams

Methods and computer software are described in this report for determining flow duration, low-flow frequency statistics, and August median flows. These low-flow statistics can be estimated for unregulated streams in Massachusetts using different methods depending on whether the location of interest is at a streamgaging station, a low-flow partial-record station, or an ungaged site where no data are available. Low-flow statistics for streamgaging stations can be estimated using standard U.S. Geological Survey methods described in the report. The MOVE.1 mathematical method and a graphical correlation method can be used to estimate low-flow statistics for low-flow partial-record stations. The MOVE.1 method is recommended when the relation between measured flows at a partial-record station and daily mean flows at a nearby, hydrologically similar streamgaging station is linear, and the graphical method is recommended when the relation is curved. Equations are presented for computing the variance and equivalent years of record for estimates of low-flow statistics for low-flow partial-record stations when either a single or multiple index stations are used to determine the estimates. The drainage-area ratio method or regression equations can be used to estimate low-flow statistics for ungaged sites where no data are available. The drainage-area ratio method is generally as accurate as or more accurate than regression estimates when the drainage-area ratio for an ungaged site is between 0.3 and 1.5 times the drainage area of the index data-collection site. Regression equations were developed to estimate the natural, long-term 99-, 98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, and 50-percent duration flows; the 7-day, 2-year and the 7-day, 10-year low flows; and the August median flow for ungaged sites in Massachusetts. Streamflow statistics and basin characteristics for 87 to 133 streamgaging stations and low-flow partial-record stations were used to develop the equations. The streamgaging stations had from 2 to 81 years of record, with a mean record length of 37 years. The low-flow partial-record stations had from 8 to 36 streamflow measurements, with a median of 14 measurements. All basin characteristics were determined from digital map data. The basin characteristics that were statistically significant in most of the final regression equations were drainage area, the area of stratified-drift deposits per unit of stream length plus 0.1, mean basin slope, and an indicator variable that was 0 in the eastern region and 1 in the western region of Massachusetts. The equations were developed by use of weighted-least-squares regression analyses, with weights assigned proportional to the years of record and inversely proportional to the variances of the streamflow statistics for the stations. Standard errors of prediction ranged from 70.7 to 17.5 percent for the equations to predict the 7-day, 10-year low flow and 50-percent duration flow, respectively. The equations are not applicable for use in the Southeast Coastal region of the State, or where basin characteristics for the selected ungaged site are outside the ranges of those for the stations used in the regression analyses. A World Wide Web application was developed that provides streamflow statistics for data collection stations from a data base and for ungaged sites by measuring the necessary basin characteristics for the site and solving the regression equations. Output provided by the Web application for ungaged sites includes a map of the drainage-basin boundary determined for the site, the measured basin characteristics, the estimated streamflow statistics, and 90-percent prediction intervals for the estimates. An equation is provided for combining regression and correlation estimates to obtain improved estimates of the streamflow statistics for low-flow partial-record stations. An equation is also provided for combining regression and drainage-area ratio estimates to obtain improved e

Massachusetts↗
USGS1983

Seismology in Chile

The Department of Geology and Geophysics, which is under the faculties of Mathematics and Physical Sciences of the University of Chile, is the organization that is responsible for the Seismological Service of Chile and for installing,operating, and maintaining the seismological stations as well as all the strong-motion stations in Chile.

Earthquake Information Bulletin (USGS)↗
USGS2017

Geohydrologic considerations in the management of radioactive waste

Nongaseous radioactive wastes occur as liquids containing high-level concentrations of radionuclides, liquids containing low concentrations of radionuclides, and solids contaminated by radioactivity. Whether released by accident or design into the earth or onto the earth’s surface, only water is capable of transporting significant quantities of radionuclides away from burial sites. Geohydrologic information that must be determined to predict the velocity and direction of waste movement from a site include climate, hydrology, detailed subsurface geology, permeability, porosity, sorptive potential, seismic potential, and geologic history of the area. Since the late 1960’s mathematical models have been used to make predictions of waste transport in some hydrologic systems. Intensive field investigations at each site are needed before these models can be used.

Nuclear Technology↗
USGS2006

Performance assessments of nuclear waste repositories: A dialogue on their value and limitations

Performance Assessment (PA) is the use of mathematical models to simulate the long-term behavior of engineered and geologic barriers in a nuclear waste repository; methods of uncertainty analysis are used to assess effects of parametric and conceptual uncertainties associated with the model system upon the uncertainty in outcomes of the simulation. PA is required by the U.S. Environmental Protection Agency as part of its certification process for geologic repositories for nuclear waste. This paper is a dialogue to explore the value and limitations of PA. Two “skeptics” acknowledge the utility of PA in organizing the scientific investigations that are necessary for confident siting and licensing of a repository; however, they maintain that the PA process, at least as it is currently implemented, is an essentially unscientific process with shortcomings that may provide results of limited use in evaluating actual effects on public health and safety. Conceptual uncertainties in a PA analysis can be so great that results can be confidently applied only over short time ranges, the antithesis of the purpose behind long-term, geologic disposal. Two “proponents” of PA agree that performance assessment is unscientific, but only in the sense that PA is an engineering analysis that uses existing scientific knowledge to support public policy decisions, rather than an investigation intended to increase fundamental knowledge of nature; PA has different goals and constraints than a typical scientific study. The “proponents” describe an ideal, sixstep process for conducting generalized PA, here called probabilistic systems analysis (PSA); they note that virtually all scientific content of a PA is introduced during the model-building steps of a PSA, they contend that a PA based on simple but scientifically acceptable mathematical models can provide useful and objective input to regulatory decision makers. The value of the results of any PA must lie between these two views and will depend on the level of knowledge of the site, the degree to which models capture actual physical and chemical processes, the time over which extrapolations are made, and the proper evaluation of health risks attending implementation of the repository. The challenge is in evaluating whether the quality of the PA matches the needs of decision makers charged with protecting the health and safety of the public.

Risk Analysis↗
USGS1962

Theory of aquifer tests

The development of water supplies from wells was placed on a rational basis with Darcy's development of the law governing the movement of fluids through sands and with Dupuit's application of that law to the problem of radial flow toward a pumped well. As field experience increased, confidence in the applicability of quantitative methods was gained and interest in developing solutions for more complex hydrologic problems was stimulated. An important milestone was Theis' development in 1935 of a solution for the nonsteady flow of ground water, which enabled hydrologists for the first time to predict future changes in ground-water levels resulting from pumping or recharging of wells. In the quarter century since, quantitative ground-water hydrology has been enlarging so rapidly as to discourage the preparation of comprehensive textbooks. This report surveys developments in fluid mechanics that apply to groundwater hydrology. It emphasizes concepts and principles, and the delineation of limits of applicability of mathematical models for analysis of flow systems in the field. It stresses the importance of the geologic variable and its role in governing the flow regimen. The report discusses the origin, occurrence, and motion of underground water in relation to the development of terminology and analytic expressions for selected flow systems. It describes the underlying assumptions necessary for mathematical treatment of these flow systems, with particular reference to the way in which the assumptions limit the validity of the treatment.

Water Supply Paper↗
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↗
USGS2019

The Appalachian Geo-STEM Camp: Learning about geology through experiential adventure recreation

The inaugural Appalachian Geo-STEM Camp (AGC) was a partnership between West Virginia University (WVU), the U.S. Geological Survey (USGS) and the West Virginia Geological and Economic Survey (WVGES). Designed to engage high school students in geoscience-oriented Science, Technology, Engineering and Mathematics (STEM) activities through adventure-based outdoor recreation, the inaugural AGC took place in June 2018, with its base operations at the WVU Natural Resources Center (NRC), located northeast of Morgantown, West Virginia. The goals of the AGC are to increase the knowledge of the teenaged campers about the geological formations and biodiversity in the region, to acquaint them with geologic mapping technology used by USGS, WVGES, and WVU, and to foster interest in STEM-based careers. Nine students participated, with a cadre from the USGS, WVGES, and WVU teaching lessons in local geology and ecology. Inaugural-year efforts were focused on development and logistics of the camp and what activities best complimented the STEM research. Post-evaluations by the participants were generally favorable. Year-two goals are to fully develop a curriculum, and conduct a thorough pre-camp and post-camp participant survey to quantify learning objectives and guide the sustainability of the effort.

West Virginia↗
USGS2016

Undergraduate research projects help promote diversity in the geosciences

A workforce that draws from all segments of society and mirrors the ethnic, racial, and gender diversity of the United States population is important. The geosciences (geology, hydrology, geospatial sciences, environmental sciences) continue to lag far behind other science, technology, engineering and mathematical (STEM) disciplines in recruiting and retaining minorities (Valsco and Valsco, 2010). A report published by the National Science Foundation in 2015, “Women, Minorities, and Persons with Disabilities in Science and Engineering” states that from 2002 to 2012, less than 2% of the geoscience degrees were awarded to African-American students. Data also show that as of 2012, approximately 30% of African-American Ph.D. graduates obtained a bachelor’s degree from a Historic Black College or University (HBCU), indicating that HBCUs are a great source of diverse students for the geosciences. This paper reviews how an informal partnership between Tennessee State University (a HBCU), the U.S. Geological Survey, and Mammoth Cave National Park engaged students in scientific research and increased the number of students pursuing employment or graduate degrees in the geosciences.

Conference Paper↗
USGS1979

Plan of study for the northern Great Plains regional aquifer-system analysis in parts of Montana, North Dakota, South Dakota, and Wyoming

The Northern Great Plains, an area of about 250,000 square miles in parts of Montana, North Dakota, South Dakota, and Wyoming, is underlain by an accumulation of sediments eroded from the Black Hills and from mountains to the west. Principal aquifers are areally extensive beds of sandstone within these sedimentary rocks, some at great depths. Anticipated future water needs dictate that available ground-water supplies be evaluated for management of this natural resource. The U.S. Geological Survey has started (1978) a 4-year study of the Northern Great Plains aquifer system. The objective of this study is to define availability and quality of ground water and to predict the effects of using this resource. To achieve this objective, the ground-water system will be described in terms of spatial distribution, hydraulics, geology, and geochemistry. Once described, the ground-water system will be simulated by mathematical models that will be used to define responses of the system to various management alternatives and assumed development patterns.

Montana, North Dakota, South Dakota, Wyoming↗
USGS2018

A snapshot of women of the U.S. Geological Survey in STEM and related careers

Introduction The term “STEM” has been used to group together the fields of science, technology, engineering, and mathematics and to describe education and professions related to these fields. The professional fields connected to STEM education are thought of as engineering, medicine, and computer technology. Yet these professional fields are merely the tip of the iceberg. Numerous opportunities in these fields encompass environmental research. The possibilities range from predicting the next earthquake to saving polar bears from extinction to developing a vaccine for salmon measles. The science of natural systems is complex and often requires people from a variety of fields of expertise to make headway with a solution. To that end, the U.S. Geological Survey (USGS) has long recognized the need for a diversity of STEM expertise to address the Nation’s environmental research needs and the vision to facilitate integration of these fields. We are team builders! In this book, we point out the many facets of research carried out by USGS STEM scientists in an effort to show career options and pathways not typically pursued. The women portrayed were selected by USGS associate and regional directors as representative of particular fields and to inspire future generations.

Circular↗
USGS1993

Laboratory procedures and data reduction techniques to determine rheologic properties of mass flows

Determining the rheologic properties of coarse- grained mass flows is an important step to mathematically simulate potential inundation zones. Using the vertically rotating flume designed and built by the U.S. Geological Survey, laboratory procedures and subsequent data reduction have been developed to estimate shear stresses and strain rates of various flow materials. Although direct measurement of shear stress and strain rate currently (1992) are not possible in the vertically rotating flume, methods were derived to estimate these values from measurements of flow geometry, surface velocity, and flume velocity.

Water-Resources Investigations Report↗
USGS2025

A partnership between the USGS and the Klamath Tribes to apply structured decision making for chronic wasting disease management

Project Overview: The Klamath Tribes (TKT) are the Klamath, Modoc, and Yahooskin Paiute peoples, and are the first peoples of the land, having lived in ancestral lands of Oregon and California since time immemorial. Members of TKT have rights to hunt, fish, trap, and gather, including the harvest of mule deer ( Odocoileus hemionus ) and elk ( Cervus canadensis nelsoni ) within the 1.19 million acres of their Reserved Treaty Rights Area. Anthropogenic changes threaten the well-being of mule deer and elk and of the Tribes that rely on them. Today, these species are a primary protein source for TKT. They are traded within TKT and among other Tribes and provide materials for cultural and sacred items such as regalia. However, mule deer numbers have been declining across the western states for the past several decades because of multiple stressors, including persistent and frequent drought and wildfires, habitat loss and degradation, vehicle mortality, and increasing barriers to migratory movements between summer and winter ranges. The migratory movements of mule deer, which allow deer to access the best available seasonal habitats, put them at risk of another potential stressor—infection with chronic wasting disease (CWD). Chronic wasting disease is a fatal prion disease of deer that has been detected in 36 U.S. states. It was detected in free-ranging mule deer in northern Idaho in 2021, prompting the Tribes to initiate a planning process for CWD surveillance, prevention, and response measures to preserve and protect the deer and elk within the Reserved Treaty Rights Area. In 2023, the Klamath Tribes Natural Resources Department began to develop their CWD plan by incorporating preliminary input provided by the Klamath Indian Game Commission (KIGC) and working with scientists from the U.S. Geological Survey (USGS). This collaborative effort includes the application of structured decision making and the development of mathematical models to analyze potential CWD management strategies. The result will be a transparent assessment that incorporates TKT values throughout the process and can inform place-based management of the cultural, natural, and physical resources upon which the Tribes depend. In addition, this process may provide opportunities for broader coordination by natural resource management agencies to work together to ensure the long-term health and sustainability of deer and elk populations within the Reserved Treaty Rights Area and throughout the state of Oregon.

Oregon↗
USGS1978

The hydrothermal system of Long Valley Caldera, California

Long Valley caldera, an elliptical depression covering 450 km 2 on the eastern front of the Sierra Nevada in east-central California, contains a hot-water convection system with numerous hot springs and measured and estimated aquifer temperatures at depths of 180?C to 280?C. In this study we have synthesized the results of previous geologic, geophysical, geochemical, and hydrologic investigations of the Long Valley area to develop a generalized conceptual and mathematical model which describes the gross features of heat and fluid flow in the hydrothermal system. Cenozoic volcanism in the Long Valley region began about 3.2 m.y. (million years) ago and has continued intermittently until the present time. The major event that resulted in the formation of the Long Valley caldera took place about 0.7 m.y. ago with the eruption of 600 km 3 or more of Bishop Tuff of Pleistocene age, a rhyolitic ash flow, and subsequent collapse of the roof of the magma chamber along one or more steeply inclined ring fractures. Subsequent intracaldera volcanism and uplift of the west-central part of the caldera floor formed a subcircular resurgent dome about 10 km in diameter surrounded by a moat containing rhyolitic, rhyodacitic, and basaltic rocks ranging in age from 0.5 to 0.05 m.y. On the basis of gravity and seismic studies, we estimate an aver- age thickness of fill of 2.4 km above the precaldera granitic and metamorphic basement rocks. A continuous layer of densely welded Bishop Tuff overlies the basement rocks, with an average thickness of 1.4 km; the fill above the welded Bishop Tuff consists of intercalated volcanic flows and tuffs and fluvial and lacustrine deposits. Assuming the average grain density of the fill is between 2.45 and 2.65 g/cm 3 , we calculate the average bulk porosity of the total fill as from 0.11 to 0.21. Comparison of published values of porosity of the welded Bishop Tuff exposed southeast of the caldera with calculated values indicates average bulk porosity for the welded tuff (including fracture porosity) from 0.05 to 0.10. Because of its continuity and depth and the likelihood of significant fracture permeability in the more competent rocks such as the welded tuff, our model of the hydrothermal system assumes that the Bishop Tuff provides the principal hot-water reservoir. However, because very little direct information exists from drill holes below 300 m, this assumption must be considered tentative. Long Valley caldera is drained by the Owens River and several tributaries which flow into Lake Crowley in the southeast end of the caldera. Streamflow and springflow measurements for water years 1964-74 indicate a total inflow to Lake Crowley of about 10,900 L/s. In contrast, the total discharge of hot water from the hydrothermal reservoir is about 300 L/s. For modeling purposes, the ground-water system is considered as comprising a shallow subsystem in the fill above the densely welded Bishop Tuff containing relatively cold ground water, and a deep subsystem or hydrothermal reservoir in the welded tuff containing relatively hot ground water. Hydrologic, isotopic, and thermal data indicate that recharge to the hydrothermal reservoir occurs in the upper Owens River drainage basin along the western periphery of the caldera. Temperature profiles in a 2.11- km-deep test well drilled by private industry in the southeastern part of the caldera suggest that an additional flux of relatively cool ground water recharges the deep subsystem around the northeast rim. Flow in the shallow ground-water subsystem is neglected in the model except in recharge areas and along Hot Creek gorge, where approximately 80 percent of the hot-water discharge from the hydrothermal reservoir moves upward along faults toward springs in the gorge. Heat-flow data from the Long Valley region indicate that the resurgent dome overlies a residual magma chamber more circular in plan than the original magma chamber that supplied the Bishop Tuff

California↗
USGS1981

The Lasky cumulative tonnage-grade relationship; a reexamination

The need for interdisciplinary research on resource appraisal techniques was recognized by Samuel G. Lasky, a U.S. Geological Survey geologist, more than 30 years ago. His efforts to devise an appraisal technique that incorporated many attributes of mineral resources resulted in a cumulative tonnage-grade relationship that has been referred to as "the arithmetic-geometric (A/G) ratio" or "Lasky's law" by later writers. A review of subsequent studies of the increases in available metal to be expected as grade decreases indicates that Lasky's work has at times been misinterpreted. Lasky's relationship is shown to be consistent with studies of the correlation between average grades and tonnages of mineralized material in ore deposits. The projection of Lasky's analysis to lower grades is limited because the mathematical formulation predicts physically impossible situations below some limiting grade.

Economic Geology↗
USGS2020

Partly cloudy with a chance of lava flows: Forecasting volcanic eruptions in the 21st century

A primary goal of volcanology is forecasting hazardous eruptive activity. Despite much progress over the last century, however, volcanoes still erupt with no detected precursors, lives and livelihoods are lost to eruptive activity, and forecasting the onsets of eruptions remains fraught with uncertainty. Long‐term forecasts are generally derived from the geological and historical records, from which recurrence intervals and styles of activity can be inferred, while shorter‐term forecasts are derived from patterns in monitoring data. Information from geology and monitoring data can be evaluated and combined using statistical analysis, expert elicitation, and conceptual and or mathematical models. Integrative frameworks, such as event trees, combine this diversity of information to produce probabilistic forecasts that can inform the style and scale of the societal response to a potential future eruption. Several developments show promise to revolutionize the utility and accuracy of these forecasts. These include growth in the quantity and quality of multidisciplinary monitoring data, coupled with increases in computing power; machine learning algorithms, which will allow far better utilization of this growing volume of data; and new physiochemical volcano models and data assimilation algorithms, which take advantage of a wide range of monitoring data and realistic physics to better predict the evolution of a given physical state. Although eruption forecasts may never be as generally reliable as weather forecasts, and great caution must be exercised when attempting to predict highly complex volcanic behavior, these and other innovations—particularly when combined in integrative, fully probabilistic forecasting frameworks—should help volcanologists to better issue warnings of volcanic activity on societally relevant time frames.

Hawaii↗