Search USGS⌕ Search

SEARCH · Search USGS

Results for “Mathematical Geology”

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

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9Linked to original sources
USGS2010

Recent (2001-09) hydrologic history and regionalization studies in Texas-Statistical characterization of storms, floods, and rainfall-runoff relations

As part of numerous cooperative studies investigating rainfall and streamflow during 1991-2009 with the Texas Department of Transportation and Texas Commission on Environmental Quality, the U.S. Geological Survey (USGS) published about 20 reports describing either historical streamflow conditions (hydrologic history) in Texas or the results of studies involving regional rainfall and streamflow statistics (regionalization studies). Both types of studies are widely used in engineering and scientific applications. Long-term rainfall and streamflow records are essential for deriving reliable rainfall and streamflow statistics. Whereas the need for such records is regionwide, rainfall and streamflow records are site-specific. The USGS has pioneered ways to mathematically transfer site-specific rainfall and streamflow information to provide regional statistical models. In addition to publishing reports describing historical hydrologic data at many monitored locations throughout Texas, the USGS has published reports describing regional models for estimating rainfall and streamflow statistics at unmonitored locations. The primary objectives of these regionalization studies were to provide historical perspectives of streamflow conditions in Texas or estimates of specific statistics of rainfall or streamflow. Statistics such as 6-hour, 1-percent annual exceedance rainfall (a large storm) or 2-percent annual exceedance streamflow (a substantial flood) can be estimated for locations lacking sufficient direct observations of rainfall and streamflow data. This fact sheet provides a brief synopsis of 12 recent (2001-09) USGS hydrologic history and regionalization studies in Texas organized thematically and chronologically.

Fact Sheet↗
USGS1997

The Universal Transverse Mercator (UTM) grid

The most convenient way to identify points on the curved surface of the Earth is with a system of reference lines called parallels of latitude and meridians of longitude. On some maps the meridians and parallels appear as straight lines. On most modern maps, however, the meridians and parallels may appear as curved lines. These differences are due to the mathematical treatment required to portray a curved surface on a flat surface so that important properties of the map (such as distance and areal accuracy) are shown with minimum distortion. The system used to portray a portion of the round Earth on a flat surface is called a map projection.

Fact Sheet↗
USGS2018

Groundwater salinity mapping using geophysical log analysis within the Fruitvale and Rosedale Ranch oil fields, Kern County, California, USA

A method is presented for deriving a volume model of groundwater total dissolved solids (TDS) from borehole geophysical and aqueous geochemical measurements. While previous TDS mapping techniques have proved useful in the hydrogeologic setting in which they were developed, they may yield poor results in settings with lithological heterogeneity, complex water chemistry, or limited data. Problems arise because of assumed values for empirical constants in Archie’s Equation, unrealistic porosity and temperature gradients, or bicarbonate-rich groundwater. These issues become critical in complex geologic settings such as the San Joaquin Valley of California, USA. To address this, a method to map TDS in three dimensions is applied to the Fruitvale and Rosedale Ranch oil fields near Bakersfield, California. Borehole resistivity, porosity, and temperature data are used to derive TDS using Archie’s Equation, and are then kriged to interpolate TDS. Archie’s a and m (tortuosity factor and cementation exponent, respectively) are found by comparing model predictions, after kriging, to TDS measurements, and minimizing the differences via mathematical optimization. Contributions of abundant bicarbonate ions to TDS were corrected using an empirical model. This work was motivated by federal and state law requirements to monitor and protect underground sources of drinking water. Modeling shows the legally significant boundary of 10,000 ppm TDS is at ~1,067 m below sea level in Rosedale Ranch, and deepens into Fruitvale to ~1,341 m. Mapping groundwater TDS at this resolution reveals that TDS is primarily controlled by depth, recharge, stratigraphy, and in some places, by faulting and facies changes.

California↗
USGS2022

Fundamental science and engineering questions in planetary cave exploration

Nearly half a century ago, two papers postulated the likelihood of lunar lava tube caves using mathematical models. Today, armed with an array of orbiting and fly-by satellites and survey instrumentation, we have now acquired cave data across our solar system—including the identification of potential cave entrances on the Moon, Mars, and at least six other planetary bodies. These discoveries gave rise to the study of planetary caves. To help advance this field, we leveraged the expertise of an interdisciplinary group to identify a strategy to explore caves beyond Earth. Focusing primarily on astrobiology, the cave environment, geology, robotics, instrumentation, and human exploration, our goal was to produce a framework to guide this subdiscipline through at least the next decade. To do this, we first assembled a list of 198 science and engineering questions. Then, through a series of social surveys, 114 scientists and engineers winnowed down the list to the top 53 highest priority questions. This exercise resulted in identifying emerging and crucial research areas that require robust development to ultimately support a robotic mission to a planetary cave—principally the Moon and/or Mars. With the necessary financial investment and institutional support, the research and technological development required to achieve these necessary advancements over the next decade are attainable. Subsequently, we will be positioned to robotically examine lunar caves and search for evidence of life within martian caves; in turn, this will set the stage for human exploration and potential habitation of both the lunar and martian subsurface.

JGR Planets↗
USGS2015

PRMS-IV, the precipitation-runoff modeling system, version 4

Computer models that simulate the hydrologic cycle at a watershed scale facilitate assessment of variability in climate, biota, geology, and human activities on water availability and flow. This report describes an updated version of the Precipitation-Runoff Modeling System. The Precipitation-Runoff Modeling System is a deterministic, distributed-parameter, physical-process-based modeling system developed to evaluate the response of various combinations of climate and land use on streamflow and general watershed hydrology. Several new model components were developed, and all existing components were updated, to enhance performance and supportability. This report describes the history, application, concepts, organization, and mathematical formulation of the Precipitation-Runoff Modeling System and its model components. This updated version provides improvements in (1) system flexibility for integrated science, (2) verification of conservation of water during simulation, (3) methods for spatial distribution of climate boundary conditions, and (4) methods for simulation of soil-water flow and storage.

Techniques and Methods↗
USGS2000

The use of mathematical models to predict beach behavior for U.S. coastal engineering: A critical review

A number of assumed empirical relationships (e.g., the Bruun Rule, the equilibrium shoreface profile, longshore transport rate equation, beach length: durability relationship, and the renourishment factor) and deterministic numerical models (e.g., GENESIS, SBEACH) have become important tools for investigating coastal processes and for coastal engineering design in the U.S. They are also used as the basis for making public policy decisions, such as the feasibility of nourishing recreational beaches. A review of the foundations of these relationships and models, however, suggests that they are inadequate for the tasks for which they are used. Many of the assumptions used in analytical and numerical models are not valid in the context of modern oceanographic and geologic principles. We believe the models are oversimplifications of complex systems that are poorly understood. There are several reasons for this, including: (1) poor assumptions and important omissions in model formulation; (2) the use of relationships of questionable validity to predict the morphologic response to physical forcing; (3) the lack of hindsighting and objective evaluation of beach behavior predictions for engineering projects; (4) the incorrect use of model calibration and verification as assertions of model veracity; and (5) the fundamental inability to predict coastal evolution quantitatively at the engineering and planning time and space scales our society assumes and demands. It is essential that coastal geologists, beach designers and coastal modelers understand these model limitations. Each important model assumption must be examined in isolation; incorporating them into a model does not improve their validity. It is our belief that the models reviewed here should not be relied on as a design tool until they have been substantially modified and proven in real-world situations. The 'solution,' however, is not to increase the complexity of a model by increasing the number of variables. What is needed is a thoughtful review of what beach behavior questions should or could be answered by modeling. Viable alternatives to the use of models do exist to predict the behavior of beaches. Three such alternatives to models are discussed for nourished beach design.

Journal of Coastal Research↗
USGS1980

A comparison of analog and digital modeling techniques for simulating three-dimensional ground-water flow on Long Island, New York

A three-dimensional electric-analog model of the Long Island, NY , groundwater system constructed by the U.S. Geological Survey in the early 1970 's was used as the basis for developing a digital, three-dimensional finite-difference model. The digital model was needed to provide faster modifications and more rapid solutions to water-management questions. Results generated by the two models are depicted as potentiometric-surface maps of the upper glacial and Magothy aquifers. Results compare favorably for all parts of Long Island except the northwestern part, where hydrologic discontinuities are most prevalent and which the two models represent somewhat differently. The mathematical and hydrologic principles used in development of ground-water models, and the procedures for calibration and acceptance, are presented in nontechnical terms. (USGS)

Water-Resources Investigations Report↗
USGS1990

Time-of-travel of solutes in the Trinity River from Dallas to Trinidad, Texas, May and August 1987

The U.S. Geological Survey (USGS), in cooperation with the city of Dallas, conducted a study of the time of travel of solutes during moderate flow conditions in a reach of the Trinity River from the outfall of the Dallas Central Wastewater Treatment Plant (DCWTP) to the USGS streamflow-gaging station 08062700, Trinity River at Trinidad, in May and August 1987. Previous USGS time-of-travel studies of this reach of the river (Ollman, 1973; 1975) provided low- and moderate-flow data. The data were included in the calibrartion of a mathematical water-quality model used by the city of Dallas and other public and private entities involved in water resources managemnt of the area. The purpose of this study was to provide additional data to extend calibration of that model to include moderately higher streamflow conditions.

Texas↗
USGS1976

Solute transport and modeling of water quality in a small stream

An injection of chloride, sodium, and stable strontium was made at a constant rate for 3 hours into Uvas Creek, Santa Clara County, Calif., to determine the mass transport processes in a small stream. Five observation points were selected within a 610-metre reach of the stream below the injection site. Water samples were collected at the observation points during and immediately after the injection. A mathematical model of the stream was obtained by solving analytically and optimally the one-dimensional mass transport equation of the solutes in the stream. Comparison of field results with a simplified mathematical model indicates the dominance of convection in the behavior of sodium and chloride. The concentration of chloride and sodium can be closely simulated by the model. However, strontium cannot be well represented by the simplified model, which contains a first-order decay-type sink.

California↗
USGS2018

The Midwest Stream Quality Assessment—Influences of human activities on streams

Healthy streams and the fish and other organisms that live in them contribute to our quality of life. Extensive modification of the landscape in the Midwestern United States, however, has profoundly affected the condition of streams. Row crops and pavement have replaced grasslands and woodlands, streams have been straightened, and wetlands and fields have been drained. Runoff from agricultural and urban land brings sediment and chemicals to streams. What is the chemical, physical, and biological condition of Midwestern streams? Which physical and chemical stressors are adversely affecting biological communities, what are their origins, and how might we lessen or avoid their adverse effects? In 2013, the U.S. Geological Survey (USGS) conducted the Midwest Stream Quality Assessment to evaluate how human activities affect the biological condition of Midwestern streams. In collaboration with the U.S. Environmental Protection Agency National Rivers and Streams Assessment, the USGS sampled 100 streams, chosen to be representative of the different types of watersheds in the region. Biological condition was evaluated based on the number and diversity of fish, algae, and invertebrates in the streams. Changes to the physical habitat and chemical characteristics of the streams—“stressors”—were assessed, and their relation to landscape factors and biological condition was explored by using mathematical models. The data and models help us to better understand how the human activities on the landscape are affecting streams in the region.

Fact Sheet↗
USGS1978

Trend analysis of vegetation in Louisiana's Atchafalaya river basin

The purpose of the study was to determine vegetation succession trends; produce a current vegetation map of the basin; and to develop a mathematical model capable of predicting vegetation changes based on hydrologic factors. A statistical relationship of forests and hydrological variables with forest succession constraints predicted forest acreage totals for 16 forest categories within 70% or better of actual values in two-thirds of the cases. Using time-lapsed photography covering 42 years, 23 categories were described. The succession trend of vegetation since 1930, by sedimentation, had been toward mixed hardwoods, except for isolated areas. Satellite MSS Band 7 imagery was used to map the current vegetation into three main categories and for assessment of acreage. Additionally, a geological anomaly was recognized on satellite imagery indication an effect on drainage and sedimentation.

Louisiana↗
USGS1961

Simplified methods for computing total sediment discharge with the modified Einstein procedure

A procedure was presented in 1950 by H. A. Einstein for computing the total discharge of sediment particles of sizes that are in appreciable quantities in the stream bed. This procedure was modified by the U.S. Geological Survey and adapted to computing the total sediment discharge of a stream on the basis of samples of bed sediment, depth-integrated samples of suspended sediment, streamflow measurements, and water temperature. This paper gives simplified methods for computing total sediment discharge by the modified Einstein procedure. Each of four homographs appreciably simplifies a major step in the computations. Within the stated limitations, use of the homographs introduces much less error than is present in either the basic data or the theories on which the computations of total sediment discharge are based. The results are nearly as accurate mathematically as those that could be obtained from the longer and more complex arithmetic and algebraic computations of the Einstein procedure.

Water Supply Paper↗
USGS1973

A review of benthic faunal surveys in San Francisco Bay

During the past 60 years, considerable effort has been expended in studies of the relations of the biotic community and physicochemical characteristics of San Francisco Bay water. In very recent years these studies have emphasized the relations between the 'state of health' of bottom-living invertebrates (the benthos) and the levels of pollutants in the bay. Benthic organisms, generally sessile, are unable to escape deleterious environmental changes, and they reflect these changes in alterations of normal species composition of assemblages and species abundance. Data that expands understanding of these relations in urbanized areas such as San Francisco Bay are critical. Because of the implications of such data in control of water quality, the U.S. Geological Survey undertook a review of the results and major conclusions of San Francisco Bay benthic surveys. The size and species composition of faunal assemblages are largely controlled by the salinity of the water, the texture of the bottom sediments, and locally by wastes discharged into the bay. Efforts to describe the structure and function of benthic communities of the bay and to quantify the effects of waste discharge on them have been hampered by inconsistent and often faulty sampling methodology and species identification. Studies made show a lack of information on the normal life processes of the organisms concerned. The diversity index (a mathematical expression of the number of kinds of organisms present at a location), commonly used to describe the 'health' of the benthic community, has been employed without regard for the need for standardizing methodology and species identifications or for understanding natural biological processes that affect such mathematical indices. There are few reliable quantitative data on the distribution of benthic organisms in San Francisco Bay with which future assessments of the 'health' of the benthic community might be compared. Methods for study of the benthos must be standardized, identifications of species verified by trained taxonomists, and new field and laboratory studies undertaken before we can expect to obtain an accurate description of the benthic fauna and its relations with the environment.

Circular↗
USGS2008

Introduction. Pliocene climate, processes and problems

Climate predictions produced by numerical climate models, often referred to as general circulation models (GCMs), suggest that by the end of the twenty-first century global mean annual surface air temperatures will increase by 1.1-6.4??C. Trace gas records from ice cores indicate that atmospheric concentrations of CO2 are already higher than at any time during the last 650000 years. In the next 50 years, atmospheric CO2 concentrations are expected to reach a level not encountered since an epoch of time known as the Pliocene. Uniformitarianism is a key principle of geological science, but can the past also be a guide to the future? To what extent does an examination of the Pliocene geological record enable us to successfully understand and interpret this guide? How reliable are the 'retrodictions' of Pliocene climates produced by GCMs and what does this tell us about the accuracy of model predictions for the future? These questions provide the scientific rationale for this Theme Issue. ?? 2008 The Royal Society.

Philosophical Transactions of the Royal Society A:↗
USGS1971

A method for discriminating between biogenic and chemical origins of the ore-stage pyrite in a roll-type uranium deposit

Some roll-type uranium deposits are marginal to an altered tongue in sandstone beds that originally contained more-or-less uniformly distributed pyrite. Mineralizing solutions percolated through the sandstone, oxidized nearly all the pre-existing pyrite, and then redeposited part of the pyrite downstream in an embryonic ore zone. The pyrite and the entire ore zone continued to migrate downstream in the sandstone, much as a sand dune migrates. The amount of pyrite in mature deposits varies systematically with the position in the ore body. It is postulated that the rate at which the pyrite was redeposited controlled the systematic variation in distribution of pyrite.Biogenic and chemical models which are described in the literature provide alternate explanations for the genesis of roll-type uranium deposits in sandstone. The different theoretical rates for the precipitation of pyrite in the two genetic models provide a distinctive distribution of pyrite that characterizes each process. The theoretical difference between the biogenic and chemical models provides a mathematical technique for identifying the origin of a deposit. Mathematical analysis of the pyrite content of a uranium deposit in the Shirley Basin, Wyoming, illustrates a practical application of the theory. Although a definite conclusion about the origin of roll-type deposits would require considerably more data than are now available, the pyrite content of this deposit does correspond to the theoretical pyrite content of the chemical model, suggesting that a disproportionation reaction was involved in its formation.

Wyoming↗
USGS2007

Mineral deposit densities for estimating mineral resources

Estimates of numbers of mineral deposits are fundamental to assessing undiscovered mineral resources. Just as frequencies of grades and tonnages of well-explored deposits can be used to represent the grades and tonnages of undiscovered deposits, the density of deposits (deposits/area) in well-explored control areas can serve to represent the number of deposits. Empirical evidence presented here indicates that the processes affecting the number and quantity of resources in geological settings are very general across many types of mineral deposits. For podiform chromite, porphyry copper, and volcanogenic massive sulfide deposit types, the size of tract that geologically could contain the deposits is an excellent predictor of the total number of deposits. The number of mineral deposits is also proportional to the type’s size. The total amount of mineralized rock is also proportional to size of the permissive area and the median deposit type’s size. Regressions using these variables provide a means to estimate the density of deposits and the total amount of mineralization. These powerful estimators are based on analysis of ten different types of mineral deposits (Climax Mo, Cuban Mn, Cyprus massive sulfide, Franciscan Mn, kuroko massive sulfide, low-sulfide quartz-Au vein, placer Au, podiform Cr, porphyry Cu, and W vein) from 108 permissive control tracts around the world therefore generalizing across deposit types. Despite the diverse and complex geological settings of deposit types studied here, the relationships observed indicate universal controls on the accumulation and preservation of mineral resources that operate across all scales. The strength of the relationships ( R 2 =0.91 for density and 0.95 for mineralized rock) argues for their broad use. Deposit densities can now be used to provide a guideline for expert judgment or used directly for estimating the number of most kinds of mineral deposits.

Mathematical Geosciences↗
USGS2013

Conditional spectrum computation incorporating multiple causal earthquakes and ground-motion prediction models

The conditional spectrum (CS) is a target spectrum (with conditional mean and conditional standard deviation) that links seismic hazard information with ground-motion selection for nonlinear dynamic analysis. Probabilistic seismic hazard analysis (PSHA) estimates the ground-motion hazard by incorporating the aleatory uncertainties in all earthquake scenarios and resulting ground motions, as well as the epistemic uncertainties in ground-motion prediction models (GMPMs) and seismic source models. Typical CS calculations to date are produced for a single earthquake scenario using a single GMPM, but more precise use requires consideration of at least multiple causal earthquakes and multiple GMPMs that are often considered in a PSHA computation. This paper presents the mathematics underlying these more precise CS calculations. Despite requiring more effort to compute than approximate calculations using a single causal earthquake and GMPM, the proposed approach produces an exact output that has a theoretical basis. To demonstrate the results of this approach and compare the exact and approximate calculations, several example calculations are performed for real sites in the western United States. The results also provide some insights regarding the circumstances under which approximate results are likely to closely match more exact results. To facilitate these more precise calculations for real applications, the exact CS calculations can now be performed for real sites in the United States using new deaggregation features in the U.S. Geological Survey hazard mapping tools. Details regarding this implementation are discussed in this paper.

Bulletin of the Seismological Society of America↗
USGS2010

Aggregation methodology for the circum-arctic resource appraisal

This paper presents a methodology that intends to aggregate the results of a recent assessment of undiscovered conventional oil and gas resources of the Arctic by the U.S. Geological Survey. The assessment occurred in 48 geologically defined regions called assessment units. The methodology includes using assessor specified pair-wise correlations as the basis to construct a correlation matrix. Sampling from this matrix generates more realistic uncertainty estimates of aggregated resources than if assumptions of total independence or total dependence are made. The latter two assumptions result in overly narrow or overly broad estimates. Aggregation results for resources in regions north of the Arctic Circle are presented.

Mathematical Geosciences↗