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USGS2019

Analog experiments of lava flow emplacement

Laboratory experiments that simulate lava flows have been in use by volcanologists for many years. The behavior of flows in the lab, where “eruption” parameters, material properties, and environmental settings are tightly controlled, provides insight into the influence of various factors on flow evolution. A second benefit of laboratory lava flows is to provide a set of observations with which numerical models of flow emplacement can be tested. Models of lava flow emplacement vary in mathematical approach, physical assumptions, and computational cost. Nonetheless, all models require thorough testing and evaluation, and laboratory experiments produce an excellent test for models. This paper provides a primer on modern analog laboratory lava flow experiments. It reviews scaling con- siderations and provides quantitative information meant to guide future experimentalists in designing their experiments to be relevant to natural processes. Traditional and novel laboratory techniques are described, including a discussion of current limitations. New insights from recent experiments highlight the impact of topographic conditions and highlight the importance of considering bed roughness, major obstacles, and slope breaks. The influence of episodic or non-uniform effusion rate is demonstrated through recent experi- mental works. Lastly, the paper discusses several open questions about lava flow emplacement and the ways in which future improvements in experimental methods, such as the ability to utilize three-phase suspensions and materials with complex rheologies and to image the interior of flows could help answer these.

Annals of Geophysics↗
USGS2016

Simulating groundwater flow in karst aquifers with distributed parameter models—Comparison of porous-equivalent media and hybrid flow approaches

Understanding karst aquifers, for purposes of their management and protection, poses unique challenges. Karst aquifers are characterized by groundwater flow through conduits (tertiary porosity), and (or) layers with interconnected pores (secondary porosity) and through intergranular porosity (primary or matrix porosity). Since the late 1960s, advances have been made in the development of numerical computer codes and the use of mathematical model applications towards the understanding of dual (primary [matrix] and secondary [fractures and conduits]) porosity groundwater flow processes, as well as characterization and management of karst aquifers. The Floridan aquifer system (FAS) in Florida and parts of Alabama, Georgia, and South Carolina is composed of a thick sequence of predominantly carbonate rocks. Karst features are present over much of its area, especially in Florida where more than 30 first-magnitude springs occur, numerous sinkholes and submerged conduits have been mapped, and numerous circular lakes within sinkhole depressions are present. Different types of mathematical models have been applied for simulation of the FAS. Most of these models are distributed parameter models based on the assumption that, like a sponge, water flows through connected pores within the aquifer system and can be simulated with the same mathematical methods applied to flow through sand and gravel aquifers; these models are usually referred to as porous-equivalent media models. The partial differential equation solved for groundwater flow is the potential flow equation of fluid mechanics, which is used when flow is dominated by potential energy and has been applied for many fluid problems in which kinetic energy terms are dropped from the differential equation solved. In many groundwater model codes (basic MODFLOW), it is assumed that the water has a constant temperature and density and that flow is laminar, such that kinetic energy has minimal impact on flow. Some models have been developed that incorporate the submerged conduits as a one-dimensional pipe network within the aquifer rather than as discrete, extremely transmissive features in a porous-equivalent medium; these submerged conduit models are usually referred to as hybrid models and may include the capability to simulate both laminar and turbulent flow in the one-dimensional pipe network. Comparisons of the application of a porous-equivalent media model with and without turbulence (MODFLOW-Conduit Flow Process mode 2 and basic MODFLOW, respectively) and a hybrid (MODFLOW-Conduit Flow Process mode 1) model to the Woodville Karst Plain near Tallahassee, Florida, indicated that for annual, monthly, or seasonal average hydrologic conditions, all methods met calibration criteria (matched observed groundwater levels and average flows). Thus, the increased effort required, such as the collection of data on conduit location, to develop a hybrid model and its increased computational burden, is not necessary for simulation of average hydrologic conditions (non-laminar flow effects on simulated head and spring discharge were minimal). However, simulation of a large storm event in the Woodville Karst Plain with daily stress periods indicated that turbulence is important for matching daily springflow hydrographs. Thus, if matching streamflow hydrographs over a storm event is required, the simulation of non-laminar flow and the location of conduits are required. The main challenge in application of the methods and approaches for developing hybrid models relates to the difficulty of mapping conduit networks or having high-quality datasets to calibrate these models. Additionally, hybrid models have long simulation times, which can preclude the use of parameter estimation for calibration. Simulation of contaminant transport that does not account for preferential flow through conduits or extremely permeable zones in any approach is ill-advised. Simulation results in other karst aquifers or other parts of the FAS may differ from the comparison demonstrated herein.

Florida↗
USGS2015

Bayesian models: A statistical primer for ecologists

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals. This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management. Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticians Covers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and more Deemphasizes computer coding in favor of basic principles Explains how to write out properly factored statistical expressions representing Bayesian models

Book↗
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↗
USGS1971

Techniques for assessing water resource potentials in the developing countries: with emphasis on streamflow, erosion and sediment transport, water movement in unsaturated soils, ground water, and remote sensing in hydrologic applications

Hydrologic instrumentation and methodology for assessing water-resource potentials have originated largely in the developed countries of the temperature zone. The developing countries lie largely in the tropic zone, which contains the full gamut of the earth's climatic environments, including most of those of the temperate zone. For this reason, most hydrologic techniques have world-wide applicability. Techniques for assessing water-resource potentials for the high priority goals of economic growth are well established in the developing countries--but much more are well established in the developing countries--but much more so in some than in other. Conventional techniques for measurement and evaluation of basic hydrologic parameters are now well-understood in the developing countries and are generally adequate for their current needs and those of the immediate future. Institutional and economic constraints, however, inhibit growth of sustained programs of hydrologic data collection and application of the data to problems in engineering technology. Computer-based technology, including processing of hydrologic data and mathematical modelling of hydrologic parameters i also well-begun in many developing countries and has much wider potential application. In some developing counties, however, there is a tendency to look on the computer as a panacea for deficiencies in basic hydrologic data collection programs. This fallacy must be discouraged, as the computer is a tool and not a "magic box." There is no real substitute for sound programs of basic data collection. Nuclear and isotopic techniques are being used increasingly in the developed countries in the measurement and evaluation of virtually all hydrologic parameter in which conventional techniques have been used traditionally. Even in the developed countries, however, many hydrologists are not using nuclear techniques, simply because they lack knowledge of the principles involved and of the potential benefits. Nuclear methodology in hydrologic applications is generally more complex than the conventional and hence requires a high level of technical expertise for effective use. Application of nuclear techniques to hydrologic problems in the developing countries is likely to be marginal for some years to come, owing to the higher costs involved and expertise required. Nuclear techniques, however, would seem to have particular promise in studies of water movement in unsaturated soils and of erosion and sedimentation where conventional techniques are inadequate, inefficient and in some cases costly. Remote sensing offers great promise for synoptic evaluations of water resources and hydrologic processes, including the transient phenomena of the hydrologic cycle. Remote sensing is not, however, a panacea for deficiencies in hydrologic data programs in the developing countries. Rather it is a means for extending and augmenting on-the-ground observations ans surveys (ground truth) to evaluated water resources and hydrologic processes on a regionall or even continental scale. With respect to economic growth goals in developing countries, there are few identifiable gaps in existing hydrologic instrumentation and methodology insofar as appraisal, development and management of available water resources are concerned. What is needed is acceleration of institutional development and professional motivation toward more effective use of existing and proven methodology. Moreover, much sophisticated methodology can be applied effectively in the developing countries only when adequate levels of indigenous scientific skills have been reached and supportive institutional frameworks are evolved to viability.

Open-File Report↗
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↗
USGS1987

Linear error analysis of slope-area discharge determinations

The slope-area method can be used to calculate peak flood discharges when current-meter measurements are not possible. This calculation depends on several quantities, such as water-surface fall, that are subject to large measurement errors. Other critical quantities, such as Manning's n , are not even amenable to direct measurement but can only be estimated. Finally, scour and fill may cause gross discrepancies between the observed condition of the channel and the hydraulic conditions during the flood peak. The effects of these potential errors on the accuracy of the computed discharge have been estimated by statistical error analysis using a Taylor-series approximation of the discharge formula and the well-known formula for the variance of a sum of correlated random variates. The resultant error variance of the computed discharge is a weighted sum of covariances of the various observational errors. The weights depend on the hydraulic and geometric configuration of the channel. The mathematical analysis confirms the rule of thumb that relative errors in computed discharge increase rapidly when velocity heads exceed the water-surface fall, when the flow field is expanding and when lateral velocity variation (alpha) is large. It also confirms the extreme importance of accurately assessing the presence of scour or fill.

Journal of Hydrology↗
USGS1982

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

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

Open-File Report↗
USGS1979

One-dimensional steady-state stream water-quality model

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

Water-Resources Investigations Report↗
USGS1965

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

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

Crustal Studies Technical Letters↗
USGS1971

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

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

Report↗
USGS2003

Probabilistic assessment methodology for continuous-type petroleum accumulations

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

International Journal of Coal Geology↗
USGS1975

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

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

New Mexico, Texas↗
USGS1994

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

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

Water-Resources Investigations Report↗
USGS1998

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

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

Water-Resources Investigations Report↗
USGS1989

Thermal maturity of the Anadarko Basin

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

Oklahoma↗
USGS1981

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

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

Open-File Report↗
USGS2004

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

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

Wisconsin↗