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Results for “Mathematics of Computation”

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 145 records · Page 8Linked to original sources
USGS1971

Reduction of lithologic-log data to numbers for use in the digital computer

The development of a standardized system for conveniently coding lithologic-log data for use in the digital computer has long been needed. The technique suggested involves a reduction of the original written alphanumeric log to a numeric log by use of computer programs. This numeric log can then be retrieved as a written log, interrogated for pertinent information, or analyzed statistically.

Journal of the International Association for Mathe↗
USGS2005

Comparison of methods used to estimate conventional undiscovered petroleum resources: World examples

Various methods for assessing undiscovered oil, natural gas, and natural gas liquid resources were compared in support of the USGS World Petroleum Assessment 2000. Discovery process, linear fractal, parabolic fractal, engineering estimates, PETRIMES, Delphi, and the USGS 2000 methods were compared. Three comparisons of these methods were made in: (1) the Neuquen Basin province, Argentina (different assessors, same input data); (2) provinces in North Africa, Oman, and Yemen (same assessors, different methods); and (3) the Arabian Peninsula, Arabian (Persian) Gulf, and North Sea (different assessors, different methods). A fourth comparison (same assessors, same assessment methods but different geologic models), between results from structural and stratigraphic assessment units in the North Sea used only the USGS 2000 method, and hence compared the type of assessment unit rather than the method. In comparing methods, differences arise from inherent differences in assumptions regarding: (1) the underlying distribution of the parent field population (all fields, discovered and undiscovered), (2) the population of fields being estimated; that is, the entire parent distribution or the undiscovered resource distribution, (3) inclusion or exclusion of large outlier fields; (4) inclusion or exclusion of field (reserve) growth, (5) deterministic or probabilistic models, (6) data requirements, and (7) scale and time frame of the assessment. Discovery process, Delphi subjective consensus, and the USGS 2000 method yield comparable results because similar procedures are employed. In mature areas such as the Neuquen Basin province in Argentina, the linear and parabolic fractal and engineering methods were conservative compared to the other five methods and relative to new reserve additions there since 1995. The PETRIMES method gave the most optimistic estimates in the Neuquen Basin. In less mature areas, the linear fractal method yielded larger estimates relative to other methods. A geologically based model, such as one using the total petroleum system approach, is preferred in that it combines the elements of petroleum source, reservoir, trap and seal with the tectono-stratigraphic history of basin evolution with petroleum resource potential. Care must be taken to demonstrate that homogeneous populations in terms of geology, geologic risk, exploration, and discovery processes are used in the assessment process. The USGS 2000 method (7th Approximation Model, EMC computational program) is robust; that is, it can be used in both mature and immature areas, and provides comparable results when using different geologic models (e.g. stratigraphic or structural) with differing amounts of subdivisions, assessment units, within the total petroleum system. ?? 2005 International Association for Mathematical Geology.

Conference Paper↗
USGS2011

A two-phase debris-flow model that includes coupled evolution of volume fractions, granular dilatancy, and pore-fluid pressure

Pore-fluid pressure plays a crucial role in debris flows because it counteracts normal stresses at grain contacts and thereby reduces intergranular friction. Pore-pressure feedback accompanying debris deformation is particularly important during the onset of debrisflow motion, when it can dramatically influence the balance of forces governing downslope acceleration. We consider further effects of this feedback by formulating a new, depth-averaged mathematical model that simulates coupled evolution of granular dilatancy, solid and fluid volume fractions, pore-fluid pressure, and flow depth and velocity during all stages of debris-flow motion. To illustrate implications of the model, we use a finite-volume method to compute one-dimensional motion of a debris flow descending a rigid, uniformly inclined slope, and we compare model predictions with data obtained in large-scale experiments at the USGS debris-flow flume. Predictions for the first 1 s of motion show that increasing pore pressures (due to debris contraction) cause liquefaction that enhances flow acceleration. As acceleration continues, however, debris dilation causes dissipation of pore pressures, and this dissipation helps stabilize debris-flow motion. Our numerical predictions of this process match experimental data reasonably well, but predictions might be improved by accounting for the effects of grain-size segregation.

Conference Paper↗
USGS2021

The application of ensemble wave forcing to quantify uncertainty of shoreline change predictions

Reliable predictions and accompanying uncertainty estimates of coastal evolution on decadal to centennial time scales are increasingly sought. So far, most coastal change projections rely on a single, deterministic realization of the unknown future wave climate, often derived from a global climate model. Yet, deterministic projections do not account for the stochastic nature of future wave conditions across a variety of temporal scales (e.g., daily, weekly, seasonally, and interannually). Here, we present an ensemble Kalman filter shoreline change model to predict coastal erosion and uncertainty due to waves at a variety of time scales. We compare shoreline change projections, simulated with and without ensemble wave forcing conditions by applying ensemble wave time series produced by a computationally efficient statistical downscaling method. We demonstrate a sizable (site-dependent) increase in model uncertainty compared with the unrealistic case of model projections based on a single, deterministic realization (e.g., a single time series) of the wave forcing. We support model-derived uncertainty estimates with a novel mathematical analysis of ensembles of idealized process models. Here, the developed ensemble modeling approach is applied to a well-monitored beach in Tairua, New Zealand. However, the model and uncertainty quantification techniques derived here are generally applicable to a variety of coastal settings around the world.

JGR Earth Surface↗
USGS2022

Absolute accuracy assessment of lidar point cloud using amorphous objects

The accuracy assessment of airborne lidar point cloud typically estimates vertical accuracy by computing RMSEz (root mean square error of the z coordinate) from ground check points (GCPs). Due to the low point density of the airborne lidar point cloud, there is often not enough accurate semantic context to find an accurate conjugate point. To advance the accuracy assessment in full three-dimensional (3D) context, geometric features, such as the three-plane intersection point or two-line intersection point, are often used. Although the point density is still low, geometric features are mathematically modeled from many points. Thus, geometric features provide a robust determination of the intersection point, and the point is considered as a GCP. When no regular built objects are available, we describe the process of utilizing features of irregular shape called amorphous natural objects, such as a tree or a rock. When scanned to a high-density point cloud, an amorphous natural object can be used as ground truth reference data to estimate 3D georeferencing errors of the airborne lidar point cloud. The algorithm to estimate 3D accuracy is the optimization that minimizes the sum of the distance between the airborne lidar points to the ground scanned data. The search volume partitioning was the most important procedure to improve the computational efficiency. We also performed an extensive study to address the external uncertainty associated with the amorphous object method. We describe an accuracy assessment using amorphous objects (108 trees) spread over the project area. The accuracy results for ∆ x , ∆ y , and ∆ z obtained using the amorphous object method were 3.1 cm, 3.6 cm, and 1.7 cm RMSE, along with a mean error of 0.1 cm, 0.1 cm, and 4.5 cm, respectively, satisfying the accuracy requirement of U.S. Geological Survey lidar base specification. This approach shows strong promise as an alternative to geometric feature methods when artificial targets are scarce. The relative convenience and advantages of using amorphous targets, along with its good performance shown here, make this amorphous object method a practical way to perform 3D accuracy assessment.

Remote Sensing↗
USGS2000

Uncertainty estimation for resource assessment-an application to coal

The U.S. Geological Survey is conducting a national assessment of coal resources. As part of that assessment, a geostatistical procedure has been developed to estimate the uncertainty of coal resources for the historical categories of geological assurance: measured, indicated, inferred, and hypothetical coal. Data consist of spatially clustered coal thickness measurements from coal beds and/or zones that cover, in some cases, several thousand square kilometers. Our procedure involved trend removal, an examination of spatial correlation, computation of a sample semivariogram, and fitting a semivariogram model. This model provided standard deviations for the uncertainty estimates. The number of sample points (drill holes) in each historical category also was estimated. Measurement error in the thickness of the coal bed/zone was obtained from the fitted model or supplied exogenously. From this information approximate estimates of uncertainty on the historical categories were computed. We illustrate the methodology using drill hole data from the Harmon coal bed located in southwestern North Dakota. The methodology will be applied to approximately 50 coal data sets.

Mathematical Geology↗
USGS2010

Bayesian Inference: with ecological applications

This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.

Book↗
USGS1989

Simulation of ground-water flow at Anchorage, Alaska, 1955-83

The groundwater system at Anchorage, Alaska was analyzed by using a two-layer three-dimensional mathematical model. By use of existing data, both nonpumping and pumping steady-state conditions and transient conditions were simulated. Under steady-state conditions, calculated directions of groundwater flow were similar to observed flow patterns, and calculated stream discharges generally were within 10% of observed values. However, in many parts of the modeled area computed hydraulic head values were more than 20 ft higher or lower than observed values. Hydraulic conductivity and transmissivity are the most sensitive hydraulic parameters under steady-state conditions. Under steady-state conditions, a pumping rate of 18.8 Mgal/d lowers heads in the confined aquifer by as much as 30 ft, but reduces streamflow by less than 5%. Transient conditions show that drawndowns due to withdrawals by production wells follow similar patterns of nearby observation wells. On the basis of analytical techniques, the confining layer does not appear to hold significant quantities of water. (USGS)

Water-Resources Investigations Report↗
USGS1993

Relationship of geological and geothermal field properties: Midcontinent area, USA, an example

Quantitative approaches to data analysis in the last decade have become important in basin modeling and mineral-resource estimation. The interrelation of geological, geophysical, geochemical, and geohydrological variables is important in adjusting a model to a real-world situation. Revealing the interdependences of variables can contribute in understanding the processes interacting in sedimentary basins. It is reasonably simple to compare spatial data of the same type but more difficult if different properties are involved. Statistical techniques, such as cluster analysis or principal components analysis, or some algebraic approaches can be used to ascertain the relations of standardized spatial data. In this example, structural configuration on five different stratigraphic horizons, one total sediment thickness map, and four maps of geothermal data were copared. As expected, the structural maps are highly related because all had undergone about the same deformation with differing degrees of intensity. The temperature gradients derived (1) from shallow borehole logging measurements under equilibrium conditions with the surrounding rock, and (2) from non-equilibrium bottom-hole temperatures (BHT) from deeper depths are mainly independent of each other. This was expected and confirmed also for the two temperature maps at 1000 ft which were constructed using both types of gradient values. Thus, it is evident that the use of a 2-point (BHT and surface temperature) straightline calculation of a mean temperature gradient gives different information about the geothermal regime than using gradients from temperatures logged under equilibrium conditions. Nevertheless, it is useful to determine to what a degree the larger dataset of nonequilibrium temperatures could reflect quantitative relationships to geologic conditions. Comparing all maps of geothermal information vs. the structural and the sediment thickness maps, it was determined that all correlations are moderately negative or slightly positive. These results are clearly shown by the cluster analysis and the principal components. Considering a close relationship between temperature and thermal conductivity of the sediments as observed for most of the Midcontinent area and relatively homogeneous heat-flow density conditions for the study area these results support the following assumptions: (1) undifferentiated geothermal gradients, computed from temperatures of different depth intervals and differing sediment properties, cannot contribute to an improved understanding of the temperature structure and its controls within the sedimentary cover, and (2) the quantitative approach of revealing such relations needs refined datasets of temperature information valid for the different depth levels or stratigraphic units. ?? 1993 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1987

Estimating threshold values for the land disposal of organic solvent-contaminated wastes

This paper describes conceptual and mathematical modeling approaches to evaluate environmentally suitable waste management practices that prevent ground water pollution from landfill disposal of solid wastes contaminated with organic solvents. Threshold values for disposal of solid wastes contaminated with acetone, nitrobenzene, chlorobenzene, and carbon tetrachloride were estimated using a disposal site model using a two-dimensional advection-,dispersion solute transport computer code. For example, the threshold value for disposal of carbon tetrachloride at the site model was approximately 600 g/acre, while the value for acetone was limited only by the characteristics of the waste to prevent free drainage of liquid solvent. The study indicated that the toxicity, mass loading rate, and the mass of solvent initially disposed are critical parameters determining the relative success of a given site to attenuate contaminants to environmentally acceptable levels.

Journal of Hazardous Materials↗
USGS2011

Partnership of Environmental Education and Research-A compilation of student research, 1999-2008

The U.S. Geological Survey (USGS) Tennessee Water Science Center and the College of Engineering and Technology at Tennessee State University developed a Partnership in Environmental Education and Research (PEER) to support environmental research at TSU and to expand the environmental research capabilities of the USGS in Tennessee. The PEER program is driven by the research needs to better define the occurrence, fate, and transport of contaminants in groundwater and surface water. Research in the PEER program has primarily focused on the transport and remediation of organic contamination in karst settings. Research conducted through the program has also expanded to a variety of media and settings. Research areas include contaminant occurrence and transport, natural and enhanced bioremediation, geochemical conditions in karst aquifers, mathematical modeling for contaminant transport and degradation, new methods to evaluate groundwater contamination, the resuspension of bacteria from sediment in streams, the use of bioluminescence and chemiluminescence to identify the presence of contaminants, and contaminant remediation in wetlands. The PEER program has increased research and education opportunities for students in the College of Engineering, Technology, and Computer Science and has provided students with experience in presenting the results of their research. Students in the program have participated in state, regional, national and international conferences with more than 140 presentations since 1998 and more than 40 student awards. The PEER program also supports TSU outreach activities and efforts to increase minority participation in environmental and earth science programs at the undergraduate and graduate levels. TSU students and USGS staff participate in the TSU summer programs for elementary and high school students to promote earth sciences. The 2007 summer camps included more than 130 students from 20 different States and Washington DC.

Tennessee↗
USGS2011

Computational considerations for collecting and using data in the equidistant cylindrical map projection and the bounds of sampling geographic data at progressively higher resolution

The Equidistant Cylindrical Map projection is popular with digital modelers and others for storing and processing worldwide data sets because of the simple association of latitude and longitude to cell values or pixels in the resulting grid. This projection does not accurately display area, and the diminished geographic area represented by cells at high latitudes is not often carefully considered. A simple mathematical analysis quantifies the discrepancy in area sampled by cells at different latitudes. The presence of this discrepancy indicates that the use of this projection can induce bias in data sets when both sampling and reporting data. It is demonstrated that as the resolution requirements of input data for models increase, the necessity of providing data to accurately describe smaller cells, particularly at high latitude, will be a challenge.

Techniques and Methods↗
USGS1988

The geometric signature: Quantifying landslide-terrain types from digital elevation models

Topography of various types and scales can be fingerprinted by computer analysis of altitude matrices (digital elevation models, or DEMs). The critical analytic tool is the geometric signature, a set of measures that describes topographic form well enough to distinguish among geomorphically disparate landscapes. Different surficial processes create topography with diagnostic forms that are recognizable in the field. The geometric signature abstracts those forms from contour maps or their DEMs and expresses them numerically. This multivariate characterization enables once-in-tractable problems to be addressed. The measures that constitute a geometric signature express different but complementary attributes of topographic form. Most parameters used here are statistical estimates of central tendency and dispersion for five major categories of terrain geometry; altitude, altitude variance spectrum, slope between slope reversals, and slope and its curvature at fixed slope lengths. As an experimental application of geometric signatures, two mapped terrain types associated with different processes of shallow landsliding in Marin County, California, were distinguished consistently by a 17-variable description of topography from 21??21 DEMs (30-m grid spacing). The small matrix is a statistical window that can be used to scan large DEMs by computer, thus potentially automating the mapping of contrasting terrain types. The two types in Marin County host either (1) slow slides: earth flows and slump-earth flows, or (2) rapid flows: debris avalanches and debris flows. The signature approach should adapt to terrain taxonomy and mapping in other areas, where conditions differ from those in Central California. ?? 1988 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1988

Use of the truncated shifted Pareto distribution in assessing size distribution of oil and gas fields

The truncated shifted Pareto (TSP) distribution, a variant of the two-parameter Pareto distribution, in which one parameter is added to shift the distribution right and left and the right-hand side is truncated, is used to model size distributions of oil and gas fields for resource assessment. Assumptions about limits to the left-hand and right-hand side reduce the number of parameters to two. The TSP distribution has advantages over the more customary lognormal distribution because it has a simple analytic expression, allowing exact computation of several statistics of interest, has a "J-shape," and has more flexibility in the thickness of the right-hand tail. Oil field sizes from the Minnelusa play in the Powder River Basin, Wyoming and Montana, are used as a case study. Probability plotting procedures allow easy visualization of the fit and help the assessment. ?? 1988 International Association for Mathematical Geology.

Mathematical 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↗
USGS2014

A universal Model-R Coupler to facilitate the use of R functions for model calibration and analysis

Mathematical models are useful in various fields of science and engineering. However, it is a challenge to make a model utilize the open and growing functions (e.g., model inversion) on the R platform due to the requirement of accessing and revising the model's source code. To overcome this barrier, we developed a universal tool that aims to convert a model developed in any computer language to an R function using the template and instruction concept of the Parameter ESTimation program (PEST) and the operational structure of the R-Soil and Water Assessment Tool (R-SWAT). The developed tool (Model-R Coupler) is promising because users of any model can connect an external algorithm (written in R) with their model to implement various model behavior analyses (e.g., parameter optimization, sensitivity and uncertainty analysis, performance evaluation, and visualization) without accessing or modifying the model's source code.

Environmental Modelling and Software↗
USGS2001

User's Guide for Mixed-Size Sediment Transport Model for Networks of One-Dimensional Open Channels

This user's guide describes a mathematical model for predicting the transport of mixed sizes of sediment by flow in networks of one-dimensional open channels. The simulation package is useful for general sediment routing problems, prediction of erosion and deposition following dam removal, and scour in channels at road embankment crossings or other artificial structures. The model treats input hydrographs as stepwise steady-state, and the flow computation algorithm automatically switches between sub- and supercritical flow as dictated by channel geometry and discharge. A variety of boundary conditions including weirs and rating curves may be applied both external and internal to the flow network. The model may be used to compute flow around islands and through multiple openings in embankments, but the network must be 'simple' in the sense that the flow directions in all channels can be specified before simulation commences. The location and shape of channel banks are user specified, and all bedelevation changes take place between these banks and above a user-specified bedrock elevation. Computation of sediment-transport emphasizes the sand-size range (0.0625-2.0 millimeter) but the user may select any desired range of particle diameters including silt and finer (<0.0625 millimeter). As part of data input, the user may set the original bed-sediment composition of any number of layers of known thickness. The model computes the time evolution of total transport and the size composition of bed- and suspended-load sand through any cross section of interest. It also tracks bed -surface elevation and size composition. The model is written in the FORTRAN programming language for implementation on personal computers using the WINDOWS operating system and, along with certain graphical output display capability, is accessed from a graphical user interface (GUI). The GUI provides a framework for selecting input files and parameters of a number of components of the sediment-transport process. There are no restrictions in the use of the model as to numbers of channels, channel junctions, cross sections per channel, or points defining the cross sections. Following completion of the simulation computations, the GUI accommodates display of longitudinal plots of either bed elevation and size composition, or of transport rate and size composition of the various components, for individual channels and selected times during the simulation period. For individual cross sections, the GUI also allows display of time series of transport rate and size composition of the various components and of bed elevation and size composition.

Water-Resources Investigations Report↗
USGS2020

Dimensional effects of inter-phase mass transfer on attenuation of structurally trapped gaseous carbon dioxide in shallow aquifers

Based on experimental evidence and using mathematical modeling, inter-phase mass transfer processes of CO 2 exsolving from and dissolving into water in heterogeneous porous media are investigated under two fundamentally different flow conditions: in a quasi one dimensional vertical column and in a two-dimensional tank with a lateral background water flow, both at laboratory scale. In both cases, the CO 2 dissolved in water under a given overpressure is injected for a certain period at the bottom of the tank, exsolves, and migrates upwards. A layer of fine sand is present in the tanks designed to mimic geological scenarios of accumulation and trapping of exsolved CO 2 in shallow aquifers. Then, clean water is injected and the accumulated CO 2 is dissolved back into the flowing water. The study aims to point out the differences in the mass transfer processes between the quasi-1D and 2D cases using a mathematical model of two-phase compositional flow in heterogeneous porous media calibrated to the experimental datasets, and expose strategies that should be explored in future research. Additionally, temperature variations observed during the 2D experiments allow for analysis of isothermal versus non-isothermal effects on the processes of multiphase CO 2 evolution. The mathematical model is discretized and solved using the mixed hybrid finite element method in 2D that allows for the simulation of both advection- and diffusion-dominated processes accurately.

Journal of Computational Physics↗