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Results for “Mathematics of Computation”

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167 records · Page 10Linked to original sources
USGS1985

Three-dimensional trend mapping from wire-line logs

Mapping of lithofacies and porosities of stratigraphic units is complicated because these properties vary in three dimensions. The method of moments was proposed by Krumbein and Libby (1957) as a technique to aid in resolving this problem. Moments are easily computed from wireline logs and are simple statistics which summarize vertical variation in a log trace. Combinations of moment maps have proved useful in understanding vertical and lateral changes in lithology of sedimentary rock units. Although moments have meaning both as statistical descriptors and as mechanical properties, they also define polynomial curves which approximate lithologic changes as a function of depth. These polynomials can be fitted by least-squares methods, partitioning major trends in rock properties from finescale fluctuations. Analysis of variance yields the degree of fit of any polynomial and measures the proportion of vertical variability expressed by any moment or combination of moments. In addition, polynomial curves can be differentiated to determine depths at which pronounced expressions of facies occur and to determine the locations of boundaries between major lithologic subdivisions. Moments can be estimated at any location in an area by interpolating from log moments at control wells. A matrix algebra operation then converts moment estimates to coefficients of a polynomial function which describes a continuous curve of lithologic variation with depth. If this procedure is applied to a grid of geographic locations, the result is a model of variability in three dimensions. Resolution of the model is determined largely by number of moments used in its generation. The method is illustrated with an analysis of lithofacies in the Simpson Group of south-central Kansas; the three-dimensional model is shown as cross sections and slice maps. In this study, the gamma-ray log is used as a measure of shaliness of the unit. However, the method is general and can be applied, for example, to suites of neutron, density, or sonic logs to produce three-dimensional models of porosity in reservoir rocks. ?? 1985 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS2004

A visual basic program to generate sediment grain-size statistics and to extrapolate particle distributions

Measures that describe and summarize sediment grain-size distributions are important to geologists because of the large amount of information contained in textural data sets. Statistical methods are usually employed to simplify the necessary comparisons among samples and quantify the observed differences. The two statistical methods most commonly used by sedimentologists to describe particle distributions are mathematical moments (Krumbein and Pettijohn, 1938) and inclusive graphics (Folk, 1974). The choice of which of these statistical measures to use is typically governed by the amount of data available (Royse, 1970). If the entire distribution is known, the method of moments may be used; if the next to last accumulated percent is greater than 95, inclusive graphics statistics can be generated. Unfortunately, earlier programs designed to describe sediment grain-size distributions statistically do not run in a Windows environment, do not allow extrapolation of the distribution's tails, or do not generate both moment and graphic statistics (Kane and Hubert, 1963; Collias et al., 1963; Schlee and Webster, 1967; Poppe et al., 2000) 1 . Owing to analytical limitations, electro-resistance multichannel particle-size analyzers, such as Coulter Counters, commonly truncate the tails of the fine-fraction part of grain-size distributions. These devices do not detect fine clay in the 0.6–0.1 μm range (part of the 11-phi and all of the 12-phi and 13-phi fractions). Although size analyses performed down to 0.6 μm microns are adequate for most freshwater and near shore marine sediments, samples from many deeper water marine environments (e.g. rise and abyssal plain) may contain significant material in the fine clay fraction, and these analyses benefit from extrapolation. The program (GSSTAT) described herein generates statistics to characterize sediment grain-size distributions and can extrapolate the fine-grained end of the particle distribution. It is written in Microsoft Visual Basic 6.0 and provides a window to facilitate program execution. The input for the sediment fractions is weight percentages in whole-phi notation (Krumbein, 1934; Inman, 1952), and the program permits the user to select output in either method of moments or inclusive graphics statistics (Fig. 1). Users select options primarily with mouse-click events, or through interactive dialogue boxes.

Computers & Geosciences↗
USGS2002

SUTRA: A model for 2D or 3D saturated-unsaturated, variable-density ground-water flow with solute or energy transport

SUTRA (Saturated-Unsaturated Transport) is a computer program that simulates fluid movement and the transport of either energy or dissolved substances in a subsurface environment. This upgraded version of SUTRA adds the capability for three-dimensional simulation to the former code (Voss, 1984), which allowed only two-dimensional simulation. The code employs a two- or three-dimensional finite-element and finite-difference method to approximate the governing equations that describe the two interdependent processes that are simulated: 1) fluid density-dependent saturated or unsaturated ground-water flow; and 2) either (a) transport of a solute in the ground water, in which the solute may be subject to: equilibrium adsorption on the porous matrix, and both first-order and zero-order production or decay; or (b) transport of thermal energy in the ground water and solid matrix of the aquifer. SUTRA may also be used to simulate simpler subsets of the above processes. A flow-direction-dependent dispersion process for anisotropic media is also provided by the code and is introduced in this report. As the primary calculated result, SUTRA provides fluid pressures and either solute concentrations or temperatures, as they vary with time, everywhere in the simulated subsurface system. SUTRA flow simulation may be employed for two-dimensional (2D) areal, cross sectional and three-dimensional (3D) modeling of saturated ground-water flow systems, and for cross sectional and 3D modeling of unsaturated zone flow. Solute-transport simulation using SUTRA may be employed to model natural or man-induced chemical-species transport including processes of solute sorption, production, and decay. For example, it may be applied to analyze ground-water contaminant transport problems and aquifer restoration designs. In addition, solute-transport simulation with SUTRA may be used for modeling of variable-density leachate movement, and for cross sectional modeling of saltwater intrusion in aquifers at near-well or regional scales, with either dispersed or relatively sharp transition zones between freshwater and saltwater. SUTRA energy-transport simulation may be employed to model thermal regimes in aquifers, subsurface heat conduction, aquifer thermal-energy storage systems, geothermal reservoirs, thermal pollution of aquifers, and natural hydrogeologic convection systems. Mesh construction, which is quite flexible for arbitrary geometries, employs quadrilateral finite elements in 2D Cartesian or radial-cylindrical coordinate systems, and hexahedral finite elements in 3D systems. 3D meshes are currently restricted to be logically rectangular; in other words, they are similar to deformable finite-difference-style grids. Permeabilities may be anisotropic and may vary in both direction and magnitude throughout the system, as may most other aquifer and fluid properties. Boundary conditions, sources and sinks may be time dependent. A number of input data checks are made to verify the input data set. An option is available for storing intermediate results and restarting a simulation at the intermediate time. Output options include fluid velocities, fluid mass and solute mass or energy budgets, and time-varying observations at points in the system. Both the mathematical basis for SUTRA and the program structure are highly general, and are modularized to allow for straightforward addition of new methods or processes to the simulation. The FORTRAN-90 coding stresses clarity and modularity rather than efficiency, providing easy access for later modifications.

Water-Resources Investigations Report↗
USGS2018

Real-time decision-making during emergency disease outbreaks

In the event of a new infectious disease outbreak, mathematical and simulation models are commonly used to inform policy by evaluating which control strategies will minimize the impact of the epidemic. In the early stages of such outbreaks, substantial parameter uncertainty may limit the ability of models to provide accurate predictions, and policymakers do not have the luxury of waiting for data to alleviate this state of uncertainty. For policymakers, however, it is the selection of the optimal control intervention in the face of uncertainty, rather than accuracy of model predictions, that is the measure of success that counts. We simulate the process of real-time decision-making by fitting an epidemic model to observed, spatially-explicit, infection data at weekly intervals throughout two historical outbreaks of foot-and-mouth disease, UK in 2001 and Miyazaki, Japan in 2010, and compare forward simulations of the impact of switching to an alternative control intervention at the time point in question. These are compared to policy recommendations generated in hindsight using data from the entire outbreak, thereby comparing the best we could have done at the time with the best we could have done in retrospect. Our results show that the control policy that would have been chosen using all the data is also identified from an early stage in an outbreak using only the available data, despite high variability in projections of epidemic size. Critically, we find that it is an improved understanding of the locations of infected farms, rather than improved estimates of transmission parameters, that drives improved prediction of the relative performance of control interventions. However, the ability to estimate undetected infectious premises is a function of uncertainty in the transmission parameters. Here, we demonstrate the need for both real-time model fitting and generating projections to evaluate alternative control interventions throughout an outbreak. Our results highlight the use of using models at outbreak onset to inform policy and the importance of state-dependent interventions that adapt in response to additional information throughout an outbreak.

PLOS Computational Biology↗
USGS2007

Yellowstone grizzly bear investigations: Annual report of the Interagency Grizzly Bear Study Team, 2006

The contents of this Annual Report summarize results of monitoring and research from the 2006 field season. The report also contains a summary of nuisance grizzly bear ( Ursus arctos horribilis ) management actions. The Interagency Grizzly Bear Study Team (IGBST) continues to work on issues associated with counts of unduplicated females with cubs-of- the-year (COY). These counts are used to establish a minimum population size, which is then used to establish mortality thresholds for the Recovery Plan (U.S. Fish and Wildlife Service [USFWS] 1993). After considerable delays due to programming issues, a computer program that defines the rule set used by Knight et al. (1995) to differentiate unique family groups was development and tested in 2005 and 2006. Simulations using observations of collared females with COY were randomly sampled to generate datasets of observations of random females with COY. These datasets were then run though the simulations program to test the accuracy of the rules. Data are currently being summarized. This project has been completed and a manuscript was submitted to the Journal of Wildlife Management. The grizzly bear recovery plan (USFWS 1993) established human-caused mortality quotas. We used the latest information on reproduction and survival to estimate population trajectory in the same simulation model originally used by Harris (1984). A Wildlife Monographs was published in 2006. Additionally, the study team, in cooperation with several quantitative experts, reassessed how population size is indexed and how sustainable mortality rates are established. A draft report was presented to the Yellowstone Ecosystem Subcommittee in spring 2005. It was published as part of the USFWS Delisting Rule (Federal Register Vol. 70, No. 221, Nov. 17, 2005, 69853–69884) and subjected to public comment. This workshop document can be found at http://www.fws.gov/mountain-prairie/species/mammals/grizzly/yellowstone.htm. During the summer of 2006, a second workshop was held to address public comment and professional peer review. The result of this workshop was a supplement to the 2005 workshop document. This supplement can be found at http://www.fws.gov/mountain-prairie/species/mammals/grizzly/yellowstone.htm under the link Revised Methods to Estimate Population Size and Sustainable Mortality Limits. Results of those estimates are provided in Appendix A. Our project addressing the potential application of stable isotopes and trace elements to quantify consumption rates of whitebark pine ( Pinus albicaulis ) and cutthroat trout ( Oncorhynchus clarki ) by grizzly bears was completed. Our manuscript on consumption rates of whitebark pine was published in the Canadian Journal of Zoology 81:763-770. Results of the mercury studies were also published in the Canadian Journal of Zoology 82:493–501. Copies can be found on the IGBST website http://www.nrmsc.usgs.gov/research/igbst-home.htm. Based upon this work, we submitted a proposal to analyze all historic tissue samples from grizzly bears in the ecosystem. That proposal was funded and samples have been sent to a lab for isotopic analysis. We hope to have those results in early 2008. Results of DNA hair snaring work conducted on Yellowstone Lake were submitted and published in the Journal Ursus (Haroldson et al. 2005). Results of this study conducted from 1997–2000 showed a decline in fish use by grizzly bears when compared to earlier work conducted by Reinhart (1990) in 1985–1987. As a consequence, the IGBST submitted a proposal to the National Park Service and received 3 years funding to repeat that work. This project began in 2007. There are 2 graduate students and several field technicians working on the program. We completed the final field season in Grand Teton National Park evaluating habitat use both temporally and spatially between grizzly and black bears ( Ursus americanus ). We continue to use GPS technology that incorporates a spread spectrum communication system. Spread spectrum allows for transfer of stored GPS locations from the collar to a remote receiving station. Results of the 2006 field season are reported here. We plan to complete the final report in late 2007. We continued to monitor the health of whitebark pine in the Greater Yellowstone Ecosystem (GYE) in cooperation with the Greater Yellowstone Whitebark Pine Monitoring Working Group. A summary of the 2006 monitoring is also presented (Appendix B). The IGBST uses counts of winter-killed ungulates to index spring carcass abundance for grizzly bears. Likewise, we use wier counts and stream surveys to index cutthroat trout abundance. We ask Dr. Steve Cherry, Department of Mathematical Sciences, Montana State University-Bozeman, to review the protocols and make recommendations for improving them. That review and recommendations are presented in Appendix C. Finally, the state of Wyoming, following recommendations from the Yellowstone Ecosystem Subcommittee and the IGBST, launched the Bear Wise Community Effort. The focus is to minimize human/bear conflicts, minimize human-caused bear mortalities associated with conflicts, and safeguard the human community. Results of these efforts are detailed in Appendix D. The annual reports of the IGBST summarize annual data collection. Because additional information can be obtained after publication, data summaries are subject to change. For that reason, data analyses and summaries presented in this report supersede all previously published data. The study area and sampling techniques are reported by Blanchard (1985), Mattson et al. (1991 a), and Haroldson et al. (1998).

Idaho, Montana, Wyoming↗