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Results for “Applied Mathematical Modelling”

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At least 55 records · Page 3Linked to original sources
USGS2009

Why are diverse relationships observed between phytoplankton biomass and transport time?

Transport time scales such as flushing time and residence time are often used to explain variability in phytoplankton biomass. In many cases, empirical data are consistent with a positive phytoplankton‐transport time relationship (i.e., phytoplankton biomass increases as transport time increases). However, negative relationships, varying relationships, or no significant relationship may also be observed. We present a simple conceptual model, in both mathematical and graphical form, to help explain why phytoplankton may have a range of relationships with transport time, and we apply it to several real systems. The phytoplankton growth‐loss balance determines whether phytoplankton biomass increases with, decreases with, or is insensitive to transport time. If algal growth is faster than loss (e.g., grazing, sedimentation), then phytoplankton biomass increases with increasing transport time. If loss is faster than growth, phytoplankton biomass decreases with increasing transport time. If growth and loss are approximately balanced, then phytoplankton biomass is relatively insensitive to transport time. In analyses of several systems, portions of an individual system, or time periods, apparent insensitivity of phytoplankton biomass to changes in transport time could arise due to the superposition of cases with different phytoplankton‐transport time relationships. Thus, in order to understand or predict responses of phytoplankton biomass to changes in transport time, the relative rates of algal growth and loss must be known.

Limnology and Oceanography↗
USGS2025

The transition from resistance to acceptance: Managing a marine invasive species in a changing world

Marine invasive species can transform coastal ecosystems, yet mitigating their effects can be difficult, and even impractical. Often, marine invasive species are managed at poorly matched spatial scales, and at the same time, rates of spread and establishment are increasing under climate change and can outpace resources available for population suppression. These circumstances challenge traditional conservation goals of maintaining a historic environmental state, especially for a species like the European green crab ( Carcinus maenas ), a formidable invader with few examples of successful long-term removal programs. A management paradigm where decision alternatives include resisting or accepting a new ecological trajectory may be needed. We apply mathematical concepts from decision theory to develop a quantitative framework for navigating management decisions in this new resist-accept paradigm. We develop a model of European green crab growth, removal and colonization, and we find optimal levels of removal effort that minimize both ecological change and removal cost. We establish a benchmark of colonization pressure at which green crab density becomes decoupled from a decision maker's actions, such that population control can no longer shape the invasion trajectory. For informing the decision boundary between resistance and acceptance, our results highlight that a decision maker's understanding of how removal cost scales with removal effort is more important than understanding the density-impact relationship. We show that assuming stationary system dynamics can result in sub-optimal levels of species removal effort, highlighting the importance of developing anticipatory management strategies by accounting for non-stationary dynamics. Policy implications . For marine invasive species that can disperse across long distances and recolonize rapidly after removal, the focus of conservation policy should shift away from understanding how to resist change to understanding when to stop resisting change. Navigating this decision problem involves trade-offs among competing objectives, highlighting the need for structured approaches to elicit objective weights that reflect the values of the decision maker. For natural resource managers facing possible ecosystem transformation, this decision framework can enable proactive and strategic decisions made under uncertainty in a changing world.

Journal of Applied Ecology↗
USGS2012

Modeling of multiphase multicontaminant transport in the subsurface

This review addresses modeling of subsurface hydrological systems in which contaminants are transported in more than one fluid phase. The primary focus is on problems involving nonaqueous-phase liquids (NAPLs), a dynamic gas phase, or both, so that the unsaturated and saturated zones are both discussed. Basic research in simpler settings is included if it develops concepts that could be applied in modeling of such problems. Recent developments in practical models are reviewed, along with experimental work and theoretical issues related to the formulation of mathematical models. It will be seen that the extent of validity of the local equilibrium assumption (LEA) for component partitioning among phases is a major question influencing the direction of these formulations. Also emphasized are upscaling to macroscopic and grid lengths, and the choice and coupling of primary variables in multicomponent systems. Relations to and possible use of developments in petroleum reservoir simulation are discussed.

Reviews of Geophysics↗
USGS2014

Using mark-recapture distance sampling methods on line transect surveys

Mark–recapture distance sampling (MRDS) methods are widely used for density and abundance estimation when the conventional DS assumption of certain detection at distance zero fails, as they allow detection at distance zero to be estimated and incorporated into the overall probability of detection to better estimate density and abundance. However, incorporating MR data in DS models raises survey and analysis issues not present in conventional DS. Conversely, incorporating DS assumptions in MR models raises issues not present in conventional MR. As a result, being familiar with either conventional DS methods or conventional MR methods does not on its own put practitioners in good a position to apply MRDS methods appropriately. This study explains the sometimes subtly different varieties of MRDS survey methods and the associated concepts underlying MRDS models. This is done as far as possible without giving mathematical details – in the hope that this will make the key concepts underlying the methods accessible to a wider audience than if we were to present the concepts via equations. We illustrate use of the two main types of MRDS model by using data collected on two different types of survey: a survey of ungulate faecal pellets where two observers searched independently of each other; and a cetacean survey that used a search protocol that could accommodate responsive movement, with only one observer searching independently and the other being aware of all detections. Synthesis and applications . Mark–recapture DS is a widely used method for estimating animal density and abundance when detection of animals at distance zero is not certain. Two observer configurations and three statistical models are described, and it is important to choose the most appropriate model for the observer configuration and target species in question. By way of making the methods more accessible to practicing ecologists, we describe the key ideas underlying MRDS methods, the sometimes subtle differences between them, and we illustrate these by applying different kinds of MRDS method to surveys of two different target species using different survey configurations.

Methods in Ecology and Evolution↗
USGS2022

Vote-processing rules for combining control recommendations from multiple models

Mathematical modelling is used during disease outbreaks to compare control interventions. Using multiple models, the best method to combine model recommendations is unclear. Existing methods weight model projections, then rank control interventions using the combined projections, presuming model outputs are directly comparable. However, the way each model represents the epidemiological system will vary. We apply electoral vote-processing rules to combine model-generated rankings of interventions. Combining rankings of interventions, instead of combining model projections, avoids assuming that projections are comparable as all comparisons of projections are made within each model. We investigate four rules: First-past-the-post, Alternative Vote (AV), Coombs Method and Borda Count. We investigate rule sensitivity by including models that favour only one action or including those that rank interventions randomly. We investigate two case studies: the 2014 Ebola outbreak in West Africa (37 compartmental models) and a hypothetical foot-and-mouth disease outbreak in UK (four individual-based models). The Coombs Method was least susceptible to adding models that favoured a single action, Borda Count and AV were most susceptible to adding models that ranked interventions randomly. Each rule chose the same intervention as when ranking interventions by mean projections, suggesting that combining rankings provides similar recommendations with fewer assumptions about model comparability.

Philosophical Transactions of the Royal Society A:↗
USGS1996

Estimation of rates of aerobic hydrocarbon biodegradation by simulation of gas transport in the unsaturated zone

The distribution of oxygen and carbon dioxide gases in the unsaturated zone provides a geochemical signature of aerobic hydrocarbon degradation at petroleum product spill sites. The fluxes of these gases are proportional to the rate of aerobic biodegradation and are quantified by calibrating a mathematical transport model to the oxygen and carbon dioxide gas concentration data. Reaction stoichiometry is assumed to convert the gas fluxes to a corresponding rate of hydrocarbon degradation. The method is applied at a gasoline spill site in Galloway Township, New Jersey, to determine the rate of aerobic degradation of hydrocarbons associated with passive and bioventing remediation field experiments. At the site, microbial degradation of hydrocarbons near the water table limits the migration of hydrocarbon solutes in groundwater and prevents hydrocarbon volatilization into the unsaturated zone. In the passive remediation experiment a site-wide degradation rate estimate of 34,400 g yr −1 (11.7 gal. yr −1 ) of hydrocarbon was obtained by model calibration to carbon dioxide gas concentration data collected in December 1989. In the bioventing experiment, degradation rate estimates of 46.0 and 47.9 g m −2 yr −1 (1.45 × 10 −3 and 1.51 × 10 −3 gal. ft. −2 yr −1 ) of hydrocarbon were obtained by model calibration to oxygen and carbon dioxide gas concentration data, respectively. Method application was successful in quantifying the significance of a naturally occurring process that can effectively contribute to plume stabilization.

Water Resources Research↗
USGS1995

Annotated bibliography of methodology for assessment of undiscovered oil and gas resources

An annotated bibliography of methodology of assessment of undiscovered oil and gas resources is presented as a useful reference for those engaged in resource assessment. The articles that are included deal only with quantitative assessment of undiscovered or inferred resources. the articles in this bibliography are classified largely according to the major assessment method that was applied in each situation. Major assessment methods include areal and volumetric yield methods, field size distributions, historical extrapolation, deposit modeling, organic geochemical mass balance methods, and direct expert assessment. Other categories include mathematical tools, reserve growth/confirmation, quantitative characterization of undiscovered resources, and general topics. For the purpose of future updates, we solicit contributions of articles that may have been missed in the preparation of this bibliography. ?? 1995 Oxford University Press.

Nonrenewable Resources↗
USGS1974

Storage of low-level radioactive wastes in the ground; hydrogeologic and hydrochemical factors

The status of mathematical simulation techniques, as they apply to radioactive waste burial sites, is briefly reviewed, and hydrogeologic and hydrochemical data needs are listed in order of increasing difficulty and cost of acquisition. Predictive modeling, monitoring, and management of radionuclides dissolved and transported by ground water can best be done for sites in relatively simple hydrogeologic settings; namely, in unfaulted relatively flat-lying strata of intermediate permeability such as silt, siltstone and silty sandstone. In contrast, dense fractured or soluble media, and poorly permeable porous media (aquitards) are not suitable for use as burial sites, first because of media heterogeneity and difficulties of sampling, and consequently of predictive modeling, and second, because in humid zones burial trenches in aquitards may overflow. A buffer zone several thousands of feet to perhaps several miles around existing or proposed sites is a mandatory consequence of the site selection criteria. As a specific example, the Maxey Flats, Kentucky low-level waste disposal site is examined. (Woodard-USGS)

Open-File Report↗
USGS1991

On seismological moments and magnitudes

My approach to seismology over the years has always been from the point of view of applied mathematics, as exemplified broadly by the work of the late Sir Harold Jeffreys and Professor K. E. Bullen. Both stresses the development of mathematics in the context of physical systems and of modeling, with an eye always on the side of inference. Seismology provided for them and still provides today the almost perfect paradigm; the problem is the resolution of the detailed consitution of the Earth and its geologically short-term dynamics. The latter part, includes, of course, seismic-risk estimation. The last 20 years have seen the construction of a brilliant theoretical formalism for linear inverse problems in seismology , although, oddly enough, the current popular Earth models do not take account it. It is interesting too that the narrow opinion, prevelent a decade ago, to the effect that the traditional seismic body-wave approaches to structural definition were superceded, has been largely abandoned under today's banner of tomography-as though the Oldham-Jeffreys-Gutenbery inversions were not tomography.

Earthquakes & Volcanoes (USGS)↗
USGS2018

A guide to calculating habitat-quality metrics to inform conservation of highly mobile species

Many metrics exist for quantifying the relative value of habitats and pathways used by highly mobile species. Properly selecting and applying such metrics requires substantial background in mathematics and understanding the relevant management arena. To address this multidimensional challenge, we demonstrate and compare three measurements of habitat quality: graph-, occupancy-, and demographic-based metrics. Each metric provides insights into system dynamics, at the expense of increasing amounts and complexity of data and models. Our descriptions and comparisons of diverse habitat-quality metrics provide means for practitioners to overcome the modeling challenges associated with management or conservation of such highly mobile species. Whereas previous guidance for applying habitat-quality metrics has been scattered in diversified tracks of literature, we have brought this information together into an approachable format including accessible descriptions and a modeling case study for a typical example that conservation professionals can adapt for their own decision contexts and focal populations. Considerations for Resource Managers Management objectives, proposed actions, data availability and quality, and model assumptions are all relevant considerations when applying and interpreting habitat-quality metrics. Graph-based metrics answer questions related to habitat centrality and connectivity, are suitable for populations with any movement pattern, quantify basic spatial and temporal patterns of occupancy and movement, and require the least data. Occupancy-based metrics answer questions about likelihood of persistence or colonization, are suitable for populations that undergo localized extinctions, quantify spatial and temporal patterns of occupancy and movement, and require a moderate amount of data. Demographic-based metrics answer questions about relative or absolute population size, are suitable for populations with any movement pattern, quantify demographic processes and population dynamics, and require the most data. More real-world examples applying occupancy-based, agent-based, and continuous-based metrics to seasonally migratory species are needed to better understand challenges and opportunities for applying these metrics more broadly.

Natural Resource Modeling↗
USGS2004

Granular avalanches across irregular three-dimensional terrain: 2. Experimental tests

Scaling considerations indicate that miniature experiments can be used to test models of granular avalanches in which the effects of intergranular fluid and cohesion are negligible. To test predictions of a granular avalanche model described in a companion paper, we performed bench top experiments involving avalanches of dry sand across irregular basal topography that mimicked the complexity of natural terrain. The experiments employed a novel method of laser-assisted cartography to map the three-dimensional morphology of rapidly moving avalanches, thereby providing high-resolution data for comparison with model output. Model input consisted of two material properties (angles of internal and basal Coulomb friction of the sand), which were measured in independent tests, and of initial and boundary conditions that characterized the geometry of the experimental apparatus. Experimental results demonstrate that the model accurately predicts not only the gross behavior but also many details of avalanche motion, from initiation to deposition. We attribute this accuracy to a mathematical and computational formulation that conserves mass and momentum in three-dimensional physical space and satisfies the Coulomb equation in three-dimensional stress space. Our results support the hypothesis that a Coulomb proportionality between shear and normal stresses applies in moderately rapid granular flows and that complicated constitutive postulates are unnecessary if momentum conservation is strictly enforced in continuum avalanche models. Furthermore, predictions of our Coulomb continuum model contrast with those of a Coulomb point mass model, illustrating the importance of multidimensional modeling and model testing.

Journal of Geophysical Research Earth Surface↗
USGS2016

Nonlinear relationships can lead to bias in biomass calculations and drift-foraging models when using summaries of invertebrate drift data

Drift-foraging models offer a mechanistic description of how fish feed in flowing water and the application of drift-foraging bioenergetics models to answer both applied and theoretical questions in aquatic ecology is growing. These models typically include nonlinear descriptions of ecological processes and as a result may be sensitive to how model inputs are summarized because of a mathematical property of nonlinear equations known as Jensen’s inequality. In particular, we show that the way in which continuous size distributions of invertebrate prey are represented within foraging models can lead to biases within the modeling process. We begin by illustrating how different equations common to drift-foraging models are sensitive to invertebrate inputs. We then use two case studies to show how different representations of invertebrate prey can influence predictions of energy intake and lifetime growth. Greater emphasis should be placed on accurate characterizations of invertebrate drift, acknowledging that inferences from drift-foraging models may be influenced by how invertebrate prey are represented.

Environmental Biology of Fishes↗
USGS2015

Habitat suitability criteria via parametric distributions: estimation, model selection and uncertainty

Previous methods for constructing univariate habitat suitability criteria (HSC) curves have ranged from professional judgement to kernel-smoothed density functions or combinations thereof. We present a new method of generating HSC curves that applies probability density functions as the mathematical representation of the curves. Compared with previous approaches, benefits of our method include (1) estimation of probability density function parameters directly from raw data, (2) quantitative methods for selecting among several candidate probability density functions, and (3) concise methods for expressing estimation uncertainty in the HSC curves. We demonstrate our method with a thorough example using data collected on the depth of water used by juvenile Chinook salmon ( Oncorhynchus tschawytscha ) in the Klamath River of northern California and southern Oregon. All R code needed to implement our example is provided in the appendix. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

California, Oregon↗
USGS1984

Proceedings of a workshop on fish habitat suitability index models

One of the habitat-based methodologies for impact assessment currently in use by the U.S. Fish and Wildlife Service is the Habitat Evaluation Procedures (HEP) (U.S. Fish and Wildlife Service 1980). HEP is based on the assumption that the quality of an area as wildlife habitat at a specified target year can be described by a single number, called a Habitat Suitability Index (HSI). An HSI of 1.0 represents optimum habitat: an HSI of 0.0 represents unsuitable habitat. The verbal or mathematical rules by which an HSI is assigned to an area are called an HSI model. A series of Habitat Suitability Index (HSI) models, described by Schamberger et al. (1982), have been published to assist users in applying HEP. HSI model building approaches are described in U.S. Fish and Wildlife Service (1981). One type of HSI model described in detail requires the development of Suitability Index (SI) graphs for habitat variables believed to be important for the growth, survival, standing crop, or other measure of well-being for a species. Suitability indices range from 0 to 1.0, with 1.0 representing optimum conditions for the variable. When HSI models based on suitability indices are used, habitat variable values are measured, or estimated, and converted to SI's through the use of a Suitability Index graph for each variable. Individual SI's are aggregated into an HSI. Standard methods for testing this type of HSI model did not exist at the time the studies reported in this document were performed. A workshop was held in Fort Collins, Colorado, February 14-15, 1983, that brought together biologists experienced in the use, development, and testing of aquatic HSI models, in an effort to address the following objectives: (1) review the needs of HSI model users; (2) discuss and document the results of aquatic HSI model tests; and (3) provide recommendations for the future development, testing, modification, and use of HSI models. Individual presentations, group discussions, and group decision techniques were used to develop and present information at the meeting. A synthesis of the resulting concepts, results, and recommendations follows this preface. Subsequent papers describe individual tests of selected HSI models. Most of the tests involved comparison of values from HSI models or Suitability index (SI) curves with standing crop, as required contractually. Time and budget constraints generally limited tests to the use of data previously collected for other purposes. These proceedings are intended to help persons responsible for the development, testing, or use of HSI models by increasing their understanding of potential uses and limitations of testing procedures and models based on aggregated Suitability Indices. Problems encountered when testing HSI models are described, model performance during tests is documents, and recommendations for future model development and testing presented by the participants are listed and interpreted.

Biological Report↗
USGS2005

The inverse problem of refraction travel times, part I: Types of Geophysical Nonuniqueness through Minimization

In a set of two papers we study the inverse problem of refraction travel times. The purpose of this work is to use the study as a basis for development of more sophisticated methods for finding more reliable solutions to the inverse problem of refraction travel times, which is known to be nonunique. The first paper, "Types of Geophysical Nonuniqueness through Minimization," emphasizes the existence of different forms of nonuniqueness in the realm of inverse geophysical problems. Each type of nonuniqueness requires a different type and amount of a priori information to acquire a reliable solution. Based on such coupling, a nonuniqueness classification is designed. Therefore, since most inverse geophysical problems are nonunique, each inverse problem must be studied to define what type of nonuniqueness it belongs to and thus determine what type of a priori information is necessary to find a realistic solution. The second paper, "Quantifying Refraction Nonuniqueness Using a Three-layer Model," serves as an example of such an approach. However, its main purpose is to provide a better understanding of the inverse refraction problem by studying the type of nonuniqueness it possesses. An approach for obtaining a realistic solution to the inverse refraction problem is planned to be offered in a third paper that is in preparation. The main goal of this paper is to redefine the existing generalized notion of nonuniqueness and a priori information by offering a classified, discriminate structure. Nonuniqueness is often encountered when trying to solve inverse problems. However, possible nonuniqueness diversity is typically neglected and nonuniqueness is regarded as a whole, as an unpleasant "black box" and is approached in the same manner by applying smoothing constraints, damping constraints with respect to the solution increment and, rarely, damping constraints with respect to some sparse reference information about the true parameters. In practice, when solving geophysical problems different types of nonuniqueness exist, and thus there are different ways to solve the problems. Nonuniqueness is usually regarded as due to data error, assuming the true geology is acceptably approximated by simple mathematical models. Compounding the nonlinear problems, geophysical applications routinely exhibit exact-data nonuniqueness even for models with very few parameters adding to the nonuniqueness due to data error. While nonuniqueness variations have been defined earlier, they have not been linked to specific use of a priori information necessary to resolve each case. Four types of nonuniqueness, typical for minimization problems are defined with the corresponding methods for inclusion of a priori information to find a realistic solution without resorting to a non-discriminative approach. The above-developed stand-alone classification is expected to be helpful when solving any geophysical inverse problems. ?? Birkha??user Verlag, Basel, 2005.

Pure and Applied Geophysics↗
USGS2008

Parasites in food webs: the ultimate missing links

Parasitism is the most common consumer strategy among organisms, yet only recently has there been a call for the inclusion of infectious disease agents in food webs. The value of this effort hinges on whether parasites affect food-web properties. Increasing evidence suggests that parasites have the potential to uniquely alter food-web topology in terms of chain length, connectance and robustness. In addition, parasites might affect food-web stability, interaction strength and energy flow. Food-web structure also affects infectious disease dynamics because parasites depend on the ecological networks in which they live. Empirically, incorporating parasites into food webs is straightforward. We may start with existing food webs and add parasites as nodes, or we may try to build food webs around systems for which we already have a good understanding of infectious processes. In the future, perhaps researchers will add parasites while they construct food webs. Less clear is how food-web theory can accommodate parasites. This is a deep and central problem in theoretical biology and applied mathematics. For instance, is representing parasites with complex life cycles as a single node equivalent to representing other species with ontogenetic niche shifts as a single node? Can parasitism fit into fundamental frameworks such as the niche model? Can we integrate infectious disease models into the emerging field of dynamic food-web modelling? Future progress will benefit from interdisciplinary collaborations between ecologists and infectious disease biologists.

Ecology Letters↗
USGS2012

Documentation of the Surface-Water Routing (SWR1) Process for modeling surface-water flow with the U.S. Geological Survey Modular Ground-Water Model (MODFLOW-2005)

A flexible Surface-Water Routing (SWR1) Process that solves the continuity equation for one-dimensional and two-dimensional surface-water flow routing has been developed for the U.S. Geological Survey three-dimensional groundwater model, MODFLOW-2005. Simple level- and tilted-pool reservoir routing and a diffusive-wave approximation of the Saint-Venant equations have been implemented. Both methods can be implemented in the same model and the solution method can be simplified to represent constant-stage elements that are functionally equivalent to the standard MODFLOW River or Drain Package boundary conditions. A generic approach has been used to represent surface-water features (reaches) and allows implementation of a variety of geometric forms. One-dimensional geometric forms include rectangular, trapezoidal, and irregular cross section reaches to simulate one-dimensional surface-water features, such as canals and streams. Two-dimensional geometric forms include reaches defined using specified stage-volume-area-perimeter (SVAP) tables and reaches covering entire finite-difference grid cells to simulate two-dimensional surface-water features, such as wetlands and lakes. Specified SVAP tables can be used to represent reaches that are smaller than the finite-difference grid cell (for example, isolated lakes), or reaches that cannot be represented accurately using the defined top of the model. Specified lateral flows (which can represent point and distributed flows) and stage-dependent rainfall and evaporation can be applied to each reach. The SWR1 Process can be used with the MODFLOW Unsaturated Zone Flow (UZF1) Package to permit dynamic simulation of runoff from the land surface to specified reaches. Surface-water/groundwater interactions in the SWR1 Process are mathematically defined to be a function of the difference between simulated stages and groundwater levels, and the specific form of the reach conductance equation used in each reach. Conductance can be specified directly or calculated as a function of the simulated wetted perimeter and defined reach bed hydraulic properties, or as a weighted combination of both reach bed hydraulic properties and horizontal hydraulic conductivity. Each reach can be explicitly coupled to a single specific groundwater-model layer or coupled to multiple groundwater-model layers based on the reach geometry and groundwater-model layer elevations in the row and column containing the reach. Surface-water flow between reservoirs is simulated using control structures. Surface-water flow between reaches, simulated by the diffusive-wave approximation, can also be simulated using control structures. A variety of control structures have been included in the SWR1 Process and include (1) excess-volume structures, (2) uncontrolled-discharge structures, (3) pumps, (4) defined stage-discharge relations, (5) culverts, (6) fixed- or movable-crest weirs, and (7) fixed or operable gated spillways. Multiple control structures can be implemented in individual reaches and are treated as composite flow structures. Solution of the continuity equation at the reach-group scale (a single reach or a user-defined collection of individual reaches) is achieved using exact Newton methods with direct solution methods or exact and inexact Newton methods with Krylov sub-space methods. Newton methods have been used in the SWR1 Process because of their ability to solve nonlinear problems. Multiple SWR1 time steps can be simulated for each MODFLOW time step, and a simple adaptive time-step algorithm, based on user-specified rainfall, stage, flow, or convergence constraints, has been implemented to better resolve surface-water response. A simple linear- or sigmoid-depth scaling approach also has been implemented to account for increased bed roughness at small surface-water depths and to increase numerical stability. A line-search algorithm also has been included to improve the quality of the Newton-step upgrade vector, if possible. The SWR1 Process has been benchmarked against one- and two-dimensional numerical solutions from existing one- and two-dimensional numerical codes that solve the dynamic-wave approximation of the Saint-Venant equations. Two-dimensional solutions test the ability of the SWR1 Process to simulate the response of a surface-water system to (1) steady flow conditions for an inclined surface (solution of Manning's equation), and (2) transient inflow and rainfall for an inclined surface. The one-dimensional solution tests the ability of the SWR1 Process to simulate a looped network with multiple upstream inflows and several control structures. The SWR1 Process also has been compared to a level-pool reservoir solution. A synthetic test problem was developed to evaluate a number of different SWR1 solution options and simulate surface-water/groundwater interaction. The solution approach used in the SWR1 Process may not be applicable for all surface-water/groundwater problems. The SWR1 Process is best suited for modeling long-term changes (days to years) in surface-water and groundwater flow. Use of the SWR1 Process is not recommended for modeling the transient exchange of water between streams and aquifers when local and convective acceleration and other secondary effects (for example, wind and Coriolis forces) are substantial. Dam break evaluations and two-dimensional evaluations of spatially extensive domains are examples where acceleration terms and secondary effects would be significant, respectively.

Techniques and Methods↗
USGS2015

A robust calibration technique for acoustic emission systems based on momentum transfer from a ball drop

We describe a technique to estimate the seismic moment of acoustic emissions and other extremely small seismic events. Unlike previous calibration techniques, it does not require modeling of the wave propagation, sensor response, or signal conditioning. Rather, this technique calibrates the recording system as a whole and uses a ball impact as a reference source or empirical Green’s function. To correctly apply this technique, we develop mathematical expressions that link the seismic moment $M_{0}$ of internal seismic sources (i.e., earthquakes and acoustic emissions) to the impulse, or change in momentum $\Delta p $, of externally applied seismic sources (i.e., meteor impacts or, in this case, ball impact). We find that, at low frequencies, moment and impulse are linked by a constant, which we call the force‐moment‐rate scale factor $C_{F\dot{M}} = M_{0}/\Delta p$. This constant is equal to twice the speed of sound in the material from which the seismic sources were generated. Next, we demonstrate the calibration technique on two different experimental rock mechanics facilities. The first example is a saw‐cut cylindrical granite sample that is loaded in a triaxial apparatus at 40 MPa confining pressure. The second example is a 2 m long fault cut in a granite sample and deformed in a large biaxial apparatus at lower stress levels. Using the empirical calibration technique, we are able to determine absolute source parameters including the seismic moment, corner frequency, stress drop, and radiated energy of these magnitude −2.5 to −7 seismic events.

Bulletin of the Seismological Society of America↗