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At least 73 records · Page 4Linked to original sources
USGS1998

Closing the gap between regional and global travel time tomography

Recent global travel time tomography studies by Zhou [1996] and van der Hilst et al . [1997] have been performed with cell parameterizations of the order of those frequently used in regional tomography studies (i.e., with cell sizes of 1°–2°). These new global models constitute a considerable improvement over previous results that were obtained with rather coarse parameterizations (5° cells). The inferred structures are, however, of larger scale than is usually obtained in regional models, and it is not clear where and if individual cells are actually resolved. This study aims at resolving lateral heterogeneity on scales as small as 0.6° in the upper mantle and 1.2°–3° in the lower mantle. This allows for the adequate mapping of expected small-scale structures induced by, for example, lithosphere subduction, deep mantle upwellings, and mid-ocean ridges. There are three major contributions that allow for this advancement. First, we employ an irregular grid of nonoverlapping cells adapted to the heterogeneous sampling of the Earth's mantle by seismic waves [ Spakman and Bijwaard , 1998]. Second, we exploit the global data set of Engdahl et al . [1998], which is a reprocessed version of the global data set of the International Seismological Centre. Their reprocessing included hypocenter redetermination and phase reidentification. Finally, we combine all data used ( P , pP , and pwP phases) into nearly 5 million ray bundles with a limited spatial extent such that averaging over large mantle volumes is prevented while the signal-to-noise ratio is improved. In the approximate solution of the huge inverse problem we obtain a variance reduction of 57.1%. Synthetic sensitivity tests indicate horizontal resolution on the scale of the smallest cells (0.6° or 1.2°) in the shallow parts of subduction zones decreasing to approximately 2°–3° resolution in well-sampled regions in the lower mantle. Vertical resolution can be worse (up to several hundreds of kilometers) in subduction zones with rays predominantly pointing along dip. Important features of the solution are as follows: 100–200 km thick high-velocity slabs beneath all major subduction zones, sometimes flattening in the transition zone and sometimes directly penetrating into the lower mantle; large high-velocity anomalies in the lower mantle that have been attributed to subduction of the Tethys ocean and the Farallon plate; and low-velocity anomalies continuing across the 660 km discontinuity to hotspots at the surface under Iceland, east Africa, the Canary Islands, Yellowstone, and the Society Islands. Our findings corroborate that the 660 km boundary may resist but not prevent (present day) large-scale mass transfer from upper to lower mantle or vice versa. This observation confirms the results of previous, global mantle studies that employed coarser parameterizations.

Journal of Geophysical Research B: Solid Earth↗
USGS2003

Gaussian statistics for palaeomagnetic vectors

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Re??union, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Geophysical Journal International↗
USGS1992

Leaks in pipe networks

Leak detection in water‐distribution systems can be accomplished by solving an inverse problem using measurements of pressure and/or flow. The problem is formulated with equivalent orifice areas of possible leaks as the unknowns. Minimization of the difference between measured and calculated heads produces a solution for the areas. The quality of the result depends on number and location of the measurements. A sensitivity matrix is key to deciding where to make measurements. Both location and magnitude of leaks are sensitive to the quantity and quality of pressure measurements and to how well the pipe friction parameters are known. The overdetermined problem (more measurements than suspected leaks) gives the best results, but some information can be derived from the underdetermined problem. The variance of leak areas, based on the quality of system characteristics and pressure data, indicates the likely accuracy of the results. The method will not substitute for more traditional leak surveys but can serve as a guide and supplement.

Journal of Hydraulic Engineering↗
USGS2019

Revisiting “An Exercise in Groundwater Model Calibration and Prediction” after 30 years: Insights and New Directions

In 1988, an important publication moved model calibration and forecasting beyond case studies and theoretical analysis. It reported on a somewhat idyllic graduate student modeling exercise where many of the system properties were known; the primary forecasts of interest were heads in pumping wells after a river was modified. The model was calibrated using manual trial‐and‐error approaches where a model's forecast quality was not related to how well it was calibrated. Here, we investigate whether tools widely available today obviate the shortcomings identified 30 years ago. A reconstructed version of the 1988 true model was tested using increasing parameter estimation sophistication. The parameter estimation demonstrated the inverse problem was non‐unique because only head data were available for calibration. When a flux observation was included, current parameter estimation approaches were able to overcome all calibration and forecast issues noted in 1988. The best forecasts were obtained from a highly parameterized model that used pilot points for hydraulic conductivity and was constrained with soft knowledge. Like the 1988 results, however, the best calibrated model did not produce the best forecasts due to parameter overfitting. Finally, a computationally frugal linear uncertainty analysis demonstrated that the single‐zone model was oversimplified, with only half of the forecasts falling within the calculated uncertainty bounds. Uncertainties from the highly parameterized models had all six forecasts within the calculated uncertainty. The current results outperformed those of the 1988 effort, demonstrating the value of quantitative parameter estimation and uncertainty analysis methods.

Groundwater↗
USGS2011

A distribution-based parameterization for improved tomographic imaging of solute plumes

Difference geophysical tomography (e.g. radar, resistivity and seismic) is used increasingly for imaging fluid flow and mass transport associated with natural and engineered hydrologic phenomena, including tracer experiments, in situ remediation and aquifer storage and recovery. Tomographic data are collected over time, inverted and differenced against a background image to produce ‘snapshots’ revealing changes to the system; these snapshots readily provide qualitative information on the location and morphology of plumes of injected tracer, remedial amendment or stored water. In principle, geometric moments (i.e. total mass, centres of mass, spread, etc.) calculated from difference tomograms can provide further quantitative insight into the rates of advection, dispersion and mass transfer; however, recent work has shown that moments calculated from tomograms are commonly biased, as they are strongly affected by the subjective choice of regularization criteria. Conventional approaches to regularization (Tikhonov) and parametrization (image pixels) result in tomograms which are subject to artefacts such as smearing or pixel estimates taking on the sign opposite to that expected for the plume under study. Here, we demonstrate a novel parametrization for imaging plumes associated with hydrologic phenomena. Capitalizing on the mathematical analogy between moment-based descriptors of plumes and the moment-based parameters of probability distributions, we design an inverse problem that (1) is overdetermined and computationally efficient because the image is described by only a few parameters, (2) produces tomograms consistent with expected plume behaviour (e.g. changes of one sign relative to the background image), (3) yields parameter estimates that are readily interpreted for plume morphology and offer direct insight into hydrologic processes and (4) requires comparatively few data to achieve reasonable model estimates. We demonstrate the approach in a series of numerical examples based on straight-ray difference-attenuation radar monitoring of the transport of an ionic tracer, and show that the methodology outlined here is particularly effective when limited data are available.

Geophysical Journal International↗
USGS2010

Inherent Limitations of Hydraulic Tomography

We offer a cautionary note in response to an increasing level of enthusiasm regarding high-resolution aquifer characterization with hydraulic tomography. We use synthetic examples based on two recent field experiments to demonstrate that a high degree of nonuniqueness remains in estimates of hydraulic parameter fields even when those estimates are based on simultaneous analysis of a number of carefully controlled hydraulic tests. We must, therefore, be careful not to oversell the technique to the community of practicing hydrogeologists, promising a degree of accuracy and resolution that, in many settings, will remain unattainable, regardless of the amount of effort invested in the field investigation. No practically feasible amount of hydraulic tomography data will ever remove the need to regularize or bias the inverse problem in some fashion in order to obtain a unique solution. Thus, along with improving the resolution of hydraulic tomography techniques, we must also strive to couple those techniques with procedures for experimental design and uncertainty assessment and with other more cost-effective field methods, such as geophysical surveying and, in unconsolidated formations, direct-push profiling, in order to develop methods for subsurface characterization with the resolution and accuracy needed for practical field applications. Copyright ?? 2010 The Author(s). Journal compilation ?? 2010 National Ground Water Association.

Ground Water↗
USGS2019

Predicting paleoclimate from compositional data using multivariate Gaussian process inverse prediction

Multivariate compositional count data arise in many applications including ecology, microbiology, genetics and paleoclimate. A frequent question in the analysis of multivariate compositional count data is what underlying values of a covariate(s) give rise to the observed composition. Learning the relationship between covariates and the compositional count allows for inverse prediction of unobserved covariates given compositional count observations. Gaussian processes provide a flexible framework for modeling functional responses with respect to a covariate without assuming a functional form. Many scientific disciplines use Gaussian process approximations to improve prediction and make inference on latent processes and parameters. When prediction is desired on unobserved covariates given realizations of the response variable, this is called inverse prediction. Because inverse prediction is often mathematically and computationally challenging, predicting unobserved covariates often requires fitting models that are different from the hypothesized generative model. We present a novel computational framework that allows for efficient inverse prediction using a Gaussian process approximation to generative models. Our framework enables scientific learning about how the latent processes co-vary with respect to covariates while simultaneously providing predictions of missing covariates. The proposed framework is capable of efficiently exploring the high dimensional, multi-modal latent spaces that arise in the inverse problem. To demonstrate flexibility, we apply our method in a generalized linear model framework to predict latent climate states given multivariate count data. Based on cross-validation, our model has predictive skill competitive with current methods while simultaneously providing formal, statistical inference on the underlying community dynamics of the biological system previously not available.

Annals of Applied Statistics↗
USGS2024

Preliminary implications of viscoelastic ray theory for anelastic seismic tomography models

The recent developments in general viscoelastic ray theory provide a rigorous mathematical framework for anelastic seismic tomography. They provide closed‐form solutions of forward ray‐tracing and simple inverse problems for anelastic horizontal and spherical layered media with material gradients. They provide ray‐tracing computation algorithms valid for all angles of incidence that account for changes in wave speed, attenuation, and trajectory of anelastic P and S body waves induced by anelastic boundaries. They account for theoretical predictions that seismic waves refract as inhomogeneous waves across anelastic boundaries for all angles of incidence, which in turn accounts for energy carried by plane waves along seismic boundaries at head wave critical angles and wide‐angle refracted (WAR) ray paths that are not predicted by elastic models. Exact viscoelastic ray‐tracing numerical results for various models provide examples that illustrate the effects of anelastic boundaries on the travel times and amplitudes of seismic waves. They show the effects are strongly dependent on angle of incidence. For near‐critical and wide angles of incidence the anelastic effects on travel times and amplitudes can be large and are not explained by elastic ray theory, but the effects on travel times can be relatively small and difficult to distinguish from those for elastic media for pre‐near‐critical angles of incidence. The results for some models indicate that reflected anelastic WAR waves may be observable at the surface and possibly account for some prominent seismic arrivals not explained by elasticity. These preliminary results suggest that the application of exact viscoelastic ray‐tracing computation algorithms to exploration and teleseismic data sets can reveal new insights regarding the properties and distribution of anelastic materials in the Earth.

Bulletin of the Seismological Society of America↗
USGS2010

Linking process to pattern: estimating spatiotemporal dynamics of a wildlife epidemic from cross‐sectional data

Underlying dynamic event processes unfolding in continuous time give rise to spatiotemporal patterns that are sometimes observable at only a few discrete times. Such event processes may be modulated simultaneously over several spatial (e.g., latitude and longitude) and temporal (e.g., age, calendar time, and cohort) dimensions. The ecological challenge is to understand the dynamic latent processes that were integrated over several dimensions (space and time) to produce the observed pattern: a so‐called inverse problem. An example of such a problem is characterizing epidemiological rate processes from spatially referenced age‐specific prevalence data for a wildlife disease such as chronic wasting disease (CWD). With age‐specific prevalence data, the exact infection times are not observed, which complicates the direct estimation of rates. However, the relationship between the observed data and the unobserved rate variables can be described with likelihood equations. Typically, for problems with multiple timescales, the likelihoods are integral equations without closed forms. The complexity of the likelihoods often makes traditional maximum‐likelihood approaches untenable. Here, using seven years of hunter‐harvest prevalence data from the CWD epidemic in white‐tailed deer (Odocoileus virginianus) in Wisconsin, USA, we develop and explore a Bayesian approach that allows for a detailed examination of factors modulating the infection rates over space, age, and time, and their interactions. Our approach relies on the Bayesian ability to borrow strength from neighbors in both space and time. Synthesizing a number of areas of event time analysis (current‐status data, age/period/cohort models, Bayesian spatial shared frailty models), our general framework has very broad ecological applicability beyond disease prevalence data to a number of important ecological event time analyses, including general survival studies with multiple time dimensions for which existing methodology is limited. We observed strong associations of infection rates with age, gender, and location. The infection rate appears to be increasing with time. We could not detect growth hotspots, or location by time interactions, which suggests that spatial variation in infection rates is determined primarily by when the disease arrives locally, rather than how fast it grows. We emphasize assumptions and the potential consequences of their violations.

Wisconsin↗
USGS2014

Reply to: Turner, R.E., 2014. Discussion of: Olea, R.A. and Coleman, J.L., Jr., 2014. A synoptic examination of causes of land loss in southern Louisiana as related to the exploitation of subsurface geologic resources, Journal of Coastal Research, 30(5), 1025–1044; Journal of Coastal Research, 30(6), 1330–1334.

To a large extent, geology is a science of solving inverse problems based on some data and scientific principles. Solutions to these types of problems are not unique, especially when using different data, invoking different principles, or both. It is not surprising that the discussant and we have reached different conclusions on the same specific issue of land loss along the coast of Louisiana because we use different observations and view those observations in a different context. The objective of this reply is to orient the reader, who then can decide which approach is more likely to be the correct analysis.

Journal of Coastal Research↗
USGS1996

Unrealistic parameter estimates in inverse modelling: A problem or a benefit for model calibration?

Estimation of unrealistic parameter values by inverse modelling is useful for constructed model discrimination. This utility is demonstrated using the three-dimensional, groundwater flow inverse model MODFLOWP to estimate parameters in a simple synthetic model where the true conditions and character of the errors are completely known. When a poorly constructed model is used, unreasonable parameter values are obtained even when using error free observations and true initial parameter values. This apparent problem is actually a benefit because it differentiates accurately and inaccurately constructed models. The problems seem obvious for a synthetic problem in which the truth is known, but are obscure when working with field data. Situations in which unrealistic parameter estimates indicate constructed model problems are illustrated in applications of inverse modelling to three field sites and to complex synthetic test cases in which it is shown that prediction accuracy also suffers when constructed models are inaccurate.

IAHS-AISH Publication↗
USGS2024

Cross-fade sampling: Extremely efficient Bayesian inversion for a variety of geophysical problems

This paper introduces cross-fade sampling, a computationally efficient Markov Chain Monte Carlo simulation method that uses a semi-analytical approach to quickly solve Bayesian inverse problems that do not themselves have an analytical solution. Cross-fading is efficient in two ways. First, it requires fewer samples to obtain the same quality simulation of the target probability density function (PDF). Secondly, it is much faster to evaluate the posterior probability of each sample than conventional sampling methods for simulating Bayesian posterior PDFs. Conventional methods require evaluating the prior probability (which describes your a priori constraints) and data likelihood (which describes the fit between the observations and the predictions of the model) for each sample model. However, cross-fading does not require evaluating the data likelihood, meaning that ‘big data’ can be fit with zero additional computational cost. Further, the cross-fading approach can be used to calculate the marginal likelihood associated with a model design, facilitating model comparison and Bayesian model averaging. Topics covered in this paper include derivation of the cross-fade approach and how it can be used to simulate Bayesian posterior PDFs and compute the marginal likelihood, discussion of the class of problems to which cross-fading can be applied (with examples from earthquake statistics, earthquake ground motion modelling, volcanic eruption forecasting, and finite fault slip modelling), demonstration of efficiency relative to existing sampling methods and discussion of how cross-fading can be used to account for prediction errors (i.e. epistemic errors) as part of the geophysical inverse problem.

Geophysical Journal International↗
USGS2006

Joint analysis of refractions with surface waves: An inverse solution to the refraction-traveltime problem

We describe a possible solution to the inverse refraction-traveltime problem (IRTP) that reduces the range of possible solutions (nonuniqueness). This approach uses a reference model, derived from surface-wave shear-wave velocity estimates, as a constraint. The application of the joint analysis of refractions with surface waves (JARS) method provided a more realistic solution than the conventional refraction/tomography methods, which did not benefit from a reference model derived from real data. This confirmed our conclusion that the proposed method is an advancement in the IRTP analysis. The unique basic principles of the JARS method might be applicable to other inverse geophysical problems. ?? 2006 Society of Exploration Geophysicists.

Geophysics↗
USGS2010

A comparison between SWI and SEAWAT: the importance of dispersion, inversion and vertical anisotropy

SWI and SEAWAT are both computer codes designed to model variable-density systems. One of the options in SWI is to model Dupuit interface flow, where freshwater and seawater are separated by an interface. In this paper we compare seawater intrusion model results of SWI to model results of SEAWAT, which simulates full variable-density flow and transport. Results indicate that SWI is valid for many variable-density systems. For the case considered in this paper, SWI results are accurate when the simulated width of the transition zone between seawater to freshwater is 15% or less of the scale of the problem, density inversion (saltwater over freshwater) occurs over only a small part of the model domain, and the ratio of vertical to horizontal hydraulic conductivity is larger than 0.01. Results also show that the simulated interface moves further inland using SWI than for the same conditions using SEAWAT. SWI is preferable to be used in systems where run times for a fully-coupled variable-density flow and transport model would be prohibitive; for the case considered here, SWI run times were a few seconds and SEAWAT run times were almost three hours.

Conference Paper↗
USGS2010

A trade-off solution between model resolution and covariance in surface-wave inversion

Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.

Pure and Applied Geophysics↗
USGS1987

Molecular weight of aquatic fulvic acids by vapor pressure osmometry

The molecular weights of aquatic fulvic acids extracted from five rivers were determined by vapor pressure osmometry with water and tetrahydrofuran as solvents. The values obtained ranged from 500 to 950 dallons, indicating that the molecular weights of aquatic fulvic acids are not as great as has been suggested in some other molecular weight studies. The samples were shown to be relatively monodisperse from radii of gyration measurements determined by small angle x-ray scattering. THF affords greater precision and accuracy than H 2 O in VPO measurements, and was found to be a suitable solvent for the determination of molecular weight of aquatic fulvic acid because it obviates the dissociation problem. An inverse correlation was observed with these samples between the concentration of Ca ++ and Mg ++ in the river water and the radii of gyration and molecular weights of the corresponding fulvic acid samples.

Geochimica et Cosmochimica Acta↗
USGS1999

An inverse method using toroidal mode data

The author presents a numerical method for calculating the density and S-wave velocity in the upper mantle of a spherically symmetric, non-rotating Earth which consists of a perfect elastic, isotropic material. The data comes from the periods of the toroidal oscillations. She tests the method on a smoothed version of model A. The error in the reconstruction is less than 1 %. The effects of perturbations in the eigenvalues are studied and she finds that the final model is sensitive to errors in the data .

Inverse Problems↗
USGS2007

Applications of the JARS method to study levee sites in southern Texas and southern New Mexico

We apply the joint analysis of refractions with surface waves (JARS) method to several sites and compare its results to traditional refraction-tomography methods in efforts of finding a more realistic solution to the inverse refraction-traveltime problem. The JARS method uses a reference model, derived from surface-wave shear-wave velocity estimates, as a constraint. In all of the cases JARS estimates appear more realistic than those from the conventional refraction-tomography methods. As a result, we consider, the JARS algorithm as the preferred method for finding solutions to the inverse refraction-tomography problems. ?? 2007 Society of Exploration Geophysicists.

Conference Paper↗