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At least 109 records · Page 6Linked to original sources
USGS2002

Locally refined block-centred finite-difference groundwater models: Evaluation of parameter sensitivity and the consequences for inverse modelling

Models with local grid refinement, as often required in groundwater models, pose special problems for model calibration. This work investigates the calculation of sensitivities and the performance of regression methods using two existing and one new method of grid refinement. The existing local grid refinement methods considered are: (a) a variably spaced grid in which the grid spacing becomes smaller near the area of interest and larger where such detail is not needed, and (b) telescopic mesh refinement (TMR), which uses the hydraulic heads or fluxes of a regional model to provide the boundary conditions for a locally refined model. The new method has a feedback between the regional and local grids using shared nodes, and thereby, unlike the TMR methods, balances heads and fluxes at the interfacing boundary. Results for sensitivities are compared for the three methods and the effect of the accuracy of sensitivity calculations are evaluated by comparing inverse modelling results. For the cases tested, results indicate that the inaccuracies of the sensitivities calculated using the TMR approach can cause the inverse model to converge to an incorrect solution.

IAHS-AISH Publication↗
USGS2002

Locally refined block-centered finite-difference groundwater models: Evaluation of parameter sensitivity and the consequences for inverse modelling and predictions

Models with local grid refinement, as often required in groundwater models, pose special problems for model calibration. This work investigates the calculation of sensitivities and performance of regression methods using two existing and one new method of grid refinement. The existing local grid refinement methods considered are (1) a variably spaced grid in which the grid spacing becomes smaller near the area of interest and larger where such detail is not needed and (2) telescopic mesh refinement (TMR), which uses the hydraulic heads or fluxes of a regional model to provide the boundary conditions for a locally refined model. The new method has a feedback between the regional and local grids using shared nodes, and thereby, unlike the TMR methods, balances heads and fluxes at the interfacing boundary. Results for sensitivities are compared for the three methods and the effect of the accuracy of sensitivity calculations are evaluated by comparing inverse modelling results. For the cases tested, results indicate that the inaccuracies of the sensitivities calculated using the TMR approach can cause the inverse model to converge to an incorrect solution.

Acta Universitatis Carolinae, Geologica↗
USGS2001

1r2dinv: A finite-difference model for inverse analysis of two dimensional linear or radial groundwater flow

We have developed a program for inverse analysis of two-dimensional linear or radial groundwater flow problems. The program, 1r2dinv, uses standard finite difference techniques to solve the groundwater flow equation for a horizontal or vertical plane with heterogeneous properties. In radial mode, the program simulates flow to a well in a vertical plane, transforming the radial flow equation into an equivalent problem in Cartesian coordinates. The physical parameters in the model are horizontal or x-direction hydraulic conductivity, anisotropy ratio (vertical to horizontal conductivity in a vertical model, y-direction to x-direction in a horizontal model), and specific storage. The program allows the user to specify arbitrary and independent zonations of these three parameters and also to specify which zonal parameter values are known and which are unknown. The Levenberg-Marquardt algorithm is used to estimate parameters from observed head values. Particularly powerful features of the program are the ability to perform simultaneous analysis of heads from different tests and the inclusion of the wellbore in the radial mode. These capabilities allow the program to be used for analysis of suites of well tests, such as multilevel slug tests or pumping tests in a tomographic format. The combination of information from tests stressing different vertical levels in an aquifer provides the means for accurately estimating vertical variations in conductivity, a factor profoundly influencing contaminant transport in the subsurface. ?? 2001 Elsevier Science Ltd. All rights reserved.

Computers & Geosciences↗
USGS2012

Comparison of seismic waveform inversion results for the rupture history of a finite fault: Application to the 1986 North Palm Springs, California, earthquake

The July 8, 1986, North Palm Springs earthquake is used as a basis for comparison of several different approaches to the solution for the rupture history of a finite fault. The inversion of different waveform data is considered; both teleseismic P waveforms and local strong ground motion records. Linear parametrizations for slip amplitude are compared with nonlinear parametrizations for both slip amplitude and rupture time. Inversions using both synthetic and empirical Green's functions are considered. In general, accurate Green's functions are more readily calculable for the teleseismic problem where simple ray theory and flat-layered velocity structures are usually sufficient. However, uncertainties in the variation in t * with frequency most limit the resolution of teleseismic inversions. A set of empirical Green's functions that are well recorded at teleseismic distances could avoid the uncertainties in attenuation. In the inversion of strong motion data, the accurate calculation of propagation path effects other than attenuation effects is the limiting factor in the resolution of source parameters. The assumption of a laterally homogeneous velocity structure is usually not a good one, and the use of empirical Green's functions is desirable. Considering the parametrization of the problem, any degree of fault rupture complexity can be described in terms of a linear parametrization for slip amplitudes. However, a nonlinear parametrization for rupture times and slip amplitudes can have a distinct advantage over a simple linear one by limiting the number of unknown parameters. Regardless of the choice of data or the type of parametrization, the model or solution will be affected by the choice of minimization norm and the type of stabilization used.

Journal of Geophysical Research Solid Earth↗
USGS2019

Geophysical mapping of plume discharge to surface water at a crude oil spill site: Inversion versus machine learning

The interpretation of geophysical survey results to answer hydrologic, engineering, and geologic questions is critical to diverse problems for management of water, energy, and mineral resources. Although geophysical images provide valuable qualitative insight into subsurface architecture and conditions, translating geophysical images into quantitative information (e.g., saturation, concentration, and hydraulic properties) often involves substantial nonuniqueness and uncertainty owing to the limited resolution of geophysical imaging and uncertainty in petrophysical relations. We have developed a machine-learning approach to address these challenges in the context of a field-based investigation to map zones where a hydrocarbon plume was discharging to surface water at the National Crude Oil Spill Fate and Natural Attenuation Research Site in Bemidji, Minnesota, USA. The two-step approach combines multiple types of geophysical and direct information and effectively bypasses inversion and its associated assumptions. Integrating multifrequency electromagnetic induction, ground-penetrating radar, and fluid-sampling data, we first identify discharge zones and second estimate specific conductance versus depth. Compared with conventional inversion results, the machine-learning results (1) directly address the study objectives (delineating the discharge zones); (2) better extract depth-dependent information from the data, for which sensitivity diminishes rapidly with depth; and (3) quantify the uncertainty of the predictions (i.e., discharge versus nondischarge zones), rather than the uncertainty of the geophysical estimates (i.e., the standard error of estimation for the logarithm of electrical conductivity).

Minnesota↗
USGS2002

Joint inversion of acoustic and resistivity data for the estimation of gas hydrate concentration

Downhole log measurements, such as acoustic or electrical resistivity logs, are frequently used to estimate in situ gas hydrate concentrations in the pore space of sedimentary rocks. Usually the gas hydrate concentration is estimated separately based on each log measurement. However, measurements are related to each other through the gas hydrate concentration, so the gas hydrate concentrations can be estimated by jointly inverting available logs. Because the magnitude of slowness of acoustic and resistivity values differs by more than an order of magnitude, a least-squares method, weighted by the inverse of the observed values, is attempted. Estimating the resistivity of connate water and gas hydrate concentration simultaneously is problematic, because the resistivity of connate water is independent of acoustics. In order to overcome this problem, a coupling constant is introduced in the Jacobian matrix. In the use of different logs to estimate gas hydrate concentration, a joint inversion of different measurements is preferred to the averaging of each inversion result.

Bulletin↗
USGS1992

Trends and management of wolf-livestock conflicts in Minnesota

The nature and extent of wolf-livestock conflicts in Minnesota during 1975-86 was studied as part of a wolf depredation control program. The level of wolf (Canis lupus) depredation on livestock in Minnesota, as determined from the total number of complaints verified annually during 1975-86, showed a slight upward trend but did not increase significantly. A significant portion of the annual variation in verified complaints-perhaps the best index on severity of the depredation problem was explained by variation in severity of the winter before the depredation season (inverse relation). The addition of a time variable did not account for a significant portion of the remaining variation. Verified complaints of depredations averaged 30 per year, affecting an average of 21 farms (0.33% of producers) annually. Conflicts were highly seasonal and involved primarily cattle (mainly calves), sheep, and domestic turkeys. Annual variation in losses of sheep and turkeys was higher than for cattle. In recent years, sheep and turkey losses in two northwestern counties have increased; preventive control may be warranted in those areas. Site-specific trapping and removal of wolves in response to depredations was the primary control method, resulting in captures of 437 wolves in 12 depredation seasons. For the wolf range as a whole, no relation was found between wolf removal and subsequent depredation rates; however, wolf removal seemed to reduce depredations locally at some farms. When adults and yearlings were removed, no subsequent losses occurred in about 55% of instances; removal of young of the year reduced losses in 22%. Removal of breeding wolves did not reduce the incidence of subsequent losses more than removal of nonbreeding adults and yearlings did. The low number of conflicts for 1975-86 was remarkable considering the frequent contact between wolves and livestock. However, an update of complaints for 1987-89 revealed a definite upward trend in depredations (Epilogue). Improvements in farm management practices may reduce the present number of conflicts.

Resource Publication↗
USGS2008

Convergent radial dispersion: A note on evaluation of the Laplace transform solution

A numerical inversion algorithm for Laplace transforms that is capable of handling rapid changes in the computed function is applied to the Laplace transform solution to the problem of convergent radial dispersion in a homogeneous aquifer. Prior attempts by the author to invert this solution were unsuccessful for highly advective systems where the Peclet number was relatively large. The algorithm used in this note allows for rapid and accurate inversion of the solution for all Peclet numbers of practical interest, and beyond. Dimensionless breakthrough curves are illustrated for tracer input in the form of a step function, a Dirac impulse, or a rectangular input.

Water Resources Research↗
USGS2001

3-D imaging of large scale buried structure by 1-D inversion of very early time electromagnetic (VETEM) data

A simple and efficient method for large scale three-dimensional (3-D) subsurface imaging of inhomogeneous background is presented. One-dimensional (1-D) multifrequency distorted Born iterative method (DBIM) is employed in the inversion. Simulation results utilizing synthetic scattering data are given. Calibration of the very early time electromagnetic (VETEM) experimental waveforms is detailed along with major problems encountered in practice and their solutions. This discussion is followed by the results of a large scale application of the method to the experimental data provided by the VETEM system of the U.S. Geological Survey. The method is shown to have a computational complexity that is promising for on-site inversion.

IEEE Transactions on Geoscience and Remote Sensing↗
USGS2008

A trade-off between model resolution and variance with selected Rayleigh-wave data

Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (??? 2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. First, we employed a data-resolution matrix to select data that would be well predicted and to explain advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher mode data are normally more accurately predicted than fundamental mode data because of restrictions on the data kernel for the inversion system. Second, we obtained an optimal damping vector in a vicinity of an inverted model by the singular value decomposition of a trade-off function of model resolution and variance. In the end of the paper, we used a real-world example to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher mode data in inversion can provide better results. We also calculated model-resolution matrices of these examples to show the potential of increasing model resolution with selected surface-wave data. With the optimal damping vector, we can improve and assess an inverted model obtained by a damped least-square method.

Conference Paper↗
USGS2008

Data-resolution matrix and model-resolution matrix for Rayleigh-wave inversion using a damped least-squares method

Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (>2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices in these examples to show the potential of increasing model resolution with selected surface-wave data. ?? Birkhaueser 2008.

Pure and Applied Geophysics↗
USGS2017

Finite‐fault Bayesian inversion of teleseismic body waves

Inverting geophysical data has provided fundamental information about the behavior of earthquake rupture. However, inferring kinematic source model parameters for finite‐fault ruptures is an intrinsically underdetermined problem (the problem of nonuniqueness), because we are restricted to finite noisy observations. Although many studies use least‐squares techniques to make the finite‐fault problem tractable, these methods generally lack the ability to apply non‐Gaussian error analysis and the imposition of nonlinear constraints. However, the Bayesian approach can be employed to find a Gaussian or non‐Gaussian distribution of all probable model parameters, while utilizing nonlinear constraints. We present case studies to quantify the resolving power and associated uncertainties using only teleseismic body waves in a Bayesian framework to infer the slip history for a synthetic case and two earthquakes: the 2011 M w 7.1 Van, east Turkey, earthquake and the 2010 M w 7.2 El Mayor–Cucapah, Baja California, earthquake. In implementing the Bayesian method, we further present two distinct solutions to investigate the uncertainties by performing the inversion with and without velocity structure perturbations. We find that the posterior ensemble becomes broader when including velocity structure variability and introduces a spatial smearing of slip. Using the Bayesian framework solely on teleseismic body waves, we find rake is poorly constrained by the observations and rise time is poorly resolved when slip amplitude is low.

Bulletin of the Seismological Society of America↗
USGS2005

Parallel Fortran-MPI software for numerical inversion of the Laplace transform and its application to oscillatory water levels in groundwater environments

A parallel Fortran-MPI (Message Passing Interface) software for numerical inversion of the Laplace transform based on a Fourier series method is developed to meet the need of solving intensive computational problems involving oscillatory water level's response to hydraulic tests in a groundwater environment. The software is a parallel version of ACM (The Association for Computing Machinery) Transactions on Mathematical Software (TOMS) Algorithm 796. Running 38 test examples indicated that implementation of MPI techniques with distributed memory architecture speedups the processing and improves the efficiency. Applications to oscillatory water levels in a well during aquifer tests are presented to illustrate how this package can be applied to solve complicated environmental problems involved in differential and integral equations. The package is free and is easy to use for people with little or no previous experience in using MPI but who wish to get off to a quick start in parallel computing. ?? 2004 Elsevier Ltd. All rights reserved.

Environmental Modelling and Software↗
USGS2008

Effects of topography and crustal heterogeneities on the source estimation of LP event at Kilauea volcano

The main goal of this study is to improve the modelling of the source mechanism associated with the generation of long period (LP) signals in volcanic areas. Our intent is to evaluate the effects that detailed structural features of the volcanic models play in the generation of LP signal and the consequent retrieval of LP source characteristics. In particular, effects associated with the presence of topography and crustal heterogeneities are here studied in detail. We focus our study on a LP event observed at Kilauea volcano, Hawaii, in 2001 May. A detailed analysis of this event and its source modelling is accompanied by a set of synthetic tests, which aim to evaluate the effects of topography and the presence of low velocity shallow layers in the source region. The forward problem of Green's function generation is solved numerically following a pseudo-spectral approach, assuming different 3-D models. The inversion is done in the frequency domain and the resulting source mechanism is represented by the sum of two time-dependent terms: a full moment tensor and a single force. Synthetic tests show how characteristic velocity structures, associated with shallow sources, may be partially responsible for the generation of the observed long-lasting ringing waveforms. When applying the inversion technique to Kilauea LP data set, inversions carried out for different crustal models led to very similar source geometries, indicating a subhorizontal cracks. On the other hand, the source time function and its duration are significantly different for different models. These results support the indication of a strong influence of crustal layering on the generation of the LP signal, while the assumption of homogeneous velocity model may bring to misleading results.

Geophysical Journal International↗
USGS2005

A test of geographic assignment using isotope tracers in feathers of known origin

We used feathers of known origin collected from across the breeding range of a migratory shorebird to test the use of isotope tracers for assigning breeding origins. We analyzed δD, δ 13 C, and δ 15 N in feathers from 75 mountain plover ( Charadrius montanus ) chicks sampled in 2001 and from 119 chicks sampled in 2002. We estimated parameters for continuous-response inverse regression models and for discrete-response Bayesian probability models from data for each year independently. We evaluated model predictions with both the training data and by using the alternate year as an independent test dataset. Our results provide weak support for modeling latitude and isotope values as monotonic functions of one another, especially when data are pooled over known sources of variation such as sample year or location. We were unable to make even qualitative statements, such as north versus south, about the likely origin of birds using both δD and δ 13 C in inverse regression models; results were no better than random assignment. Probability models provided better results and a more natural framework for the problem. Correct assignment rates were highest when considering all three isotopes in the probability framework, but the use of even a single isotope was better than random assignment. The method appears relatively robust to temporal effects and is most sensitive to the isotope discrimination gradients over which samples are taken. We offer that the problem of using isotope tracers to infer geographic origin is best framed as one of assignment, rather than prediction.

Oecologia↗
USGS2019

Perturbational and nonperturbational inversion of Love-wave velocities

We describe a set of MATLAB codes to forward model and invert Love-wave phase or group velocities. The forward modeling is based on a finite-element method in the frequency-wavenumber domain, and we obtain the different modes with an eigenvector-eigenvalue solver. We examine the issue of parasitic modes that arises for modeling Love waves, in contrast to the Rayleigh wave case, and how to discern parasitic from physical modes. Once the matrix eigenvector-eigenvalue problem has been solved for Love waves, we show a straightforward technique to obtain sensitivity kernels for S-wave velocity and density. In practice, the sensitivity of Love waves to density is relatively small and inversions only aim to estimate the S-wave velocity. Two types of inversion accompany the forward-modeling codes: One is a perturbational scheme for updating an initial model, and the other is a nonperturbational method that is well-suited for defining a good initial model. The codes are able to implement an optimal nonuniform layering designed for Love waves, invert combinations of phase and group velocity measurements of any mode, and seamlessly handle the transition from guided to leaky modes below the cutoff frequency. Two software examples demonstrate use of the codes at near-surface and crustal scales.

Geophysics↗
USGS2010

Convergent radial dispersion: A Laplace transform solution for aquifer tracer testing

A Laplace transform solution was obtained for the injection of a tracer in a well situated in a homogeneous aquifer where steady, horizontal, radially convergent flow has been established due to pumping at a second well. The standard advection-dispersion equation for mass transfer was used as the controlling equation. For boundary conditions, mass balances that account for mixing of the tracer with the fluid residing in the injection and pumped wells were used. The derived solution, which can be adapted for either resident or flux-averaged concentration, is of practical use only for the pumped well. This problem is of interest because it is easily applied to field determination of aquifer dispersivity and effective porosity. Breakthrough curves were obtained by numerical inversion of the Laplace transform solution. It was found that tracer mixing with fluid in the pumped and injection wells, especially in low-porosity aquifers, may have a significant influence on the shape of the tracer breakthrough curves.

Water Resources Research↗