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USGS2015

A random-walk algorithm for modeling lithospheric density and the role of body forces in the evolution of the Midcontinent Rift

This paper develops a Monte Carlo algorithm for extracting three-dimensional lithospheric density models from geophysical data. Empirical scaling relationships between velocity and density create a 3D starting density model, which is then iteratively refined until it reproduces observed gravity and topography. This approach permits deviations from uniform crustal velocity-density scaling, which provide insight into crustal lithology and prevent spurious mapping of crustal anomalies into the mantle. We test this algorithm on the Proterozoic Midcontinent Rift (MCR), north-central U.S. The MCR provides a challenge because it hosts a gravity high overlying low shear-wave velocity crust in a generally flat region. Our initial density estimates are derived from a seismic velocity/crustal thickness model based on joint inversion of surface-wave dispersion and receiver functions. By adjusting these estimates to reproduce gravity and topography, we generate a lithospheric-scale model that reveals dense middle crust and eclogitized lowermost crust within the rift. Mantle lithospheric density beneath the MCR is not anomalous, consistent with geochemical evidence that lithospheric mantle was not the primary source of rift-related magmas and suggesting that extension occurred in response to far-field stress rather than a hot mantle plume. Similarly, the subsequent inversion of normal faults resulted from changing far-field stress that exploited not only warm, recently faulted crust but also a gravitational potential energy low in the MCR. The success of this density modeling algorithm in the face of such apparently contradictory geophysical properties suggests that it may be applicable to a variety of tectonic and geodynamic problems.

Iowa, Kansas, Michigan, Minnesota, Nebraska, Wisco↗

USGS2017

Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors

Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1 / f α "> 1 / f α 1/fα with frequency, f . With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013 . doi: 10.1007/s00190-012-0605-0 ) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.

Journal of Geodesy↗

USGS2015

Hydrogeochemical effects of a bulkhead in the Dinero mine tunnel, Sugar Loaf mining district, near Leadville, Colorado

The Dinero mine drainage tunnel is an abandoned, draining mine adit near Leadville, Colorado, that has an adverse effect on downstream water quality and aquatic life. In 2009, a bulkhead was constructed (creating a mine pool and increasing water-table elevations behind the tunnel) to limit drainage from the tunnel and improve downstream water quality. The goal of this study was to document changes to hydrology and water quality resulting from bulkhead emplacement, and to understand post-bulkhead changes in source water and geochemical processes that control mine-tunnel discharge and water quality. Comparison of pre-and post-bulkhead hydrology and water quality indicated that tunnel discharge and zinc and manganese loads decreased by up to 97 percent at the portal of Dinero tunnel and at two downstream sites (LF-537 and LF-580). However, some water-quality problems persisted at LF-537 and LF-580 during high-flow events and years, indicating the effects of the remaining mine waste in the area. In contrast, post-bulkhead water quality degraded at three upstream stream sites and a draining mine tunnel (Nelson tunnel). Water-quality degradation in the streams likely occurred from increased contributions of mine-pool groundwater to the streams. In contrast, water-quality degradation in the Nelson tunnel was likely from flow of mine-pool water along a vein that connects the Nelson tunnel to mine workings behind the Dinero tunnel bulkhead. Principal components analysis, mixing analysis, and inverse geochemical modeling using PHREEQC indicated that mixing and geochemical reactions (carbonate dissolution during acid weathering, precipitation of goethite and birnessite, and sorption of zinc) between three end-member water types generally explain the pre-and post-bulkhead water composition at the Dinero and Nelson tunnels. The three end members were (1) a relatively dilute groundwater having low sulfate and trace element concentrations; (2) mine pool water, and (3) water that flowed from a structure in front of the bulkhead after bulkhead emplacement. Both (2) and (3) had high sulfate and trace element concentrations. These results indicate how analysis of monitoring information can be used to understand hydrogeochemical changes resulting from bulkhead emplacement. This understanding, in turn, can help inform future decisions on the disposition of the remaining mine waste and water-quality problems in the area.

Colorado↗

USGS1967

The ternary system K2SO4 MgSO4 CaSO4

Melting and subsolidus relations in the system K 2 SO 4 MgSO 4 CaSO 4 were studied using heating-cooling curves, differential thermal analysis, optics, X-ray diffraction at room and high temperatures and by quenching techniques. Previous investigators were unable to study the binary MgSO 4 CaSO 4 system and the adjacent area in the ternary system because of the decomposition of MgSO 4 and CaSO 4 at high temperatures. This problem was partly overcome by a novel sealed-tube quenching method, by hydrothermal synthesis, and by long-time heating in the solidus. As a result of this study, we found: (1) a new compound, CaSO 4 ·3MgSO 4 (m.p. 1201°C) with a field extending into the ternary system; (2) a high temperature form of MgSO 4 with a sluggishly reversible inversion. An X-ray diffraction pattern for this polymorphic form is given; (3) the inversion of β-CaSO 4 (anhydrite) to α-CaSO 4 at 1195°C, in agreement with grahmann ; (1) (4) the melting point of MgSO 4 is 1136°C and that of CaSO 4 is 1462°C (using sealed tube methods to prevent decomposition of the sulphates); (5) calcium langbeinite (K 2 SO 4 ·2CaSO 4 ) is the only compound in the K 2 SO 4 CaSO 4 binary system. This resolved discrepancies in the results of previous investigators; (6) a continuous solid solution series between congruently melting K 2 SOP 4 ·2MgSO 4 (langbeinite) and incongruently melting K 2 SO 4 ·2CaSO 4 (calcium langbeinite); (7) the liquidus in the ternary system consists of primary phase fields of K 2 SO 4 , MgSO 4 , CaSO 4 , langbeinite-calcium langbeinite solid solution, and CaSO 4 ·3MgSO 4 . The CaSO 4 field extends over a large portion of the system. Previously reported fields for the compounds (K 2 SO 4 ·MgSO 4 ·nCaSO 4 ), K 2 SO 4 ·3CaSO 4 and K 2 SO 4 ·CaSO 4 were not found; (8) a minimum in the ternary system at: 740°C, 25% MgSO 4 , 6% CaSO 4 , 69% K 2 SO 4 ; and ternary eutectics at 882°C, 49% MgSO 4 , 19% CaSO 4 , 32% K 2 SO 4 ; and 880°, 67·5% MgSO 4 , 5% CaSO 4 , 27·5% K 2 SO 4 .

Journal of Inorganic and Nuclear Chemistry↗

USGS2006

Thickness distribution of a cooling pyroclastic flow deposit on Augustine Volcano, Alaska: Optimization using InSAR, FEMs, and an adaptive mesh algorithm

Interferometric synthetic aperture radar (InSAR) imagery documents the consistent subsidence, during the interval 1992–1999, of a pyroclastic flow deposit (PFD) emplaced during the 1986 eruption of Augustine Volcano, Alaska. We construct finite element models (FEMs) that simulate thermoelastic contraction of the PFD to account for the observed subsidence. Three-dimensional problem domains of the FEMs include a thermoelastic PFD embedded in an elastic substrate. The thickness of the PFD is initially determined from the difference between post- and pre-eruption digital elevation models (DEMs). The initial excess temperature of the PFD at the time of deposition, 640 °C, is estimated from FEM predictions and an InSAR image via standard least-squares inverse methods. Although the FEM predicts the major features of the observed transient deformation, systematic prediction errors (RMSE = 2.2 cm) are most likely associated with errors in the a priori PFD thickness distribution estimated from the DEM differences. We combine an InSAR image, FEMs, and an adaptive mesh algorithm to iteratively optimize the geometry of the PFD with respect to a minimized misfit between the predicted thermoelastic deformation and observed deformation. Prediction errors from an FEM, which includes an optimized PFD geometry and the initial excess PFD temperature estimated from the least-squares analysis, are sub-millimeter (RMSE = 0.3 mm). The average thickness (9.3 m), maximum thickness (126 m), and volume (2.1 × 10 7 m 3 ) of the PFD, estimated using the adaptive mesh algorithm, are about twice as large as the respective estimations for the a priori PFD geometry. Sensitivity analyses suggest unrealistic PFD thickness distributions are required for initial excess PFD temperatures outside of the range 500–800 °C.

Alaska↗

USGS2026

Computational electromagnetic geophysics for groundwater system studies: A review on established practices and recent advances

Identifying effective solutions for locating groundwater resources and ensuring the quality of drinking water is increasingly urgent, given the challenges posed by climate change and population growth. This review investigates electromagnetic geophysical imaging techniques, in both time- and frequency-domain, that can provide valuable insights for groundwater assessment. We explore computational electromagnetic methods used to evaluate electromagnetic data and several recent hydrogeophysical case studies. As open-source frameworks for modeling electromagnetic geophysical problems become available, a broader range of researchers can interpret their data with computationally advanced software. We provide an overview of documented open-source codes for evaluating electromagnetic data and analyze various hydrological targets in relation to their electromagnetic surveying technique and the computational method applied. Furthermore, we evaluate the potential of advanced computational techniques, including three-dimensional modeling, non-deterministic inversion and machine learning, to couple geophysical with numerical groundwater modeling and apply it in groundwater system studies. Despite obstacles such as complexity and resource demands, our findings indicate that the quantification and integration of predictive uncertainties from both electromagnetic and hydrological data and simulations would significantly improve the reliability of hydrogeophysical models. This can lead to a deeper understanding of groundwater systems and improved management practices.

Journal of Hydrology↗

USGS2020

Generalizing the inversion‐based PSHA source model for an interconnected fault system

This article represents a step toward generalizing and simplifying the procedure for constructing an inversion‐based seismic hazard source model for an interconnected fault system, including the specification of adjustable segmentation constraints. A very simple example is used to maximize understandability and to counter the notion that an inversion approach is only applicable when an abundance of data is available. Also exemplified is how to construct a range of models to adequately represent epistemic uncertainties (which should be a high priority in any hazard assessment). Opportunity is also taken to address common concerns and misunderstandings associated with the third Uniform California Earthquake Rupture Forecast, including the seemingly disproportionate number of large‐magnitude events, and how well hazard is resolved given the overall problem is very underdetermined. However, the main aim of this article is to provide a general protocol for constructing such models.

Bulletin of the Seismological Society of America↗

USGS1996

Earthquake mechanisms from linear-programming inversion of seismic-wave amplitude ratios

The amplitudes of radiated seismic waves contain far more information about earthquake source mechanisms than do first-motion polarities, but amplitudes are severely distorted by the effects of heterogeneity in the Earth. This distortion can be reduced greatly by using the ratios of amplitudes of appropriately chosen seismic phases, rather than simple amplitudes, but existing methods for inverting amplitude ratios are severely nonlinear and require computationally intensive searching methods to ensure that solutions are globally optimal. Searching methods are particularly costly if general (moment tensor) mechanisms are allowed. Efficient linear-programming methods, which do not suffer from these problems, have previously been applied to inverting polarities and wave amplitudes. We extend these methods to amplitude ratios, in which formulation on inequality constraint for an amplitude ratio takes the same mathematical form as a polarity observation. Three-component digital data for an earthquake at the Hengill-Grensdalur geothermal area in southwestern Iceland illustrate the power of the method. Polarities of P , SH , and SV waves, unusually well distributed on the focal sphere, cannot distinguish between diverse mechanisms, including a double couple. Amplitude ratios, on the other hand, clearly rule out the double-couple solution and require a large explosive isotropic component.

Bulletin of the Seismological Society of America↗

USGS2023

Reconstructing missing data by comparing interpolation techniques: Applications for long-term water quality data

Missing data are typical yet must be addressed for proper inferences or expanding datasets to guide our limnological understanding and management of aquatic systems. Interpolation methods (i.e., estimating missing values using known values within the dataset) can alleviate data gaps and common problems. We compared seven popular interpolation methods for predicting substantial missingness in a long-term water quality dataset from the Upper Mississippi River, U.S.A. The dataset included 80,000 sampling sites collected over 30 yr that had substantial missingness for total nitrogen (TN), total phosphorus (TP), and water velocity. For all three interpolated water quality variables, random forests had very high prediction accuracy and outperformed the methods of ordinary kriging, polynomial regressions, regression trees, and inverse distance weighting. TP had a mean absolute error (MAE) of 0.03 mg (L-TP) −1 , TN had a MAE of 0.39 mg (L-TN) −1 , and water velocity had a MAE of 0.10 m s −1 . The random forests' error rates were mapped and showed low spatiotemporal variability across the riverscape, indicating high model performance across many habitat types and large spatial scales. In the current era of “big data,” interpolation becomes an imperative step prior to ecological analyses yet remains unfamiliar and underutilized. Our research briefly describes the importance of addressing missingness and provides a roadmap to conduct model intercomparisons of other big datasets. We also share adaptable data analysis scripts, which allows others to readily conduct interpolation comparisons for many limnology applications and contexts.

Illinois, Iowa, Minnesota, Missouri, Wisconsin↗

USGS1991

Accumulation of trace elements and organochlorines by surf scoters wintering in the Pacific northwest

Selenium, cadmium, mercury, copper, manganese, zinc, aluminum, lead, PCBs and DDE were accumulated by segments of the surf scoter (Melanitta perspicillata) population that winters in the Pacific Northwest, but whether the uptake occurred on breeding and/or wintering grounds was uncertain for some contaminants. Surf scoters collected in Puget Sound and San Francisco Bay (in another study) during the same period (January 1985) contained similar concentrations of cadmium, but Alsea Bay scoters contained more. Cadmium was inversely related to both liver and body weights of Northwest scoters in January; similar weight losses were reported in experimental laboratory studies. Northwest and north San Francisco Bay scoters contained similar mercury concentrations, but those in south San Francisco Bay contained higher concentrations. San Francisco Bay scoters contained higher arsenic and selenium concentrations than those in the Northwest; however, the 43.4 ppm (geometric mean, dry wt) selenium in livers at Commencement Bay in January was above levels associated with the reproductive problems in aquatic birds at Kesterson National Wildlife Refuge. Even higher concentrations of some elements may be found in surf scoters in March, because a later collection (March) at San Francisco Bay yielded higher concentrations than found there in January. Trace element concentrations in birds at a given wintering location are variable among species and may be influenced by diet, breeding grounds, and physiology (e.g., at Commencement Bay surf scoters with a sediment-associated diet contained 50X more cadmium in their kidneys than did fish-eating western grebes [Aechmophorus occidentalis]). The numerous wildlife species that live on estuaries require further attention.

Northwestern Naturalist↗

USGS1977

SIPB: a seismic refraction inverse modeling program for batch computer systems

SIPB is an interactive Fortran computer program that was developed for use with a timeshare computer system with program control information submitted from a remote terminal, and output data displayed on the terminal or printed on a line printer. The program is an upgraded version of FSIPI (Scott, Tibbetts, and Burdick, 1972) with several major improvements in addition to .its adaptation to timeshare operation. The most significant improvement was made in the procedure for handling data from in-line offset shotpoints beyond the end shotpoints of the geophone spread. The changes and improvements are described, user's instructions are outlined, examples of input and output data for a test problem are presented, and the Fortran program is listed in this report. An upgraded batch-mode program, SIPB, is available for users who do not have a timeshare computer system available (Scott, 1977).

Open-File Report↗

USGS2003

Time‐lapse imaging of saline‐tracer transport in fractured rock using difference‐attenuation radar tomography

Accurate characterization of fractured‐rock aquifer heterogeneity remains one of the most challenging and important problems in groundwater hydrology. We demonstrate a promising strategy to identify preferential flow paths in fractured rock using a combination of geophysical monitoring and conventional hydrogeologic tests. Cross‐well difference‐attenuation ground‐penetrating radar was used to monitor saline‐tracer migration in an experiment at the U.S. Geological Survey Fractured Rock Hydrology Research Site in Grafton County, New Hampshire. Radar data sets were collected every 10 min in three adjoining planes for 5 hours during each of 12 tracer tests. An innovative inversion method accounts for data acquisition times and temporal changes in attenuation during data collection. The inverse algorithm minimizes a combination of two functions. The first is the sum of weighted squared data residuals. Second is a measure of solution complexity based on an a priori space‐time covariance function, subject to constraints that limit radar‐attenuation changes to regions of the tomograms traversed by high difference‐attenuation ray paths. The time series of tomograms indicate relative tracer concentrations and tracer arrival times in the image planes; from these we infer the presence and location of a preferential flow path within a previously identified zone of transmissive fractures. These results provide new insights into solute channeling and the nature of aquifer heterogeneity at the site.

New Hampshire↗

USGS1977

SIPT: a seismic refraction inverse modeling program for timeshare terminal computer systems

Open-File Report↗

USGS2007

Integrating laboratory creep compaction data with numerical fault models: A Bayesian framework

[1] We developed a robust Bayesian inversion scheme to plan and analyze laboratory creep compaction experiments. We chose a simple creep law that features the main parameters of interest when trying to identify rate-controlling mechanisms from experimental data. By integrating the chosen creep law or an approximation thereof, one can use all the data, either simultaneously or in overlapping subsets, thus making more complete use of the experiment data and propagating statistical variations in the data through to the final rate constants. Despite the nonlinearity of the problem, with this technique one can retrieve accurate estimates of both the stress exponent and the activation energy, even when the porosity time series data are noisy. Whereas adding observation points and/or experiments reduces the uncertainty on all parameters, enlarging the range of temperature or effective stress significantly reduces the covariance between stress exponent and activation energy. We apply this methodology to hydrothermal creep compaction data on quartz to obtain a quantitative, semiempirical law for fault zone compaction in the interseismic period. Incorporating this law into a simple direct rupture model, we find marginal distributions of the time to failure that are robust with respect to errors in the initial fault zone porosity.

Journal of Geophysical Research B: Solid Earth↗

USGS1988

Cobalt in ferromanganese crusts as a monitor of hydrothermal discharge on the Pacific sea floor

Ferromanganese oxide crusts, which accumulate on unsedimented surfaces in the open ocean 1–6 , derive most of their metal content from dissolved and particulate matter in ambient bottom water 7,8 , in proportions modified by the variable scavenging efficiency of the oxide phase for susceptible ions 9 . They differ in this respect from abyssal nodules, much of whose metals are remobilized from host sediments. Here we present maps of cobalt concentration and inferred accumulation rate of ferromanganese crusts from the Pacific Ocean. We propose that depletion of cobalt in Pacific crusts measures the location and intensity of submarine hydrothermal discharge. Use of the 'cobalt chronometer', an algorithm inversely relating cobalt content and crust growth rate, permits mapping of the accumulation rate of ferromanganese crusts with only indirect recourse to radioactivity-based dating methods. These maps show that crusts in hydrothermal areas grow from two to more than four orders of magnitude faster than in the Central Pacific Ocean. Cobalt-enriched crusts are found where water masses are most isolated from continental-coastal and hydrothermal sources of metals, now and in the past. This relationship can resolve the problem of cobalt enrichment in crusts without recourse to hypotheses invoking special cobalt sources or enrichment mechanisms.

Nature↗

USGS2024

Physics-based satellite-derived bathymetry (SDB) using Landsat OLI images

The estimation of depth in optically shallow waters using satellite imagery can be efficient and cost-effective. Active sensors measure the distance traveled by an emitted laser pulse propagating through the water with high precision and accuracy if the bottom peak intensity of the waveform is greater than the noise level. However, passive optical imaging of optically shallow water involves measuring the radiance after the sunlight undergoes downward attenuation on the way to the sea floor, and the reflected light is then attenuated while moving back upward to the water surface. The difficulty of satellite-derived bathymetry (SDB) arises from the fact that the measured radiance is a result of a complex association of physical elements, mainly the optical properties of the water, bottom reflectance, and depth. In this research, we attempt to apply physics-based algorithms to solve this complex problem as accurately as possible to overcome the limitation of having only a few known values from a multispectral sensor. Major analysis components are atmospheric correction, the estimation of water optical properties from optically deep water, and the optimization of bottom reflectance as well as the water depth. Specular reflection of the sky radiance from the water surface is modeled in addition to the typical atmospheric correction. The physical modeling of optically dominant components such as dissolved organic matter, phytoplankton, and suspended particulates allows the inversion of water attenuation coefficients from optically deep pixels. The atmospheric correction and water attenuation results are used in the ocean optical reflectance equation to solve for the bottom reflectance and water depth. At each stage of the solution, physics-based models and a physically valid, constrained Levenberg–Marquardt numerical optimization technique are used. The physics-based algorithm is applied to Landsat Operational Land Imager (OLI) imagery over the shallow coastal zone of Guam, Key West, and Puerto Rico. The SDB depths are compared to airborne lidar depths, and the root mean squared error (RMSE) is mostly less than 2 m over water as deep as 30 m. As the initial choice of bottom reflectance is critical, along with the bottom reflectance library, we describe a pure bottom unmixing method based on eigenvector analysis to estimate unknown site-specific bottom reflectance.

Remote Sensing↗

USGS2012

Approaches in highly parameterized inversion - GENIE, a general model-independent TCP/IP run manager

GENIE is a model-independent suite of programs that can be used to generally distribute, manage, and execute multiple model runs via the TCP/IP infrastructure. The suite consists of a file distribution interface, a run manage, a run executer, and a routine that can be compiled as part of a program and used to exchange model runs with the run manager. Because communication is via a standard protocol (TCP/IP), any computer connected to the Internet can serve in any of the capacities offered by this suite. Model independence is consistent with the existing template and instruction file protocols of the widely used PEST parameter estimation program. This report describes (1) the problem addressed; (2) the approach used by GENIE to queue, distribute, and retrieve model runs; and (3) user instructions, classes, and functions developed. It also includes (4) an example to illustrate the linking of GENIE with Parallel PEST using the interface routine.

Techniques and Methods↗

USGS1997

Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control

One problem with the application of neural networks to the multivariable control of mineral and extractive processes is determining whether and how to use them. The objective of this investigation was to compare neural network control to more conventional strategies and to determine if there are any advantages in using neural network control in terms of set-point tracking, rise time, settling time, disturbance rejection and other criteria. The procedure involved developing neural network controllers using both historical plant data and simulation models. Various control patterns were tried, including both inverse and direct neural network plant models. These were compared to state space controllers that are, by nature, linear. For grinding and leaching circuits, a nonlinear neural network-based model predictive control strategy was superior to a state space-based linear quadratic gaussian controller. The investigation pointed out the importance of incorporating state space into neural networks by making them recurrent, i.e., feeding certain output state variables into input nodes in the neural network. It was concluded that neural network controllers can have better disturbance rejection, set-point tracking, rise time, settling time and lower set-point overshoot, and it was also concluded that neural network controllers can be more reliable and easy to implement in complex, multivariable plants.

Mining, Metallurgy & Exploration (MME)↗