scholarly journals Sequential and joint hydrogeophysical inversion using a field-scale groundwater model with ERT and TDEM data

2013 ◽  
Vol 17 (10) ◽  
pp. 4043-4060 ◽  
Author(s):  
D. Herckenrath ◽  
G. Fiandaca ◽  
E. Auken ◽  
P. Bauer-Gottwein
Keyword(s):  
Geophysical Data ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Groundwater Model ◽  
Field Scale ◽  
Geophysical Model ◽  
Time Domain Electromagnetic ◽  
Synthetic Groundwater ◽  
Airborne Geophysical Data

Abstract. Increasingly, ground-based and airborne geophysical data sets are used to inform groundwater models. Recent research focuses on establishing coupling relationships between geophysical and groundwater parameters. To fully exploit such information, this paper presents and compares different hydrogeophysical inversion approaches to inform a field-scale groundwater model with time domain electromagnetic (TDEM) and electrical resistivity tomography (ERT) data. In a sequential hydrogeophysical inversion (SHI) a groundwater model is calibrated with geophysical data by coupling groundwater model parameters with the inverted geophysical models. We subsequently compare the SHI with a joint hydrogeophysical inversion (JHI). In the JHI, a geophysical model is simultaneously inverted with a groundwater model by coupling the groundwater and geophysical parameters to explicitly account for an established petrophysical relationship and its accuracy. Simulations for a synthetic groundwater model and TDEM data showed improved estimates for groundwater model parameters that were coupled to relatively well-resolved geophysical parameters when employing a high-quality petrophysical relationship. Compared to a SHI these improvements were insignificant and geophysical parameter estimates became slightly worse. When employing a low-quality petrophysical relationship, groundwater model parameters improved less for both the SHI and JHI, where the SHI performed relatively better. When comparing a SHI and JHI for a real-world groundwater model and ERT data, differences in parameter estimates were small. For both cases investigated in this paper, the SHI seems favorable, taking into account parameter error, data fit and the complexity of implementing a JHI in combination with its larger computational burden.

scholarly journals Sequential and joint hydrogeophysical inversion using a field-scale groundwater model with ERT and TDEM data

2013 ◽  
Vol 10 (4) ◽  
pp. 4655-4707 ◽  
Author(s):  
D. Herckenrath ◽  
G. Fiandaca ◽  
E. Auken ◽  
P. Bauer-Gottwein
Keyword(s):  
Parameter Estimates ◽  
Model Parameters ◽  
Groundwater Model ◽  
Field Scale ◽  
Geophysical Model ◽  
Geophysical Parameter ◽  
Coupling Constraints ◽  
Time Domain Electromagnetic ◽  
Synthetic Groundwater ◽  
Geometric Relationship

Abstract. Increasingly, ground-based and airborne geophysical datasets are used to inform groundwater models. Recent research focuses on establishing coupling relationships between geophysical and groundwater parameters. To fully exploit such information, this paper presents and compares a joint hydrogeophysical inversion (JHI) approach and sequential hydrogeophysical inversion (SHI) approach to inform a field-scale groundwater model with Time Domain Electromagnetic (TDEM) and Electrical Resistivity Tomography (ERT) data. The implemented SHI coupled inverted geophysical models with groundwater parameters, where the strength of the coupling was based on geophysical parameter resolution. To test whether the implemented SHI over- or underestimated the coupling strength between groundwater and geophysical model, we compared its results with a JHI in which a geophysical model is simultaneously inverted with a groundwater model using additional coupling constraints that explicitly account for an established petrophysical relationship and its accuracy. The first set of simulations for a synthetic groundwater model and TDEM data, employing a high-quality petrophysical and geometric relationship, showed improved estimates for groundwater model parameters that were coupled to relative well-resolved geophysical parameters. Compared to a SHI these improvements were insignificant and geophysical parameter estimates became slightly worse. In a second set of simulations, employing a low-quality petrophysical relationship, groundwater parameter improved less for both the SHI and JHI, where the SHI performed slightly better. For a real-world groundwater model and ERT data, different parameter estimates were obtained with a JHI and SHI. Parameter uncertainty was reduced but was similar for the SHI and JHI. The geometric constraint showed little impact while the petrophysical constraint showed significant changes in geophysical and groundwater parameters. For both cases investigated in this paper, the SHI seems favorable, taking in account parameter error, data fit and the complexity of implementing a JHI in combination with its larger computational burden.

scholarly journals Sensitivity of airborne geophysical data to sublacustrine permafrost thaw

2014 ◽  
Vol 8 (6) ◽  
pp. 6079-6116
Author(s):  
B. J. Minsley ◽  
T. P. Wellman ◽  
M. A. Walvoord ◽  
A. Revil
Keyword(s):  
Electrical Resistivity ◽  
Physical Property ◽  
Geophysical Data ◽  
Monte Carlo Algorithm ◽  
Permafrost Thaw ◽  
Geophysical Model ◽  
Electromagnetic Responses ◽  
Airborne Geophysical Data ◽  
Ice Content ◽  
Forward And Inverse Modeling

Abstract. A coupled hydrogeophysical forward and inverse modeling approach is developed to illustrate the ability of frequency-domain airborne electromagnetic (AEM) data to characterize subsurface physical properties associated with sublacustrine permafrost thaw during lake talik formation. Several scenarios are evaluated that consider the response to variable hydrologic forcing from different lake depths and hydrologic gradients. The model includes a physical property relationship that connects the dynamic distribution of subsurface electrical resistivity based on lithology as well as ice-saturation and temperature outputs from the SUTRA groundwater simulator with freeze/thaw physics. Electrical resistivity models are used to simulate AEM data in order to explore the sensitivity of geophysical observations to permafrost thaw. Simulations of sublacustrine talik formation over a 1000 year period modeled after conditions found in the Yukon Flats, Alaska, are evaluated. Synthetic geophysical data are analyzed with a Bayesian Markov chain Monte Carlo algorithm that provides a probabilistic assessment of geophysical model uncertainty and resolution. Major lithological and permafrost features are well resolved in the examples considered. The subtle geometry of partial ice-saturation beneath lakes during talik formation cannot be resolved using AEM data, but the gross characteristics of sub-lake resistivity models reflect bulk changes in ice content and can be used to determine the presence of a talik. A final example compares AEM and ground-based electromagnetic responses for their ability to resolve shallow permafrost and thaw features in the upper 1–2 m below ground.

Digital image processing of airborne geophysical data for uranium‐mineralized breccia pipes exploration in northwestern Arizona

Geophysics ◽  
1990 ◽  
Vol 55 (8) ◽  
pp. 965-976 ◽  
Author(s):  
A. Y. Kwarteng ◽  
P. S. Chavez
Keyword(s):  
Image Processing ◽  
Digital Image Processing ◽  
Digital Image ◽  
Apparent Resistivity ◽  
Low Frequency ◽  
Noise Removal ◽  
Geophysical Data ◽  
Data Sets ◽  
Overburden Thickness ◽  
Airborne Geophysical Data

Digital image processing and integration of data sets have been used to develop exploration models from airborne electromagnetics (EM), magnetics, and very‐low‐frequency electromagnetics (VLF-EM) data collected over an area in northwestern Arizona. The area has potential for the occurrence of uranium‐mineralized breccia pipes. Apparent resistivity and overburden thickness were derived from the EM measurements using half‐space models. Digital image processing techniques applied to the geophysical data sets included: (1) conversion of the data into gridded‐scale images, (2) spatial filtering for noise removal, (3) integration and analysis of the data sets, and (4) modeling using various parameter combinations. The general relationships between the geophysical variables/parameters and their ability to detect metallic deposits were used as guides in selecting digital number ranges that were used as input into various models. One of the best models incorporated apparent resistivity and total‐field magnetics; the results of this model outlined 13 anomalous combinations in the survey area. Field checking confirmed that two of the anomalies were previously known orebodies, and most of the other anomalies corresponded to suspected pipes that were under evaluation by the group that is exploring the property.

scholarly journals Testing alternative uses of electromagnetic data to reduce the prediction error of groundwater models

2016 ◽  
Vol 20 (5) ◽  
pp. 1925-1946 ◽  
Author(s):  
Nikolaj Kruse Christensen ◽  
Steen Christensen ◽  
Ty Paul A. Ferre
Keyword(s):  
Electrical Resistivity ◽  
Hydraulic Conductivity ◽  
Prediction Error ◽  
Model Calibration ◽  
Hydrologic Model ◽  
Geophysical Data ◽  
Model Parameters ◽  
Calibration Data ◽  
Groundwater Model ◽  
And Inversion

Abstract. In spite of geophysics being used increasingly, it is often unclear how and when the integration of geophysical data and models can best improve the construction and predictive capability of groundwater models. This paper uses a newly developed HYdrogeophysical TEst-Bench (HYTEB) that is a collection of geological, groundwater and geophysical modeling and inversion software to demonstrate alternative uses of electromagnetic (EM) data for groundwater modeling in a hydrogeological environment consisting of various types of glacial deposits with typical hydraulic conductivities and electrical resistivities covering impermeable bedrock with low resistivity (clay). The synthetic 3-D reference system is designed so that there is a perfect relationship between hydraulic conductivity and electrical resistivity. For this system it is investigated to what extent groundwater model calibration and, often more importantly, model predictions can be improved by including in the calibration process electrical resistivity estimates obtained from TEM data. In all calibration cases, the hydraulic conductivity field is highly parameterized and the estimation is stabilized by (in most cases) geophysics-based regularization. For the studied system and inversion approaches it is found that resistivities estimated by sequential hydrogeophysical inversion (SHI) or joint hydrogeophysical inversion (JHI) should be used with caution as estimators of hydraulic conductivity or as regularization means for subsequent hydrological inversion. The limited groundwater model improvement obtained by using the geophysical data probably mainly arises from the way these data are used here: the alternative inversion approaches propagate geophysical estimation errors into the hydrologic model parameters. It was expected that JHI would compensate for this, but the hydrologic data were apparently insufficient to secure such compensation. With respect to reducing model prediction error, it depends on the type of prediction whether it has value to include geophysics in a joint or sequential hydrogeophysical model calibration. It is found that all calibrated models are good predictors of hydraulic head. When the stress situation is changed from that of the hydrologic calibration data, then all models make biased predictions of head change. All calibrated models turn out to be very poor predictors of the pumping well's recharge area and groundwater age. The reason for this is that distributed recharge is parameterized as depending on estimated hydraulic conductivity of the upper model layer, which tends to be underestimated. Another important insight from our analysis is thus that either recharge should be parameterized and estimated in a different way, or other types of data should be added to better constrain the recharge estimates.

scholarly journals A Probabilistic Procedure for Anonymisation, for Assessing the Risk of Re-identification and for the Analysis of Perturbed Data Sets

2020 ◽  
Vol 36 (1) ◽  
pp. 89-115 ◽  
Author(s):  
Harvey Goldstein ◽  
Natalie Shlomo
Keyword(s):  
Random Noise ◽  
Secondary Analysis ◽  
New Method ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Data Set ◽  
Second Stage ◽  
True Model ◽  
Consistent Parameter

AbstractThe requirement to anonymise data sets that are to be released for secondary analysis should be balanced by the need to allow their analysis to provide efficient and consistent parameter estimates. The proposal in this article is to integrate the process of anonymisation and data analysis. The first stage uses the addition of random noise with known distributional properties to some or all variables in a released (already pseudonymised) data set, in which the values of some identifying and sensitive variables for data subjects of interest are also available to an external ‘attacker’ who wishes to identify those data subjects in order to interrogate their records in the data set. The second stage of the analysis consists of specifying the model of interest so that parameter estimation accounts for the added noise. Where the characteristics of the noise are made available to the analyst by the data provider, we propose a new method that allows a valid analysis. This is formally a measurement error model and we describe a Bayesian MCMC algorithm that recovers consistent estimates of the true model parameters. A new method for handling categorical data is presented. The article shows how an appropriate noise distribution can be determined.

scholarly journals Modelling to Engineering Data Using a New Class of Continuous Models

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
I. Elbatal ◽  
Naif Alotaibi
Keyword(s):  
Real Data ◽  
Exponential Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Class ◽  
Engineering Data ◽  
Continuous Models ◽  
Mathematical Characteristics

In this paper, a new flexible generator of continuous lifespan models referred to as the Topp-Leone Weibull G (TLWG) family is developed and studied. Several mathematical characteristics have been investigated. The new hazard rate of the new model can be “monotonically increasing,” “monotonically decreasing,” “bathtub,” and “J shape.” The Farlie Gumbel Morgenstern (FGM) and the modified FGM (MFGM) families and Clayton Copula (CCO) are used to describe and display simple type Copula. We discuss the estimation of the model parameters by the maximum likelihood (MLL) estimations. Simulations are carried out to show the consistency and efficiency of parameter estimates, and finally, real data sets are used to demonstrate the flexibility and potential usefulness of the proposed family of algorithms by using the TLW exponential model as example of the new suggested family.

On the Expected Errors in Calibration of the Beremin Cleavage Model Parameters

2007 ◽  
Author(s):  
D. W. Beardsmore ◽  
H. Teng ◽  
Michael Martin
Keyword(s):  
Calibration Method ◽  
Calibration Procedure ◽  
Standard Errors ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Finite Element Models ◽  
Data Sets ◽  
Mean Values ◽  
Fracture Tests ◽  
Low Constraint

We present the detailed results of a series of Monte Carlo simulations of the Gao and Dodds calibration procedure that was carried out to determine the likely size in the errors in the Beremin cleavage model parameter estimates that might be expected for fracture toughness data sets of various sizes. The calibration process was carried out a large number of times using different sample sizes, and mean values and standard errors in the parameter estimates were determined. Modified boundary layer finite element models were used to represent high and low constraint conditions (as in the fracture tests) as well as the SSY condition. The “experimental” Jc values were obtained numerically by random sampling of a Beremin distribution function with known values of the true parameters. A number of cautionary remarks in the application of the calibration method are made.

scholarly journals Computing and Using Inclusion Bayes Factors for Mixed Fixed and Random Effect Diffusion Decision Models

2021 ◽  
Author(s):  
Udo Boehm ◽  
Nathan J. Evans ◽  
Quentin Frederik Gronau ◽  
Dora Matzke ◽  
Eric-Jan Wagenmakers ◽  
...  
Keyword(s):  
Bayesian Model Averaging ◽  
Random Effect ◽  
Quantitative Description ◽  
Model Averaging ◽  
Cognitive Models ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Bayesian Hierarchical ◽  
Selective Influence

Cognitive models provide a substantively meaningful quantitative description of latent cognitive processes. The quantitative formulation of these models supports cumulative theory building and enables strong empirical tests. However, the non-linearity of these models and pervasive correlations among model parameters pose special challenges when applying cognitive models to data. Firstly, estimating cognitive models typically requires large hierarchical data sets that need to be accommodated by an appropriate statistical structure within the model. Secondly, statistical inference needs to appropriately account for model uncertainty to avoid overconfidence and biased parameter estimates. In the present work we show how these challenges can be addressed through a combination of Bayesian hierarchical modelling and Bayesian model averaging. To illustrate these techniques, we apply the popular diffusion decision model to data from a collaborative selective influence study.

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