Monitoring leaks from storage ponds using resistivity methods

Van, Gregory P.; Park, Stephen K.; Hamilton, P. J.

doi:10.1190/1.1443147

Cited by 42 publications

(21 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A common guideline is to decrease the temperature sufficiently slowly so that the importance sampling gently diffuses and concentrates around the maximum of the posterior probability [Van Laarhoven and Aarts, 1987]. Another important issue of simulated annealing is to define the model-generation process equation (14) in order to properly sample the a priori space of models.…”

Section: Simulated Annealingmentioning

confidence: 99%

“…Also, simulated annealing is a flexible method which allows a free choice of the misfit function and an easy account of a priori information concerning the conductivity distribution to reconstruct [Kirkpatrick et al, 1983;Cerny, 1985;Van Laarhoven and Aarts, 1987;Tarantola, 1987]. The basic principle of simulated annealing is to iteratively modify the model until it converges toward the minimum of the misfit function to be minimized.…”

Section: Simulated Annealingmentioning

confidence: 99%

“…This approach increases the nonlinear nature of the inverse problem since, in practice, we are faced with an inverse problem whose number of parameters increases as the iterative inversion proceeds. However, the computational power now available with desktop computers enables the use of a fully nonlinear approach, namely simulated annealing [Kirkpatrick et al, 1983;Van Laarhoven and Aarts, 1987]. This Monte Carlo method is well-suited to tackle the nonlinear nature of the inverse problem by providing possibilities to escape from local minima of the misfit function corresponding to nonoptimal solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Modern multielectrode data collection systems provide measurements with dense coverage [Asch and Morrison, 1989], and electrical impedance tomography is now currently used in hydrology [Bevc and Morrison, 1991;Daily et al, 1992;Park, 1998;Hagrey and Michaelsen, 1999;Nowroozi et al, 1999], environmental remediation [Van et al, 1991;Spies and Ellis, 1995;Daily and Ramirez, 2000], and spill monitoring [Ramirez et al, 1993]. Electrical impedance tomography is generally formulated as an inverse problem which aims at reconstructing the (possibly complex) electrical conductivity (or resistivity) distribution underground from electrical potential measurements made at the boundaries of the region to be imaged (see, for instance, Ward [1990] for a review).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multiscale electrical impedance tomography

Pessel

Gibert

2003

J. Geophys. Res.

View full text Add to dashboard Cite

[1] Electrical impedance tomography aims to recover the electrical conductivity underground from surface and/or borehole apparent resistivity measurements. This is a highly nonlinear inverse problem, and linearized inverse methods are likely to produce solutions corresponding to local minima of the misfit function to minimize. In the present paper, electrical impedance tomography is addressed through a nonlinear approach, namely, simulated annealing, in order to escape from local minima and to produce conductivity distributions independent of the starting models. Simulated annealing belongs to the Monte Carlo family which needs numerous forward modelings, and particular attention is paid both to the forward numerical solution of the Poisson equation and to the parameterization of the inverse problem, i.e., the way the conductivity distribution is mathematically represented. The 2.5-dimensional forward problem is solved through a multigrid approach which iteratively solves the Poisson equation from large to small scales. In the same spirit, the conductivity model is parameterized in a multiscale way by representing the conductivity distribution with a superimposition of block whose sizes (in suitable units) are integer powers of 2. The multiscale inversion is implemented in a sequential way by first inverting for the conductivity of the coarser blocks and by progressively incorporating finer blocks in the conductivity model. A decision stage based on a sensitivity analysis is performed before incorporating finer blocks in order to optimize the parameterization by not adding unnecessary details into the conductivity model. Both a synthetic example and a field experiment are used to explain the method, and comparisons with a linearized inversion technique are done.

show abstract

Section: Simulated Annealingmentioning

confidence: 99%

Section: Simulated Annealingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multiscale electrical impedance tomography

Pessel

Gibert

2003

J. Geophys. Res.

View full text Add to dashboard Cite

show abstract

“…At the Mojave Generating Station in Laughlin, Nevada, a resistivity monitoring system was installed beneath and around one of the evaporation ponds operated by Southern California Edison Van et al, 1991). This system uses an 8 x 8 grid of electrodes, with an approximate spacing of 90 m between electrodes.…”

Section: Analysis Of Field Datamentioning

confidence: 99%

3‐D resistivity forward modeling and inversion using conjugate gradients

Zhang¹,

Mackie²,

Madden³

1994

SEG Technical Program Expanded Abstracts 1994

View full text Add to dashboard Cite

We have developed rapid 3-D do resistivity forward modeling and inversion algorithms that use conjugate gradient relaxation techniques. In the forward network modeling calculation, an incomplete Cholesky decomposition for preconditioning and sparse matrix routines combine to produce a fast and efficient algorithm (approximately 2 minutes CPU time on a Sun SPARCstation 2 for 50 x 50 x 20 blocks). The side and bottom boundary conditions are scaled impedance conditions that take into account the local current flow at the boundaries as a result of any configuration of current sources.For the inversion, conjugate gradient relaxation is used to solve the maximum likelihood inverse equations. Since conjugate gradient techniques only require the results of the sensitivity matrix A or its transpose A T multiplying a vector, we are able to bypass the actual computation of the sensitivity matrix and the inversion of ATA, thus greatly decreasing the time needed to do 3-D inversions.We demonstrate 3-D resistivity tomographic imaging using pole-pole resistivity data collected during an experiment for a leakage monitoring system near evaporation ponds at the Mojave Generating Station in Laughlin, Nevada.

show abstract

Two‐dimensional and three‐dimensional resistivity imaging in archaeological site investigation

Papadopoulos

Τσούρλος

Τσοκασ

et al. 2006

Archaeological Prospection

136

View full text Add to dashboard Cite

In this work, the application and the effectiveness of two-and three-dimensional non-linear inversion algorithms in processing and interpretation of electrical resistivity tomography (ERT) data collected from archaeological areas are investigated in the framework of a new field technique for gathering three-dimensional pole^pole tomographic data in a relatively small amount of time using standard archaeological prospection equipment. The inversion routine, for both the two-dimensional and the three-dimensional case, is based on a smoothness constrained algorithm and the forward modelling calculations are carried out using two-dimensional and three-dimensional finite element solvers respectively.Resultsofcombined two-dimensionalinversions (quasi-three-dimensional) are compared with the fullthree-dimensionalinversions.Comparisonsare carried out inrelationto the optimum survey direction of gathering the tomographic data using the pole^pole array for synthetic data arising from three-dimensional structures commonly encountered in archaeological sites.The response of the algorithms in the presence of noisy data was also tested. The algorithms were also used in the processing of real data collected from the archaeological sites of Sikyon and Europosin Greece.The results from the synthetic and therealdata indicate the superiorityofthe three-dimensionalinversion algorithms in processing tomographic data. The reconstructed three-dimensional images do not suffer from the artefacts encountered in the quasi-three-dimensional approach, owing to the three-dimensional nature of the archaeological features. Most importantly, both synthetic and real data results indicate that a single survey direction is adequate to produce a valid three-dimensional subsurface image when full three-dimensional inversion is used in contrast to the quasi-threedimensional approach, which would require that two survey directions be used to obtain satisfactory results

show abstract

Monitoring leaks from storage ponds using resistivity methods

Cited by 42 publications

References 0 publications

Multiscale electrical impedance tomography

Multiscale electrical impedance tomography

3‐D resistivity forward modeling and inversion using conjugate gradients

Two‐dimensional and three‐dimensional resistivity imaging in archaeological site investigation

Contact Info

Product

Resources

About