A homotopy continuation inversion of geoelectrical sounding data

Ghanati, Reza; Müller‐Petke, Mike

doi:10.1016/j.jappgeo.2021.104356

Cited by 4 publications

(2 citation statements)

References 26 publications

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“…Lately, the homotopy method has also been extended for dealing with inverse problems. Many authors studied the homotopy solution of geophysical inverse problems [19][20][21]. Słota et al [22,23] and Hetmaniok et al [24] presented the applications of the homotopy method for solving inverse Stefan problems.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method

Liu

Ding

et al. 2023

Mathematics

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This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framework and the constraints such as well logs, which can restrain noise and improve the quality of inversion, are introduced. Then we propose the widely convergent homotopy method, which makes natural use of constraints and incorporates Tikhonov regularization. The effectiveness of the proposed approach is demonstrated on illustrative examples.

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Section: Introductionmentioning

confidence: 99%

Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method

Liu

Ding

et al. 2023

Mathematics

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“…This method is widely used to address a variety of near-surface exploration problems including hydrogeological (e.g., [12]; [13]; [14]) environmental, and geotechnical studies (e.g., [15]; [16]; [17]). In addition, the results of 1D inversion of electrical sounding may be used in constituting starting models or a priori information for 2D/3D interpretations [18].…”

Section: Introductionmentioning

confidence: 99%

Geoelectrical Method to Determine Andesite Rock Potential in Kepuh, Ciwandan District, Cilegon City

Arum¹,

Sulaksana²,

Yuningsih³

2022

Int. J. Adv. Sci. Eng. Inf. Technol.

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The Kepuh area has abundant andesite rock resources. These rocks can be used as building materials and for other infrastructure. Based on this, it is necessary to research the potential of andesite resources. The tools used for this research are a resistivity meter, meter, current and potential wires, electrodes, hammer, battery, a global positioning system (GPS), handy talky, laptop and software (IP2win). The research applies the geoelectric method, which measures rock resistivity values. This geoelectric investigation uses the Schlumberger array. The advantages of the Schlumberger array are that fewer electrodes need to be moved for each sounding, and the cable length for the potential electrodes is shorter. Schlumberger soundings generally have better resolution, greater probing depth, and less time-consuming field deployment. The data obtained from the measurements were processed using IP2win software by entering the magnitude of the current, the value of the potential difference, and the electrode. The results of geoelectrical interpretation, the rocks found in the research area are topsoil, tuff, and andesite lava. The resistivity value of the topsoil in the study area mostly varies from 26.3 -116 ohms -meters, tuff has resistivity values range of 18.8 -84.2 ohms -meters, and Andesite lava has a resistivity range of 128 -570 ohms -meters. The average thickness of topsoil is 1.4 meters, the average thickness of tuff is 25.9 meters, and the average thickness of andesite lava is 42.6 meters. Based on the average thickness, andesite rock can be the main commodity.

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Uncertainty quantification in electrical resistivity tomography inversion: hybridizing block-wise bootstrapping with geostatistics

Khabaz,

Ghanati,

Bérubé

2024

Geophysical Journal International

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Summary Electrical resistivity tomography inversion often encounters uncertainty stemming from two primary sources: epistemic uncertainty, arising from imperfect underlying physics and improper initial approximation of model parameters, and aleatory variability in observations due to measurement errors. Despite the widespread application of electrical resistivity tomography in imaging the resistivity distribution of subsurface structures for various hydro-geophysical and engineering purposes, the assessment of uncertainty is seldom addressed within the inverted resistivity tomograms. To explore the combined impact of epistemic and aleatory uncertainty on resistivity models, we initially perturb the observed data using non-parametric block-wise bootstrap resampling with an optimal choice of the block size, generating different realizations of the field data. Subsequently, a geostatistical method is applied to stochastically generate a set of initial models for each bootstrapped dataset from the previous step. Finally, we employ a globally convergent homotopic continuation method on each bootstrapped dataset and initial model realization to explore the posterior resistivity models. Uncertainty information about the inversion results is provided through posterior statistical analysis. Our algorithm’s simplicity enables easy integration with existing gradient-based inversion methods, requiring only minor modifications. We demonstrate the versatility of our approach through its application to various synthetic and real electrical resistivity tomography experiments. The results reveal that this approach for quantifying uncertainty is straightforward to implement and computationally efficient.

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A homotopy continuation inversion of geoelectrical sounding data

Cited by 4 publications

References 26 publications

Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method

Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method

Geoelectrical Method to Determine Andesite Rock Potential in Kepuh, Ciwandan District, Cilegon City

Uncertainty quantification in electrical resistivity tomography inversion: hybridizing block-wise bootstrapping with geostatistics

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