Multiple linear system techniques for 3D finite element method modeling of direct current resistivity

Chang-wei, LI; Xiong, Bin; Ji, Qiang; Yu-zeng, LU

doi:10.1007/s11771-012-1021-6

Cited by 11 publications

(4 citation statements)

References 19 publications

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“…Multiple constraints, such as the prior model constraint, model smoothness constraint, and regularization constraint, are needed for the inversion process to increase the accuracy of the inversion due to the unique properties of landslides under rainfall conditions. The inversion process utilizes the inexact Gauss-Newton method [38] to determine the search direction, the Wolfe criterion [38] to determine the iteration step, and the Jacobian-free Krylov solution technique [39] to avoid the direct calculation of large, dense Jacobian matrices, all of which improve inversion efficiency. effects of the proposed framework on computed FOS under various arrays, apparent resistivity noise, and WECC uncertainty were investigated to verify the proposed framework's performance and reliability.…”

Section: Methodsmentioning

confidence: 99%

“…where SD(d obs ) denotes the observed data's standard deviation and ε denotes the smallest possible data value to keep the denominator term from converging to zero, usually 0.0125. Model weights W can place smooth constraints on the inversion process and ensure the inversion model's spatial continuity [39].…”

Section: Inexact Gauss-newton Inversion Algorithm Based On Multiple C...mentioning

confidence: 99%

“…In this paper, the Jacobianfree Krylov technique is used to avoid the storage and solution of the Jacobian matrix by calculating the product of the Jacobian matrix and a certain vector x. The specific calculation procedure is referred to in Li et al [39].…”

Section: Inexact Gauss-newton Inversion Algorithm Based On Multiple C...mentioning

confidence: 99%

“…This approach uses the Jacobian-free Krylov technique to compute the Jacobian matrix and a specific vector's product, and then calculates the g with more accuracy to make sure the solution direction is accurate. After that, within a finite number of iterations, we calculate the ∆m using the preconditioned conjugate gradient method [38,39]. Once the inexact ∆m is obtained, the model can be updated iteratively using the following equation:…”

Section: Inexact Gauss-newton Inversion Algorithm Based On Multiple C...mentioning

confidence: 99%

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Using Electrical Resistivity Tomography to Monitor the Evolution of Landslides’ Safety Factors under Rainfall: A Feasibility Study Based on Numerical Simulation

Bai

Zhu

et al. 2022

Remote Sensing

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Although electrical resistivity tomography (ERT) may gather the internal resistivity information from a landslide area in a large-scale, low-cost, and non-invasive manner compared to point-based sensor monitoring technology, the indirect resistivity information obtained cannot directly evaluate the landslide’s current mechanical status, such as stress, strength, etc. Based on ERT monitoring data, a framework for quantitatively and directly evaluating the evolution of the factor of safety (FOS) of landslides during rainfall is proposed. The framework first inverts ERT observation data using the inexact Gauss–Newton method based on multiple constraints to obtain a more realistic resistivity distribution, then calculates the saturation distribution using Archie’s equation, and finally calculates the FOS of landslides using the finite element strength reduction method. Twelve sets of numerical experiments were designed and carried out based on the synthetic data of a theoretical model. The experimental results show that the proposed framework is valid and reliable under various arrays, apparent resistivity noise, and uncertainty in the water-electric correlation curve, with the Dipole-Dipole array outperforming the others in terms of accuracy, sensitivity, and anti-noise capability. The proposed framework is significant in improving ERT monitoring and early warning capabilities for rainfall-induced landslides.

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Section: Methodsmentioning

confidence: 99%

Section: Inexact Gauss-newton Inversion Algorithm Based On Multiple C...mentioning

confidence: 99%

Section: Inexact Gauss-newton Inversion Algorithm Based On Multiple C...mentioning

confidence: 99%

Section: Inexact Gauss-newton Inversion Algorithm Based On Multiple C...mentioning

confidence: 99%

See 2 more Smart Citations

Using Electrical Resistivity Tomography to Monitor the Evolution of Landslides’ Safety Factors under Rainfall: A Feasibility Study Based on Numerical Simulation

Bai

Zhu

et al. 2022

Remote Sensing

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Inversion of IP Logging with Improved Krylov Subspace Methods

Li¹,

Xiong²,

Wang³

et al. 2012

Chinese J of Geophysics

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Induced polarization logging is widely used in deep mineral exploration. The data interpretation requires fast and reliable forward and inversion solutions. We have developed an efficient inversion framework in this paper. The forward problem was solved using a finite element approximation with a recycling Krylov subspace algorithm for the multiple linear systems. Considering the model complexity in 3D modeling of logging, mixed meshes were employed to model borehole geometries. The inverse implementation is based on the GaussNewton and Jacobian-free Krylov techniques. We used a coarse mesh for inversion to reduce the ill-posedness. The formulae for Jacobian-vector and Jacobian-transport-vector products were deduced to avoid the storage of derivative matrices. Model updates were calculated efficiently by an inexact preconditioned conjugate gradient algorithm.

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Joint Inversion of DC Resistivity and Magnetic Data, Constrained by Cross Gradients, Compactness and Depth Weighting

Varfinezhad

Oskooi

Fedi

2020

Pure Appl. Geophys.

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Multiple linear system techniques for 3D finite element method modeling of direct current resistivity

Cited by 11 publications

References 19 publications

Using Electrical Resistivity Tomography to Monitor the Evolution of Landslides’ Safety Factors under Rainfall: A Feasibility Study Based on Numerical Simulation

Using Electrical Resistivity Tomography to Monitor the Evolution of Landslides’ Safety Factors under Rainfall: A Feasibility Study Based on Numerical Simulation

Inversion of IP Logging with Improved Krylov Subspace Methods

Joint Inversion of DC Resistivity and Magnetic Data, Constrained by Cross Gradients, Compactness and Depth Weighting

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