A 3-D finite-element algorithm for DC resistivity modelling using the shifted incomplete Cholesky conjugate gradient method

Wu, Xiaoping

doi:10.1046/j.1365-246x.2003.02018.x

Cited by 34 publications

(20 citation statements)

References 30 publications

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“…The iterative conjugate gradient algorithm (CG, Hestenes and Stiefel 1952) is widely used within the geophysical community (Wu 2003;Brodie and Sambridge 2006;Rücker et al 2006;Mueller-Petke and Yaramanci 2010), however, we employ the preconditioned bi-conjugate gradient stabilized algorithm (BICGSTAB, Van der Vorst 1992). Theoretically, CG should be the most suitable algorithm as our linear system is symmetric positive definite but we chose BICGSTAB due to its empirically proven stability in solving our particular problem.…”

Section: Sparse Matrices and Solversmentioning

confidence: 99%

A parallel, scalable and memory efficient inversion code for very large‐scale airborne electromagnetics surveys

Kirkegaard

Auken

2014

Geophysical Prospecting

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Over the past decade the typical size of airborne electromagnetic data sets has been growing rapidly, along with an emerging need for highly accurate modelling. One‐dimensional approximate inversions or data transform techniques have previously been employed for very large‐scale studies of quasi‐layered settings but these techniques fail to provide the consistent accuracy needed by many modern applications such as aquifer and geological mapping, uranium exploration, oil sands and integrated modelling. In these cases the use of more time‐consuming 1D forward and inverse modelling provide the only acceptable solution that is also computationally feasible. When target structures are known to be quasi layered and spatially coherent it is beneficial to incorporate this assumption directly into the inversion. This implies inverting multiple soundings at a time in larger constrained problems, which allows for resolving geological layers that are undetectable using simple independent inversions. Ideally, entire surveys should be inverted at a time in huge constrained problems but poor scaling properties of the underlying algorithms typically make this challenging. Here, we document how we optimized an inversion code for very large‐scale constrained airborne electromagnetic problems. Most importantly, we describe how we solve linear systems using an iterative method that scales linearly with the size of the data set in terms of both solution time and memory consumption. We also describe how we parallelized the core region of the code, in order to obtain almost ideal strong parallel scaling on current 4‐socket shared memory computers. We further show how model parameter uncertainty estimates can be efficiently obtained in linear time and we demonstrate the capabilities of the full implementation by inverting a 3327 line km SkyTEM survey overnight. Performance and scaling properties are discussed based on the timings of the field example and we describe the criteria that must be fulfilled in order to adapt our methodology for similar type problems.

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Section: Sparse Matrices and Solversmentioning

confidence: 99%

A parallel, scalable and memory efficient inversion code for very large‐scale airborne electromagnetics surveys

Kirkegaard

Auken

2014

Geophysical Prospecting

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“…With the development of computers, there have been studies that attempt to calculate the electrical conductivity of two-phase or multi-phase rocks with numerical simulation methods (Bigalke, 1999;2000;2003;Yue et al, 2005;Lebovka et al, 2006;Hakobyan et al, 2007). The 3-D finite element method (FEM) can be used for the numerical simulation of arbitrary complex multi-phase media (Garboczi, 1998;Wu, 2003;Wu and Wang, 2003).…”

Section: Developed a Modifiedmentioning

confidence: 99%

“…The 3-D finite element method (FEM) can be used for the numerical simulation of arbitrary complex multi-phase media (Garboczi, 1998;Wu, 2003;Wu and Wang, 2003). Rock physics experiments cannot be quantitatively controlled by setting arbitrary electrical conductivity and volume fraction of multi-phase rocks (i.e., digital rock cores).…”

Section: Developed a Modifiedmentioning

confidence: 99%

“…The periodic boundary condition means that if a neighbor is outside the model, it is periodically continued on the opposite side of the model. The voltage distribution in the 3-D digital model is determined using the fi nite element method (Garboczi , 1998;Wu, 2003;Liu et al, 2009). The effective conductivity of the multiphase rock is defi ned by a current density average over the entire model as (Garboczi, 1998) ,…”

Section: The Stochastic Model and Its Effective Conductivity Calculatmentioning

confidence: 99%

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Study of the generalized mixture rule for determining effective conductivity of two-phase stochastic models

2010

Appl. Geophys.

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The generalized mixture rule (GMR) is usually applied in determining mechanical properties such as the rheological property and Young's modulus of multi-phase rocks. However, it is rarely used to determine electrical conductivity of multi-phase rocks presently. In this paper, we calculate the effective conductivity using the 3D finite element method for a large number of two-phase medium stochastic models. The GMR is then employed as an effective conductivity model to fi t the data. It shows a very close relationship between the parameter J of GMR and the ratio of conductivities of the two phases. We obtain the equations of the parameter J with the ratio of conductivity of two phases for the fi rst time. On this basis, we can quickly predict (or calculate) the effective conductivity of any twophase medium stochastic model. The result is much more accurate than two other available effective conductivity models for the stochastic medium, which are the random model and effective medium theory model, laying a solid base for detailed evaluation of oil reservoirs.

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“…Comparison of singularity-removal method(Wu, 2003) and our adaptive finite-element method. (a) Apparent resistivities from the final adaptive iteration (third mesh); (b) relative errors on the first mesh; (c) relative errors on the third mesh…”

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confidence: 99%

Object-oriented implementation of 3D DC adaptive finite-element method

Ren

Tang

Fei-yan

et al. 2009

Front. Earth Sci. China

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In this paper, we introduced a clear objectoriented framework to implement the complicated adaptive procedure with C ++ programming language. In this framework, it consisted of the unstructured mesh generation, a-posterior error estimating, adaptive strategy, and the postprocessing. Unlike the procedure-oriented framework, which is commonly used in DC resistivity modeling with FORTRAN language, the object-oriented one, which is famous for its characteristic of encapsulation, could be used for a class of problems that would be executed by only making some changes on the user interface. To validate its flexibility, two synthetic DC examples were tested here.

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A 3-D finite-element algorithm for DC resistivity modelling using the shifted incomplete Cholesky conjugate gradient method

Cited by 34 publications

References 30 publications

A parallel, scalable and memory efficient inversion code for very large‐scale airborne electromagnetics surveys

A parallel, scalable and memory efficient inversion code for very large‐scale airborne electromagnetics surveys

Study of the generalized mixture rule for determining effective conductivity of two-phase stochastic models

Object-oriented implementation of 3D DC adaptive finite-element method

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