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A hybrid method for inversion of 3D DC resistivity logging measurements.

Gajda-Zagórska E, Schaefer R, Smołka M, Paszyński M, Pardo D - Nat Comput (2015)

Bottom Line: The computational cost of misfit evaluation by hp-FEM depends strongly on the assumed accuracy.Moreover, tree structure of demes as well as branch reduction and conditional sprouting mechanism reduces the number of expensive local searches up to the number of minima to be recognized.The common (direct and inverse) accuracy control, crucial for the hp-HGS efficiency, has been motivated by precise mathematical considerations.

View Article: PubMed Central - PubMed

Affiliation: AGH University of Science and Technology, Krakow, Poland.

ABSTRACT

This paper focuses on the application of hp hierarchic genetic strategy (hp-HGS) for solution of a challenging problem, the inversion of 3D direct current (DC) resistivity logging measurements. The problem under consideration has been formulated as the global optimization one, for which the objective function (misfit between computed and reference data) exhibits multiple minima. In this paper, we consider the extension of the hp-HGS strategy, namely we couple the hp-HGS algorithm with a gradient based optimization method for a local search. Forward simulations are performed with a self-adaptive hp finite element method, hp-FEM. The computational cost of misfit evaluation by hp-FEM depends strongly on the assumed accuracy. This accuracy is adapted to the tree of populations generated by the hp-HGS algorithm, which makes the global phase significantly cheaper. Moreover, tree structure of demes as well as branch reduction and conditional sprouting mechanism reduces the number of expensive local searches up to the number of minima to be recognized. The common (direct and inverse) accuracy control, crucial for the hp-HGS efficiency, has been motivated by precise mathematical considerations. Numerical results demonstrate the suitability of the proposed method for the inversion of 3D DC resistivity logging measurements.

No MeSH data available.


Related in: MedlinePlus

The computation of the sample logging curve consists of solving a sequel of multiple forward problems (28) over a domain composed of a borehole and five formation layers with assumed conductivities. This set of layers will be utilized in the experimental section
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Fig2: The computation of the sample logging curve consists of solving a sequel of multiple forward problems (28) over a domain composed of a borehole and five formation layers with assumed conductivities. This set of layers will be utilized in the experimental section

Mentions: The vector being the ordered collection of values of the indicator functionals obtained for the consecutive positions of the probe, will be called a logging curve. Its coordinates might be expressed by the dual solution or by both primal and dual solutions (see (32)). In other words, computing the logging curve will consist of solving a sequel of forward dual problems (28) respecting the assumed resistivities (see e.g. Fig. 2).Fig. 2


A hybrid method for inversion of 3D DC resistivity logging measurements.

Gajda-Zagórska E, Schaefer R, Smołka M, Paszyński M, Pardo D - Nat Comput (2015)

The computation of the sample logging curve consists of solving a sequel of multiple forward problems (28) over a domain composed of a borehole and five formation layers with assumed conductivities. This set of layers will be utilized in the experimental section
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4541716&req=5

Fig2: The computation of the sample logging curve consists of solving a sequel of multiple forward problems (28) over a domain composed of a borehole and five formation layers with assumed conductivities. This set of layers will be utilized in the experimental section
Mentions: The vector being the ordered collection of values of the indicator functionals obtained for the consecutive positions of the probe, will be called a logging curve. Its coordinates might be expressed by the dual solution or by both primal and dual solutions (see (32)). In other words, computing the logging curve will consist of solving a sequel of forward dual problems (28) respecting the assumed resistivities (see e.g. Fig. 2).Fig. 2

Bottom Line: The computational cost of misfit evaluation by hp-FEM depends strongly on the assumed accuracy.Moreover, tree structure of demes as well as branch reduction and conditional sprouting mechanism reduces the number of expensive local searches up to the number of minima to be recognized.The common (direct and inverse) accuracy control, crucial for the hp-HGS efficiency, has been motivated by precise mathematical considerations.

View Article: PubMed Central - PubMed

Affiliation: AGH University of Science and Technology, Krakow, Poland.

ABSTRACT

This paper focuses on the application of hp hierarchic genetic strategy (hp-HGS) for solution of a challenging problem, the inversion of 3D direct current (DC) resistivity logging measurements. The problem under consideration has been formulated as the global optimization one, for which the objective function (misfit between computed and reference data) exhibits multiple minima. In this paper, we consider the extension of the hp-HGS strategy, namely we couple the hp-HGS algorithm with a gradient based optimization method for a local search. Forward simulations are performed with a self-adaptive hp finite element method, hp-FEM. The computational cost of misfit evaluation by hp-FEM depends strongly on the assumed accuracy. This accuracy is adapted to the tree of populations generated by the hp-HGS algorithm, which makes the global phase significantly cheaper. Moreover, tree structure of demes as well as branch reduction and conditional sprouting mechanism reduces the number of expensive local searches up to the number of minima to be recognized. The common (direct and inverse) accuracy control, crucial for the hp-HGS efficiency, has been motivated by precise mathematical considerations. Numerical results demonstrate the suitability of the proposed method for the inversion of 3D DC resistivity logging measurements.

No MeSH data available.


Related in: MedlinePlus