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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 inverse problem is to find resistivities of formation layers from a given logging curve (for details of this example refer to Sect. 9)
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Fig4: The inverse problem is to find resistivities of formation layers from a given logging curve (for details of this example refer to Sect. 9)

Mentions: The hierarchic genetic strategy (HGS) produces a tree-structured set of concurrent evolutionary processes (see Fig. 4). HGS was introduced in Schaefer and Kołodziej (2003). The structure of the tree changes dynamically and its depth is bounded by .Fig. 4


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 inverse problem is to find resistivities of formation layers from a given logging curve (for details of this example refer to Sect. 9)
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig4: The inverse problem is to find resistivities of formation layers from a given logging curve (for details of this example refer to Sect. 9)
Mentions: The hierarchic genetic strategy (HGS) produces a tree-structured set of concurrent evolutionary processes (see Fig. 4). HGS was introduced in Schaefer and Kołodziej (2003). The structure of the tree changes dynamically and its depth is bounded by .Fig. 4

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