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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 logging curves corresponding to points found after binary global search phase. The bold gray curve corresponds to the exact logging curve
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Fig5: The logging curves corresponding to points found after binary global search phase. The bold gray curve corresponds to the exact logging curve

Mentions: The results of the global binary search phase (six obtained points) are presented in Table 2. For testing purposes, we have executed the self-adaptive goal-oriented –FEM algorithm on these points, in order to generate and plot the resulting logging curves. The curves corresponding to the found six points are presented in Fig. 5. The curves have also been compared to the exact logging curve, denoted by bold light gray color. The best fitted Point 2 is the most similar point to the exact logging curve, as expected. The six points obtained after the global binary phase are also depicted in Fig. 6 by six diamonds. The figure does not present the values of since they are all approximately equal to .Fig. 5


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 logging curves corresponding to points found after binary global search phase. The bold gray curve corresponds to the exact logging curve
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig5: The logging curves corresponding to points found after binary global search phase. The bold gray curve corresponds to the exact logging curve
Mentions: The results of the global binary search phase (six obtained points) are presented in Table 2. For testing purposes, we have executed the self-adaptive goal-oriented –FEM algorithm on these points, in order to generate and plot the resulting logging curves. The curves corresponding to the found six points are presented in Fig. 5. The curves have also been compared to the exact logging curve, denoted by bold light gray color. The best fitted Point 2 is the most similar point to the exact logging curve, as expected. The six points obtained after the global binary phase are also depicted in Fig. 6 by six diamonds. The figure does not present the values of since they are all approximately equal to .Fig. 5

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