A Two-Level Preconditioned Conjugate-Gradient Method in Distorted and Structured Grids

2012 ◽  
Vol 4 (2) ◽  
pp. 238-249
Author(s):  
Qiaolin He
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Experiments ◽  
Preconditioned Conjugate Gradient ◽  
Structured Grids ◽  
Structured Grid ◽  
Cpu Time ◽  
Linear Correction ◽  
Quadratic Element

AbstractIn this paper, we propose a new two-level preconditioned C-G method which uses the quadratic smoothing and the linear correction in distorted but topo-logically structured grid. The CPU time of this method is less than that of the multigrid preconditioned C-G method (MGCG) using the quadratic element, but their accuracy is almost the same. Numerical experiments and eigenvalue analysis are given and the results show that the proposed two-level preconditioned method is efficient.

Magnetization vector imaging for borehole magnetic data based on magnitude magnetic anomaly

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. D429-D444 ◽  
Author(s):  
Shuang Liu ◽  
Xiangyun Hu ◽  
Tianyou Liu ◽  
Jie Feng ◽  
Wenli Gao ◽  
...  
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Magnetization Vector ◽  
Real Data ◽  
Magnetic Anomalies ◽  
Magnetic Data ◽  
Preconditioned Conjugate Gradient ◽  
Magnetization Direction ◽  
Magnetization Intensity

Remanent magnetization and self-demagnetization change the magnitude and direction of the magnetization vector, which complicates the interpretation of magnetic data. To deal with this problem, we evaluated a method for inverting the distributions of 2D magnetization vector or effective susceptibility using 3C borehole magnetic data. The basis for this method is the fact that 2D magnitude magnetic anomalies are not sensitive to the magnetization direction. We calculated magnitude anomalies from the measured borehole magnetic data in a spatial domain. The vector distributions of magnetization were inverted methodically in two steps. The distributions of magnetization magnitude were initially solved based on magnitude magnetic anomalies using the preconditioned conjugate gradient method. The preconditioner determined by the distances between the cells and the borehole observation points greatly improved the quality of the magnetization magnitude imaging. With the calculated magnetization magnitude, the distributions of magnetization direction were computed by fitting the component anomalies secondly using the conjugate gradient method. The two-step approach made full use of the amplitude and phase anomalies of the borehole magnetic data. We studied the influence of remanence and demagnetization based on the recovered magnetization intensity and direction distributions. Finally, we tested our method using synthetic and real data from scenarios that involved high susceptibility and complicated remanence, and all tests returned favorable results.

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