Parallel computation of optimized arrays for 2-D electrical imaging surveys

• Published in: Geophysical journal international Vol. 183; no. 3; pp. 1302 - 1315
• Main Authors: Loke, M. H., Wilkinson, P. B., Chambers, J. E.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.12.2010
• Subjects: Algorithms; Arrays; Computer simulation; Electrical properties; Imaging; Inverse theory; Mathematical analysis; Mathematical models; Multiplication; Numerical approximations and analysis; Surveys; Tomography
• ISSN: 0956-540X; 1365-246X; 1365-246X
• DOI: 10.1111/j.1365-246X.2010.04796.x

Modern automatic multi-electrode survey instruments have made it possible to use non-traditional arrays to maximize the subsurface resolution from electrical imaging surveys. Previous studies have shown that one of the best methods for generating optimized arrays is to select the set of array configurations that maximizes the model resolution for a homogeneous earth model. The Sherman–Morrison Rank-1 update is used to calculate the change in the model resolution when a new array is added to a selected set of array configurations. This method had the disadvantage that it required several hours of computer time even for short 2-D survey lines. The algorithm was modified to calculate the change in the model resolution rather than the entire resolution matrix. This reduces the computer time and memory required as well as the computational round-off errors. The matrix–vector multiplications for a single add-on array were replaced with matrix–matrix multiplications for 28 add-on arrays to further reduce the computer time. The temporary variables were stored in the double-precision Single Instruction Multiple Data (SIMD) registers within the CPU to minimize computer memory access. A further reduction in the computer time is achieved by using the computer graphics card Graphics Processor Unit (GPU) as a highly parallel mathematical coprocessor. This makes it possible to carry out the calculations for 512 add-on arrays in parallel using the GPU. The changes reduce the computer time by more than two orders of magnitude. The algorithm used to generate an optimized data set adds a specified number of new array configurations after each iteration to the existing set. The resolution of the optimized data set can be increased by adding a smaller number of new array configurations after each iteration. Although this increases the computer time required to generate an optimized data set with the same number of data points, the new fast numerical routines has made this practical on commonly available microcomputers.