A method of fast, sequential experimental design for linearized geophysical inverse problems
A method of fast, sequential experimental design for linearized geophysical inverse problems
复制标题
线性化地球物理反问题的快速顺序实验设计方法
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
F. Morgan
中科院分区：
文献类型：
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作者：
D. Coles;F. Morgan
总结
SUMMARY
An algorithm for linear(ized) experimental design is developed for a determinant-based design objective function. This objective function is common in design theory and is used to design experiments that minimize the model entropy, a measure of posterior model uncertainty. Of primary significance in design problems is computational expediency. Several earlier papers have focused attention on posing design objective functions and opted to use global search methods for finding the critical points of these functions, but these algorithms are too slow to be practical. The proposed technique is distinguished primarily for its computational efficiency, which derives partly from a greedy optimization approach, termed sequential design. Computational efficiency is further enhanced through formulae for updating determinants and matrix inverses without need for direct calculation. The design approach is orders of magnitude faster than a genetic algorithm applied to the same design problem. However, greedy optimization often trades global optimality for increased computational speed; the ramifications of this tradeoff are discussed. The design methodology is demonstrated on a simple, single-borehole DC electrical resistivity problem. Designed surveys are compared with random and standard surveys, both with and without prior information. All surveys were compared with respect to a ‘relative quality’ measure, the post-inversion model per cent rms error. The issue of design for inherently ill-posed inverse problems is considered and an approach for circumventing such problems is proposed. The design algorithm is also applied in an adaptive manner, with excellent results suggesting that smart, compact experiments can be designed in real time.