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众所周知,走时层析成象不能给出高质量的地下成象。其中有两个主要原因:(1)走时反演中的分辨率严格取决于记录窗口的完整性;(2)独立的走时方程数目通常少于未知参数个数。后一个原因导致不同的解完全满足相同的走时方程,从而使得正确解不能被区分,除非附加独立(约束)条件。然而,近期的研究表明,约束条件(即最优化过程中的附加边界条件)可能补偿不完整的数据组,而有约束的最优化是较完整的。如果利用层析矩阵的稀疏性,便可以导出有效的反演算法。例如,若一组走时方程由900个走时(30个震源和30个接收器)和10 000个未知延迟的象素组成,在一台IBM3090
It is well known that time-of-flight tomography can not give a high-quality underground image. There are two main reasons for this: (1) The resolution in travel-time inversion depends strictly on the integrity of the recording window; and (2) the number of independent travel-time equations is usually less than the number of unknown parameters. The latter reason leads to different solutions that completely satisfy the same travel time equation, so that the correct solutions can not be distinguished unless an independent (constrained) condition is attached. However, recent studies have shown that constraints (ie, additional boundary conditions in the optimization process) may compensate for incomplete data sets, while constrained optimization is more complete. If we take advantage of the sparseness of the chromatographic matrix, we can derive effective inversion algorithms. For example, if a set of travel-time equations consists of 900 traveltimes (30 sources and 30 receivers) and 10,000 unknown delayed pixels, an IBM 3090