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虽然最小平方反演是数据分析常用的工具,而非单性问题是不可避免的问题;不过,这个问题通过考查模型响应对参数估算的灵度敏可以进行分析,这种灵敏度分方法还可产生只满足某些分解(或稳定度)准则的极值解。产生这种解的两种非常相似的的方法为“边界弯曲(Edgehog)”法和“最大平方法”,这两种方法是Jackson(1973、1976)提出来的。最小平方反演测定“非单值性度”的这些方法只需要奇异值分解(SVD)解中计算的数据。“边界弯曲”和“最大平方”方法在数学上是相似的,“最大平方”估算在计算上比较简单。这两方法都说明,一种反演的可靠性取决于特殊的误差准则以及与最小平方解有关的雅科毕(Jacobian)矩阵的特征等两个方面。两种相似方法的相似性由合成和实际垂直地震剖面(VSP)的旅行时间反演得到了证明。反演问题的灵敏度分析还提供了解的可靠性的定量测量值。
Although least squares inversion is a commonly used tool for data analysis, non-singularity is an inevitable problem; however, this problem can be analyzed by examining the sensitivity of the model to the parameter estimates, which can also be generated Extremal solutions that satisfy only some decomposition (or stability) criteria. The two very similar methods that produce this solution are the “Edgehog” method and the “Maximal Method”, both of which were proposed by Jackson (1973, 1976). These methods of least squares inversion to measure “non-monotonicity” require only the data calculated in the singular value decomposition (SVD) solution. The methods of “Boundary Bending” and “Least Squares” are mathematically similar, and the “largest square” estimation is computationally simpler. Both of these methods show that the reliability of an inversion depends on both the special error criterion and the characteristics of the Jacobian matrix associated with the least square solution. The similarity of the two similar methods is evidenced by the travel times of the composite and actual vertical seismic profiles (VSPs). Sensitivity analysis of the inversion problem also provides quantitative measures of the reliability of the solution.