地球物理反问题中的随机反演理论

STOCHASTIC INVERSION THEORY IN GEOPHYSICAL INVERSE PROBLEM

本文从最大后验概率密度观点出发，在数据噪音向量和待求模型向量为具有零均值的独立高斯随机过程的假设前提下，建立起了随机反演的非线性系统方程；给出了模型方差估计的函数表达式，并在文章最后，证明了反演解的稀疏性，即解释了随机反演的输出解的高分辨率特征。文章在最小二乘反演方法的基础上，发展并完善了随机反演方法的理论基础；揭示了随机反演方法与最小二乘反演方法之间的本质区别；阐述了随机反演方法的优越性，并指出了其广阔的应用前景。

Starting from the view point of a maximum posterior probability density and under the assumption that data noise vector and model vetcor to be estimated are all independent Gaussian random processes with zero average values, this paper establishes the nonlinear systematic equation of stochastic inversion, puts forward the functional expressions of model variance estimates, and finally, has proved the sparse nature of solutions inverted by stochastic inversion to explain their high resolution properties. On the basis of the least squares inversion method, the paper expands and perfects the theoretical basis of the stochastic inversion method, reveals the essential differences between the stochastic inversion method and least squares inversion method, expounds the advantages of the stochastic inversion method and indicates its broad prospects for application.