Inversion of noisy data by probabilistic methodology
含噪声数据反演的概率描述

Based on Bayesian theory of parameter estimation,we present specific and detailed procedures to demonstrate how to invert noisy data in applied geophysics.The probabilistic methodology of inversion consists of evaluation of likelihood function and calculation of posterior probability.To obtain the likelihood function indicating the uncertainty of observed information,noisy data is firstly expressed by a set of data vectors instead of a single vector,and then transferred to probability density curve defined in model space through confidence value defined in data space.Because the artificial operations are avoided in data space when processing,the probability density functions of model parameters only reflect data noise;observed information and feasible solutions can be preserved as much as possible.At the second stage of Bayesian theory,in which prior information and likelihood function should be combined to get posterior distribution,we propose a method of probabilistic analysis using weighting matrix.This method can impose strong restriction on non-uniqueness of inversion due to noises,since geological information is imported into model space directly.The entire process of probabilistic methodology is exemplified and explained by inversion of magnetotelluric sounding.