Study Of Transient Electromagnetic Probabilistic Inversion And Uncertainty Evaluation Based On Bayesian Probability Framework

Transient Electromagnetic(TEM)method has been widely used in engineering investigation,seawater intrusion investigation,metal ore and groundwater exploration,geological survey and other fields.In order to obtain intuitive and accurate electrical distribution of underground media,geophysicists have summarized a variety of data interpretation methods.In the early stage,they mostly relied on qualitative judgment,measurement plate and apparent resistivity imaging methods to obtain general geoelectric distribution.Later,they used inversion methods to interprate transient electromagnetic data and recover underground electrical distribution.The nonlinear characteristics of geophysical inversion determine that the inversion solution is non-unique.One of the key problems to solve the geophysical inverse problem is the quantification of non-uniqueness.That is,how the parameters of the predicted earth model changed when fitting a group of observation data.At present,there are two mainstream inversion viewpoints:deterministic inversion and probabilistic inversion.Deterministic inversion regards the inversion parameters as the determined values,and solves the "single optimal model" by the minimum objective function and the optimization criterion.But deterministic inversion cannot provide the results' reliability and parameters uncertainty,and it is easy to be caught in the local optimum when solving the inversion equation.Probability inversion takes the inversion parameters as random variables,and obtains reasonable posterior probability distribution through prior distribution,likelihood function and various sampling strategies.It can comprehensively consider the real underground electrical structure and the distribution range of resistivity,and then analyze the uncertainty of model parameters.The "single optimal model" obtained by the deterministic inversion based on the optimization criterion to explain the electrical structure of underground media cannot achieve the quantification of multiple solutions of inversion,so probabilistic inversion is particularly necessary under this requirement.At present,there are few researches on transient electromagnetic inversion based on probability theory,so this thesis plans to carry out researches on transient electromagnetic inversion and uncertainty analysis based on Bayesian framework.From the perspective of fixed-dimensional and trans-dimensional,we quantitatively analyze and evaluate the non-uniqueness of the transient electromagnetic inversion results.In terms of fixed-dimensional Bayesian inversion,? we use the optimal model of nonlinear inversion as the initial model to reduce sampling waste;? we propose weighted prior distribution to balance the function of data fitting term and model constraint term,so that we can improve the low resolution of deep resistivity.? In the proposed distribution,a scale factor is added in stages to control the sampling step size,so as to ensure the ergodicity of the full space sampling and improve the sampling rate.Finally,we implement Markov Chain Monte Carlo(MCMC)based on M-H criterion for large-scale parallel sampling and to realize the uncertainty analysis of geoelectric parameters.Trans-dimensional Bayesian inversion is based on a Reversible Jump Markov Chain Monte Carlo(RJMCMC)method for sampling,and the main improvements include:? We propose a multi-parameter mixed prior distribution function,and the prior probability function is selected according to the characteristics of different TEM parameters for reasonable posterior sampling.?We set up a model sampling update mode with unequal probability to realize reversible sampling and use multi-chain parallel method to improve sampling efficiency.?In order to ensure the ergodicity of the full space sampling and sufficient sampling in the high probability interval,we construct the sampling step size using the two-factor control proposed distribution.We use PSRF to judge the sampling convergence in a multi-chain parallel framework.And we use RMS to control the output of the reasonable model in the stationary convergence stage,and finally obtain the reasonable model posterior distribution statistics.To verify the feasibility of these two algorithms,firstly,we adopt four groups of 1D 3-layer model(adding gaussian noise)to carry out the synthetic model inversion and uncertainty analysis.Secondly,we implement these algorithms in field data inversion to compare and dissect on fixed-dimensional and trans-dimensional inversion results.Besides,we apply these inversion results of field data for the uncertainty analysis of and reliability evaluation.In the end,in combination with Occam inversion result,drilling data and geological data,we verify the rationality and accuracy of Bayesian inversion results.