| Transient electromagnetic method has been widely used in engineering practice because of its sensitive response to low-resistance anomalies and simple construction.The transient electromagnetic method faces great challenges in inversion calculation due to its highly nonlinear characteristics.At present,the main inversion method is the one-dimensional transient electromagnetic inversion,and the two-and threedimensional inversions develop slowly due to the huge computational complexity of the sensitivity matrix.The traditional deterministic inversion method makes a linear approximation of the inversion problem,and finally can only give a deterministic solution with limited precision.It is highly dependent on the initial reference model,which makes it difficult to solve the multi-solution problem of geophysical inversion,and it is impossible to evaluate the accuracy of the inversion effect.In this thesis,based on Bayesian principle,using the Metropolis sampler based on Markov Chain Monte Carlo Method(MCMC)as a tool,a parallel tempering algorithm and Fourier sliding based on geostatistics are introduced.Fast Fourier TransformMoving Average(FFT-MA)spectrum fast stochastic modeling algorithm for the purpose of accurate inversion of transient electromagnetic data,taking regular and irregular geoelectric models as examples,and developed a large ground loop Source transient electromagnetic 2.5-dimensional(2D geological model,3D source)Bayesian inversion interpretation research.The main work is as follows:(1)Starting from the vertical magnetic dipole source,the three-dimensional source and two-dimensional geological body model in the time domain are converted into Maxwell’s equations in the Laplace transform domain,and the finite element functional in the Laplace transform domain is deduced.Equation,realizes the ground large loop source electromagnetic method 2.5-dimensional finite element forward modeling.The introduction of the Open MPI module realizes the parallelization of forward calculation,which greatly shortens the forward running time.Using the method of time domain convolution between the transient electromagnetic decay curve and the emission waveform,the transient electromagnetic method forward simulation of the non-zero turn-off time is realized,which enhances the practicability.(2)The parallel tempering algorithm is introduced into the Bayesian inversion Metropolis sampler.By adding multiple Markov chains with different temperatures,the ergodicity and reducibility of the Markov chain are enhanced,and efficient sampling is achieved.The Metropolis sampler that introduces the parallel tempering algorithm can easily jump out of the local optimum state and enter the next optimal solution,and the burn-in stage is shortened significantly;jumping out of the local optimum also greatly reduces the average number of iterations;the average number of iterations after burnin The log-likelihood is improved.(3)The FFT-MA algorithm based on geostatistics is introduced into the prior sample feeder for Bayesian inversion,which reduces the spatial scope of understanding and search and improves the efficiency and accuracy of Bayesian inversion.Using the kriging interpolation method,the mapping from the stochastic geological model based on uniform grid to the forward model based on non-uniform grid is realized to match the requirements of various inversion grid settings.(4)Compared with the traditional deterministic inversion,the probabilistic nonlinear Bayesian inversion takes the probability distribution of resistivity as the prior information,and cancels the dependence of the inversion algorithm on the initial model by means of stochastic geological modeling.And the Bayesian inversion method can give the probability density distribution of the inversion results,which can be used as a reference for evaluating the quality of the inversion.At the same time,the probabilistic inversion results solve the multi-solution problem of geophysical exploration to a certain extent. |
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