MCMC Simulation And Variational Reconstruction For 3D Geological Interface Of Metallogenic Structure

The evaluation of the mineral resources relies more on the knowledge and inference of metallogenic structures with the exploration depth increase.The three-dimensional(3D)geological model can express the morphology of the geological interface,which is important for geological process simulation,geological structure morphology visualization and mineralization prediction.However,the geological models usually have great uncertainties due to the lack of data in depth.And there are series of stochastic simulated methods for the uncertainties estimation,which are difficult to ensure effective exploration of possible models and consider the topology and morphology of the 3D geological interface.In addition,it is also difficult for the existing methods to combine geological and geophysical information to reconstruct 3D geological models effectively and reliably.To this end,this paper proposes a Markov Chain Monte Carlo(MCMC)simulation method for the geological interface of metallogenic structure,which combines geological and geophysical data.And then based on the variational method,we realize the reconstruction of the 3D geological interface.The main results are as follows:(1)This paper presents the MCMC simulation via the abstract graphs to infer the uncertainties distribution of the geological interface in the highdimensional space.The geometric topological features of the model are expressed by abstract graphs.And the graphs are used to constrain the stochastic simulation process for flexible,reliable and efficient perturbation and sample from the complex probability distributions.With the constraints of the geological and geophysical information,a series of highly perturbed models are generated,which can be used to observe the uncertainty distribution of the Jiaojia fault.(2)This paper presents a variational inference method for the maximum information entropy of lithology to reconstruct the 3D geological interface.Based on the Bayesian posterior probability of the MCMC simulation,the reconstruction of the interface can be cast as a variational inference for the maximum information entropy of lithology,which can be solved by the dynamic programming algorithm.The lithological maximum information entropy interface of the Jiaojia fault is represented the maximum possible position of fault surface.And through the position expectation of probabilistic statistics,we can observe the morphological variation of the 3D geologicla interface.(3)This paper also proposes a continuous and high-precision reconstruction for 3D geological interface based on the variational implicit functions.With the constraints of geological and geophysical data,an implicit variational model of the geological interface is established.This method utilize the Gauss-Newton strategy to establish the variational framework.And it solve the Gauss-Newton update formula for the implicit models,which realize the fine and analytical expression of the 3D geological interface.In the experiments,it is found that the variational implicit model has a high reconstruction accuracy.In summary,this paper proposes the MCMC simulation and variational methods for 3D geological interface.And we verify the reliability and accuracy of these methods by examples,which provides support for mineralized exploration of structures and application of mineralization search.