Numerical Modeling And Inversion Imaging Of Self-Potential By Natural Element Method

With the development of industry,agriculture,and social civilization,water resources and ecological circumstances worldwide are facing significant challenges.Industrial and municipal landfilling is one of the major sources of underground pollution.When leaks occur in landfills,toxic substances such as heavy metals in leachate infiltrate the soil,contaminating groundwater.It poses a severe threat to agriculture,vegetation,freshwater resources,and even human living environments.Researching non-intrusive environmental monitoring techniques can help promptly detect pollution leakage and take remedial measures.The natural electric field(more commonly known as self-potential,SP)method has gained widespread attention and application in the field of environmental investigation due to its advantages such as portable instrumentation,simple operation,high exploration efficiency,and direct correlation with fluid flow and redox gradients associated with subsurface contamination.However,SP signals are complex in origin,highly nonunique,and difficult to obtain depth information,making them typically used for qualitative analysis.In response to the environmental issues related to underground pollution monitoring,comprehensive research incorporating high-precision numerical simulation,physical modeling,and quantitative inversion of complex SP models has been carried out.The achievements are as follows:(1)The boundary value problems and their variational formulations for multi-source SP models were derived,and the 3D structured finite element method(FEM)was adopted to solve the variational problems.Starting from the quasi-static Maxwell’s equations,the Poisson equation and its boundary value problems were derived.By applying the variational principle,the boundary value problems were transformed into equivalent variational problems.Subsequently,numerical simulations of multi-source SP models were conducted using the hexahedral FEM and structured tetrahedral FEM.(2)To address the computational accuracy limitations of the conventional FEM in multi-source SP models,the 3D structured FEMRUMIFEM(radially unidirectional mapping infinite element method,RUMIFEM)and FEM-MVMIFEM(vertically multidirectional mapping infinite element method,MVMIFEM)coupling methods were proposed.The coupling methods avoided the use of truncated boundary conditions while maintaining the sparsity and symmetry of the stiffness matrix.They exhibited high computational efficiency and accuracy in the numerical simulation of multi-source SP models.(3)To overcome the constraints of conventional FEM imposed by mesh partitioning,the natural element method(NEM)was introduced into the numerical simulation of SP models.Building upon the achievements of 2D and 3D NEM for numerical simulation of SP models,a 3D NEM-IFEM coupling method was proposed,which simultaneously avoided the grid limitations and truncated boundary conditions.Numerical results demonstrated that the NEM and its coupling approach are effective techniques for solving the SP Poisson equation,offering applicability to complex models.(4)Physical simulation experiments involving water drainage and injection and iron-copper metal redox polarization were designed and conducted to obtain measured time-series streaming potential signals and redox SP signals.To obtain two types of measured SP data relevant to underground pollution detection and investigate the anomalous characteristics of real SP signals,experimental setups including a multichannel SP acquisition system and two non-polarized Ag-Ag Cl electrode systems were utilized.Sequential experiments were conducted,including water injection and drainage experiments in a sandbox to measure 3D time-series streaming potential signals,as well as redox polarization experiments of iron-copper sphere and cylinder to measure time-series redox SP data.The streaming potential simulation experiment effectively illustrated the dynamic process of water flow,while the iron-copper metal redox experiments revealed the electrochemical characteristics and polarization features of the geobattery model.(5)The NEM and its coupling approach were employed for forward modeling to achieve least-squares regularization inversion(LSRI)and quantitative interpretation of SP data.First,the basic formula for LSRI applicable to SP data was derived.Then,the effectiveness of 2D and 3D inversion was tested through synthetic models.Finally,quantitative inversion was conducted using field and laboratory measured SP data.The results demonstrated that the LSRI can effectively reveal the spatial distribution characteristics of underground SP current sources,aiding in the identification of fluid migration in subsurface environments.(6)Bayesian framework-based Markov Chain Monte Carlo(MCMC)inversion studies were conducted to quantitatively interpret the response of regularized polarization body models and quantify the uncertainty of model parameters.Firstly,an adaptive MCMC inversion method suitable for SP data was proposed.Then,the effectiveness of the algorithm was validated using a spherical model.Finally,quantitative inversion was carried out based on measured data from the iron-copper metal redox experiments.The results indicated that the algorithm can effectively recover model parameters with high efficiency while quantifying the uncertainty of model parameters.It provided parameter confidence intervals,facilitated the investigation of parameter correlations,and helped address the issue of non-uniqueness of SP inversion.The related research in this paper contributes to enhancing the application effectiveness of the SP method in underground pollution detection and monitoring,providing a theoretical foundation and technical support for the protection of soil,groundwater resources,and the ecological environment.