| Time-domain airborne EM(ATEM)system,using airplane as its moving platform,can perform fast and efficient exploration in the areas that are difficult for human accessing,such as rugged mountain,dessert and swamps.Now it has been widely used in minearl exploration,environmental and engineering investigation etc.However,the existing 3D ATEM simulation methods have many problems,such as instability,inefficiency and poor capability of dealing with complex structures,which seriously limit the development of 3D ATEM data processing and interpretation.To solve these problems,I do research on 3D ATEM modeling for complex structures using unstructured time-domain edge finite-element method,and analyze the characteristics of ATEM responses and effects of topography and electrical anisotropy.Firstly,starting from the time-domain electric field diffusion equation,I discretize the calculating space with fine unstructured tetrahedral grids,which provides the flexibility to accurately model the complex geoelectric structures.Secondly,the vector basic functions that can automatically satisfy the divergence-free property and tangential continuity are applied to space discretization.The Galerkin’s method is used to establish the governing equation.Then I adopt the Back Euler scheme to discretize the governing equation in time-domain and obtain an unconditionally stable implicit equation,relaxing the limitation on time steps.This allows to flexibly set the time step based on the changing rate of transmitting current and diffusion law of EM field.Parallel computation and compression storage techniques are used to improve the efficiency and to save memory.I adopt the homogeneous Dirichlet boundary condition,which is the most effective method for modeling EM diffusion problem.Finally,the Multifrontal Massively Parallel Solver(MUMPS)is used to solve the finite-element equations.When the time step stays unchanged,only one factorization is required,and the electric fields for all time channels are solved by back substitution of right-hand term.I check the accuracy of my algorithm by comparing with the 1D semi-analytical solution for homogeneous half space.To improve the efficiency of multi-source modeling for airborne EM,local mesh strategy is carried out by designing independent mesh for each group of survey stations,which is based on the “footprint” of airborne EM system.By taking the 3D model wirh horizontal plate for example and comparing with the global mesh,I check the validity of this method.The EM responses for complex transmitting source with arbitrary current waves are simulated by discretizing the transmitter into dipoles and instantaneous current pulse technique.The transmitter loop with arbitrary shape and attitude is divided into current segments,each segment is treated as an electric dipole.I further analyze via numerical experiments the effects caused by the change of attitude and shape of transmitter.I model the full-wave ATEM responses of arbitrary transmitting waves by directly using the instantaneous impulse for different time.As it is unnecessary to calculate the two-order derivative of transmitting current as in traditional ATEM modeling,the numerical stability is improved greatly.I check its capability of simulating the responses of complicated wave by comparing with the traditional convolution result for 3D models.Considering the mesh has a great effect on the numerical precision of 3D forward modeling,I apply the technique based on the goal-oriented adaptive optimizing mesh to time-domain finite-element(FETD)modeling.Firstly,I estimate the posterior error based on the continuity conditions of normal current.Then I calculate the influence functions by bringing in a set of dummy sources to weigh the posterior error of every element.Finally,I refine the mesh locally according to the weighted posterior error to obtain better grid and improve the numerical precision.I check the validity of the adaptive algorithm by doing experiments on homogeneous half space and topographic models.Based on the above work,I firstly simulate the ATEM responses on typical models,such as sphere,vertical-/horizon-/dipping plate,basement uplift and fault model,and analyze the responses characteristics.The results show that the ATEM responses can reflect the underground electric structures clearly.The occurrence and position of the target can be identified from the pattern of responses,which can provide reference for abnormity picking up.Secondly,I simulate the ATEM responses of hill-,valley-and undulating topography models to analyze the topographic effect.The numerical experiments show that the topography can have big influences on the survey responses,especially on the early time channels,and the effects decrease with time.There is mirror relationship between the response pattern and topography.The mixture of EM responses from topography and abnormal body makes survey signal very complex,leading to big difficulty for ATEM data interpretation.Finally,I simulate the ATEM responses for an arbitrarily anisotropic earth of complex structures.I take the anisotropic abnormal body,anisotropic host rock and anisotropic earth with topography for example to discuss the anisotropic effects.From the numerical results,I can find that the anisotropy has a big effect on both the distribution pattern and strength of ATEM responses.The former can be used to determine the principal axis orientations and rotation angle of the anisotropic resistivity.The FETD method studied in this dissertation can provide synthetic data for system design and development and production planning.The achievement has important theoretical and practical value in promoting the level of airborne electromagnetic data interpretation. |
