3D Forward Modeling And Inversion For Time-domain Marine CSEM Based On Unstructured Finite-Element Method

With the large-scale exploitation of land resources,the reserves showing a declining trend,and the mining costs increasing,people are paying more and more attention to the development of marine resources.The marine controlled-source electromagnetic(MCSEM)method is sensitive to high-resistivity targets and has better resolution than the gravity & magnetic method.This MCSEM method has been widely used in oil and gas and gas hydrate exploration independently or as an auxiliary means to marine seismic.The MCSEM method can be divided into frequency-domain and time-domain method according to different emission currents.The frequency domain MCSEM method is affected by airwaves in the shallow sea environment and cannot obtain good exploration results.In contrast,the time-domain method is not affected by airwaves and can be applied to shallow sea exploration.Moreover,the seabed topography is undulating,and the electrical structure under the seafloor is complex,so that the one/two-dimensional data interpretation technology no longer satisfies the requirements of refined exploration.It is necessary to study the three-dimensional timedomain MCSEM forward modeling and inversion methods.At present,there is little research on three-dimensional marine CSEM forward modeling and inversions in the time-domain.Most of the existing researches only study the response of the step-off wave and cannot do the inversion in the complex environment of seabed terrain.To solve these problems,this paper uses the finiteelement method based on the unstructured tetrahedral grids to carry out the threedimensional time-domain marine CSEM forward modeling.Systematically analyze the characteristics of EM responses for typical high-resistance reservoirs and the influence of seafloor topography on EM responses,and compare the EM responses for step-off wave and the square wave.For the forward method based on finite element,solving large-scale linear equations leads to huge computational memory consumption.Therefore,based on the existing finite element method,this paper proposes a domain decomposition method in time-domain(DDTD)based on the finite-element method.This method can reduce the problem's scale and can easily allocate memory to multicore.So,it is suitable for computing large-scale models,which lays the foundation for the processing and interpretation of large-scale three-dimensional time-domain marine CSEM data.Further,utilize the limited memory BFGS method to carry out the threedimensional time-domain marine CSEM inversion.This paper discusses the effect of this method under seabed terrain,and compares the recovery capability of the step-off wave with the square wave to the high-resistivity reservoirs in the shallow sea environment.To achieve the above research goals,this paper first derives the electric field diffusion equation based on the time-domain Maxwell's equations.It uses unstructured tetrahedral grids and vector basis functions for spatial discretization to fit seabed topography and complex anomalies under the seafloor.Applying the Galerkin method and adopting the second-order backward Euler method to discretize the time derivative,an unconditionally stable time-discrete finite-element equation can be established.Moreover,for the case where the transmitting source used in MCSEM-a long wire,while the EM theory is based on the dipole model,this paper uses dipole-based field decomposition method to approximate finite-length electric sources.Finally,the initial electric fields for an electric source transmitting a step-off wave can be calculated by utilizing the nodal finite-element method to solve the Poisson equation of electric potential.To test the accuracy of the algorithm proposed in this thesis,use the onedimensional semi-analytic solution and the three-dimensional numerical solution for comparison.The results show that the 3D time-domain marine electromagnetic forward modeling algorithm presented in this paper is accurate and the calculation results are reliable.On this basis,this paper analyzes the characteristics of EM responses for typical marine models and draws the following conclusions: for step-off transmitting wave,the relative percentage anomaly of high-resistivity reservoirs decreases as the seawater depth increases,indicating it is more suitable for shallow sea exploration.Through the simulation of the seafloor topography,it is found that the topography has an impact on the shape of the electric field curve,the shape changes of which are consistent with the topography.However,it has little effect on the percentage anomaly of high-resistivity reservoirs.As the resistivity of sediments increases,the relative percentage anomaly of high-resistivity reservoirs becomes small.When there is a highresistivity basement,the high-resistivity reservoirs are affected by it,and the relative percentage anomaly becomes smaller.For the square wave,it can clearly distinguish the airwave and signal diffusing from sediment by the electric field curves according to the arrival time,and it maintains a relatively large relative percentage anomaly when the seawater depth increases.This indicates that the square wave is suitable for deepand shallow-water exploration.The electric field characteristics of high-resistivity reservoir for a square wave are consistent with the step-off wave,but its ability to identify high-resistivity reservoirs is significantly better than the step-off wave.The memory consumption in solving the forward equations has always been a technical problem in the simulation of MCSEM.To solve it,this paper further proposes a 3D domain decomposition method in the time-domain.Partition the mesh used by the finite-element method into several subdomains with the partition software METIS.By renumbering the grid in each subdomain and establishing the mapping relationship to the global grid number,the time-discrete finite element equations can be independently established in each subdomain,and all subdomain can be coupled together by Lagrange multiplier to construct the interface equation.The size of the equation is the number of variables shared by two subdomains on the interface,which significantly reduces the dimensionality to be solved.The generalized minimum residual method is used to iteratively solve the interface equation to avoid constructing the coefficient matrix explicitly.Using the solved Lagrange multipliers can obtain all the variables in each subdomain.Since all subdomain calculations are independent,the multi-core memory allocation can be performed,realizing the solutions of very large-scale problems.With a step-off wave via an electric source,the initial electric fields are obtained by solving the Poisson equation of potential utilizing the domain decomposition method based on the nodal finite-element method.Comparing with the one-dimensional semi-analytical solution and traditional finite-element results,verify the accuracy and precision of the domain decomposition method in the time-domain.On this basis,discuss the influence of air resistivity and the number of partitions on the domain decomposition method in the time-domain,and analyze the memory consumption characteristics of this method,further proving that it can be used for large-scale model calculation.In this paper,use the limited memory BFGS method to realize the threedimensional time-domain MCSEM inversion.Due to the tetrahedral grids,it can handle the seabed terrain environment and complex constructure under the seafloor.For calculating the sensitivity information,utilize the adjoint forward method to calculate the product of the transpose of the sensitivity matrix and a vector.This method avoids directly calculating and storing the sensitivity matrix,reducing calculation and memory consumption.When the initial electric field is not equal to zero,the source term's derivative also needs to be calculated with adjoint forward modeling.To reduce the size of the solution space,the model roughness operator is introduced,and the upper and lower limits are imposed on the inversion parameters to avoid obtaining the unreal inversion results.In this paper,systematically introduce the derivation process from Newton method,BFGS method to L-BFGS method,and give the linear search method for step length.Based on the inversions of a serial of typical marine models,verify the effectiveness of the inversion algorithm in this paper for topographic seafloor.From the inversion results,it can be found that the square wave is better than the step-off wave in detecting high-resistivity reservoirs.When there are serval sediments and highresistivity basement under the topographic seafloor,the square wave can still obtain good inversion results.The 3D marine EM forward and inversion research in this paper based on the unstructured finite-element method will provide an effective inversion and interpretation technique for the exploration of oil and gas resources under the ocean,and the 3D time-domain marine electromagnetic simulation technology based on domain decomposition will also lay a good foundation for the large-scale MCSEM problems.It is expected that the researches of this thesis will play a role in promoting the development of our marine EM technology.