Semi-airborne Transient Electromagnetic 3D Anisotropy Forward Modeling Based On Finite Volume Method

The electromagnetic method can be divided into time-domain electromagnetic method and frequency domain electromagnetic method.Semi-airborne transient electromagnetic method(SATEM)is a kind of time domain electromagnetic method,which combines ground-based transient electromagnetic method(TEM)and flight-based electromagnetic method.The characteristics of the semi-airborne transient electromagnetic method are that it transmits signals from the ground through transmitting equipment such as transmitting coils,and receives signals in the air through receiving equipment such as receiving coils or magnetic rods suspended in the air.This method has many advantages so it can be applied to many geological exploration fields,such as water resources exploration,tunnel construction,karst development area investigation,mineral resource exploration,etc.Semi-airborne transient electromagnetic is an effective method for complex regional engineering exploration.There are many complex terrain areas in China,and there is no effective geological information support in the complex terrain areas,which makes it difficult to carry out the project normally.There are a large number of karst development areas concentrated in the southwest area of China.The area accounts for more than one-third of the whole southwest area,and the karst area has complex topography,fragile ecological environment,weak transportation and other infrastructure,and people’s lives are relatively poor.It is extremely difficult to carry out bridge and tunnel construction in such areas,and safety accidents often occur.Also,there is currently no effective exploration technology in China,so the application of semi-airborne transient electromagnetic is extremely important.In electromagnetic(EM)numerical simulation,the commonly used methods include finite difference method(FDTD),finite element method(FED)and finite volume method(FV).The finite difference method developed earlier,is easy to implement through programming,and can better solve the problem of discontinuity in the electromagnetic field.In recent years,the finite difference method has been widely used in electromagnetic simulation calculations,and the algorithm has become mature.It has been relatively maturely applied in related calculations such as isotropy,anisotropy and full-waveform problems.The finite element method can be understood as a numerical solution method for elastic mechanics problems.It has also achieved good results in electromagnetic field calculations,and has been widely used in adaptive algorithm research,plane wave,two-dimensional and three-dimensional simulation calculations.The finite volume method was originally mainly used to solve fluid problems and heat conduction problems.In recent years,it has also been gradually applied to electromagnetic field calculations.This method satisfies the characteristics of flux conservation in the control volume,so it can ensure the conservation of the field in the calculation area.The finite volume method is selected for the study of semi-airborne transient electromagnetic 3D forward modeling.The isotropic medium,axial anisotropic medium and arbitrary anisotropic medium are studied respectively,and the semi-airborne transient electromagnetic three-dimensional finite volume forward modeling is formed.program.The specific formula derivation process is as follows:First,the basic equations of transient electromagnetics in the time domain are discussed,and a new set of equations can be obtained by substituting the constitutive relation into Maxwell’s equations.and arbitrary anisotropy equations,take the equations as the basic formula to carry out the research on the threedimensional forward modeling theory;secondly,after a series of transformations of the basic equations,the double curl equation can be obtained;finally,the double curl equation can be obtained by Yee net Lattice space discretization,finite volume integral and implicit Euler technique time discretization,the discrete equations in three directions of x,y,and z can be obtained.In the discrete equation,the coefficient matrix can be given by the designed grid and the time trace(time step)used,while the right-hand background field term can be obtained by the Hankel transform through a one-dimensional semi-analytical solution in the frequency domain.When solving the equation system,it is necessary to add initial conditions and boundary conditions.The initial conditions are the initial conditions of the step waveform,and the boundary conditions are Dirichlet boundary conditions,that is,the electromagnetic field decays with distance.It is assumed that the tangential component of the electric field is outside the calculation area.A boundary condition of zero at the boundary.The large-scale equation system is then solved.At present,the solution methods for large-scale linear equations mainly include iterative method and direct solving method.The iterative method is mainly based on the conjugate gradient method,the minimum residual method,etc.,which are characterized by small memory footprint and low requirements on computer hardware.However,the iteration number and solution accuracy of the iterative method are greatly affected by the condition number of the equation coefficient matrix.Usually,in order to improve the convergence speed,it is necessary to use preprocessing technology to reduce the condition number of the solution equation.The direct solution method generally solves the equation by directly decomposing the coefficient matrix.In the research,the Pardiso solver is proposed to solve the forward equation of semi-airborne transient electromagnetic,and the solution of the forward equation can be completed.The accuracy verification and simulation calculation of the semi-airborne transient electromagnetic 3D forward modeling program are carried out.First,the isotropic model is used to verify the accuracy of the uniform half-space model and the layered model.The response analysis of the model was carried out;then the simulation calculation was carried out for the main axis anisotropy model,and the influence of the three main axes on the decay voltage was analyzed;finally,the arbitrary anisotropy model was simulated and calculated,and the anisotropic dip angle and strike angle on the response were analyzed.Finally,a model in line with the actual geology was designed for further calculation.