| Airborne transient electromagnetic method(ATEM)has been widely used in the exploration of metal and oil and gas resources,groundwater and geothermal resources,engineering geological survey,geological survey,geological mapping and other fields due to its high efficiency and suitable for working in areas with complex terrain or poor surface conditions.In the research of forward and inversion of airborne transient electromagnetic method,there are more researches on one-dimensional forward and inversion of airborne transient electromagnetic method,but less researches on two-dimensional and three-dimensional forward and inversion.The 3D model is more suitable for the distribution of underground medium in practical work.At present,there is no practical 3D forward inversion technology of airborne tem for the processing and interpretation of measured data,The research of back propagation field in airborne TEM inversion is helpful to promote the development of airborne TEM 3D inversion method,so the main content of this paper is airborne TEM 3D forward modeling and back propagation field.The three-dimensional forward modeling adopts the finite-difference time-domain(FDTD)method to carry out the three-dimensional forward modeling of airborne TEM directly in the time domain,which avoids the disadvantage of converting the frequency domain response into the time domain response(it takes a lot of time to calculate dozens of frequency responses to ensure the accuracy,especially in the case of multi-source).At the same time,the explicit FDTD scheme is adopted to avoid solving the implicit FDTD In order to improve the computational efficiency,the large-scale linear equations are needed in the scheme.The time domain staggered sampling finite difference method is used to discretize the study area.The finite nodes are used to replace the continuous space,and the difference is used to replace the differential.The Maxwell differential equations are discretized,and the discrete explicit time step iterative equations are derived.The transmitting source is a rectangular loop source with trapezoidal waveform.In order to avoid the singularity of the field source,Biot Savart law is used to calculate the analytical solution of the response of the air rectangular loop source in the underground uniform half space at t = 0,which is used as the initial condition to replace the source in the equations,and the source response problem is transformed into an initial value problem.In order to calculate the magnetic field in the air,the traditional idea is to discretize the air in the region to be solved,but it needs a very small iterative time step to ensure the calculation accuracy(the conductivity value of the air is close to zero),resulting in a sharp increase in the calculation time.In order to avoid this problem,this paper proposes to calculate the surface magnetic field value iteratively,and then use the new method of magnetic field upward continuation to obtain the air magnetic field value.The code is written in FORTRAN language to realize the 3D finite difference time domain forward modeling of airborne TEM.A uniform half space model is established,and the results are compared with the analytical results of the surface and the mature calculation results of the foreign aarhusinv program,which verifies the correctness of the three-dimensional forward algorithm of airborne TEM.As the large Jacobian matrix needs to be solved in the three-dimensional inversion of airborne TEM,the electromagnetic migration imaging method is used to solve the Jacobian matrix,which avoids the calculation and storage of large time-domain Jacobian matrix.The method of electromagnetic migration imaging needs to calculate the back propagation field.This paper uses FORTRAN language to realize the calculation of the back propagation field. |
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