Abstract
Airborne electromagnetic (AEM) method uses aircraft as a carrier to tow EM instruments for geophysical survey. Because of its huge amount of data, the traditional AEM data inversions take one-dimensional (1D) models. However, the underground earth is very complicated, the inversions based on 1D models can frequently deliver wrong results, so that the modeling and inversion for three-dimensional (3D) models are more practical. In order to obtain precise underground electrical structures, it is important to have a highly effective and efficient 3D forward modeling algorithm as it is the basis for EM inversions. In this paper, we use time-domain spectral element (SETD) method based on Gauss-Lobatto-Chebyshev (GLC) polynomials to develop a 3D forward algorithm for modeling the time-domain AEM responses. The spectral element method combines the flexibility of finite-element method in model discretization and the high accuracy of spectral method. Starting from the Maxwell's equations in time-domain, we derive the vector Helmholtz equation for the secondary electric field. We use the high-order GLC vector interpolation functions to perform spectral expansion of the EM field and use the Galerkin weighted residual method and the backward Euler scheme to do the space- and time-discretization to the controlling equations. After integrating the equations for all elements into a large linear equations system, we solve it by the multifrontal massively parallel solver (MUMPS) direct solver and calculate the magnetic field responses by the Faraday's law. By comparing with 1D semi-analytical solutions for a layered earth model, we validate our SETD method and analyze the influence of the mesh size and the order of interpolation functions on the accuracy of our 3D forward modeling. The numerical experiments for typical models show that applying SETD method to 3D time-domain AEM forward modeling we can achieve high accuracy by either refining the mesh or increasing the order of interpolation functions.
Highlights
We demonstrate the flexibility of our SETD algorithm in terms of the accuracy improvement by refining the mesh or increasing the order of the interpolation functions
There exists a minimum over the top of the dyke due to zero coupling between the transmitter-receiver pair and the dyke; (3) at later time, the EM field passes through the dyke, the EM signal diffuses into the underlying half-space and becomes broader and weaker; (4) the center of the dyke can be determined by the minimum location of the EM responses, while the boundaries of the dyke can be roughly estimated from the middle points between the maximum and minimum peaks
We have successfully developed and applied the SETD method to
Summary
Wang et al used the SE method to model the seismic wave field in transversely isotropic media They used the GLL basis functions and explicitly discretized time derivatives to improve computational efficiency [36]. It can directly solve the EM field and avoid the time discretization, so that high accuracy and efficiency can be achieved [42] This method has the disadvantage that the basis functions are not easy to find and is difficult to be applied in EM inversions. We use the GLC vector interpolation basis functions to spectrally expand the electric and magnetic fields and discretize the controlling equation in space- and time-domain by the Galerkin’s weighted residual method and backward difference scheme.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
