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Time Evolution of the Electric Field Using the Rapid Expansion Method: Inclusion of the Free Surface and Anisotropy
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 80th EAGE Conference and Exhibition 2018, Jun 2018, Volume 2018, p.1 - 5
Abstract
We present an extension of the rapid expansion method (REM) for 3D time-domain electromagnetic (EM) modelling with pseudo-spectral (PS) evaluation of spatial derivatives that includes the free surface of the earth and anisotropic conductivity in the earth. The governing equation is the second-order diffusive equation for the electric field. The spatial derivatives are solved by a Fourier PS method. The temporal derivative is solved by a Chebyshev expansion of the exponential operator. We model the response of the free surface by using the upward continuation of the time derivative of the magnetic induction. We show that, in principle, any type of anisotropy can be included in the modelling with the manipulation of the conductivity tensor. All three electric field components are collocated with the electric conductivities and are modelled independently and simultaneously with spectral accuracy in both space and time. We demonstrate the excellent accuracy of REM in 1D vertical transverse isotropy (VTI) layered earth against spectral methods, and show the imaging of a 3D resistive body by REM to demonstrate its ability to handle 3D problems.