A modified-boundary condition algorithm for efficient 3D forward modeling of CSEM data

<p>I present a newly developed 3D forward modeling algorithm for controlled-source electromagnetic data. The algorithm is based on the finite-difference method, where the source term vector is redefined by combining a modified boundary condition vector and source term vector. The forward modeling scheme includes a two-step modeling approach that exploits the smoothness of the electromagnetic field. The first step involves a coarse grid finite-difference modeling and the computation of a modified boundary field vector called radiation boundary field vector. In the second step, a relatively fine grid modeling is performed using radiation boundary conditions. The fine grid discretization does not include stretched grid and air medium. The proposed algorithm derives computational efficiency from a stretch-free discretization, air-free computational domain, and a better initial guess for an iterative solver. The numerical accuracy and efficiency of the algorithm are demonstrated using synthetic experiments. Numerical tests indicate that the developed algorithm is one order faster than the finite-difference modeling algorithm in most of the cases analyzed during the study. The radiation boundary method concept is very general; hence, it can be implemented in other numerical schemes such as finite-element algorithms.</p>

3D Airborne EM Forward Modeling Based on Time-Domain Spectral Element Method

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.