Modeling Of Controlled-source Electromagnetic Data Research Articles

3D forward modeling of controlled-source electromagnetic data based on the radiation boundary method

I have developed an efficient 3D forward modeling algorithm based on radiation boundary conditions for controlled-source electromagnetic data. The proposed algorithm derives computational efficiency from a stretch-free discretization, air-free computational domain, and a better initial guess for an iterative solver. A technique for estimation of optimum grid stretching for multifrequency modeling of electromagnetic (EM) data is developed. This technique is similar to the L-curve method used for the estimation of the trade-off parameter in inversion. Using wavenumber-domain analysis, it is illustrated that, as one moves away from the source, the EM field varies smoothly even in the case of a complex model. A two-step modeling algorithm based on radiation boundary conditions is developed by exploiting the smoothness of the EM field. The first step involves a coarse-grid finite-difference modeling and computation of a radiation boundary field vector. In the second step, a relatively fine grid modeling is performed with radiation boundary conditions. The fine-grid discretization does not include the stretched grid and air medium. An initial solution derived from coarse-grid modeling is used for fine-grid modeling. Numerical experiments demonstrate that the developed algorithm is one order faster than the finite-difference modeling algorithm in most of the cases presented.

Finite element time domain modeling of controlled-source electromagnetic data with a hybrid boundary condition

We implemented an edge-based finite element time domain (FETD) modeling algorithm for simulating controlled-source electromagnetic (CSEM) data. The modeling domain is discretized using unstructured tetrahedral mesh and we consider a finite difference discretization of time using the backward Euler method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies.

3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: Direct solution and optimization for high accuracy

Three-dimensional modeling of marine controlled-source electromagnetic (CSEM) data is vital to improve the understanding of electromagnetic (EM) responses collected in increasingly complex geologic settings. A modeling tool for simulating 3D marine CSEM surveys, based on a finite-difference discretization of the Helmholtz equation for the electric fields, has been developed. Optimizations for CSEM simulations include the use of a frequency-domain technique, a staggering scheme that reduces inaccuracies especially for horizontal electric-dipole sources located near the seafloor, and a new interpolation technique that provides highly accurate EM field values for receivers located in the immediate vicinity of the seafloor. Source singularities are eliminated through a secondary-field approach, in which the primary fields are computed analytically for a homogeneous or a 1D layered background; the secondary fields are computed using the finite-difference technique. Exploiting recent advances in computer technology and algorithmic developments, the system of finite-difference equations is solved using the MUMPS direct-matrix solver. In combination with the other optimizations, this allows accurate EM field computations for moderately sized models on small computer clusters. The explicit availability of matrix factorizations is advantageous for multisource modeling and makes the algorithm well suited for future use within an inversion scheme. Comparisons of simulated data for (1) 1D models to data generated using a 1D reflectivity technique and (2) 3D models to published 3D data demonstrate the accuracy and benefits of the approach.