Iterative extended Born approximation based on CG-FFT integral equation method for low-frequency 3D modeling

We present a fast method for modeling three-dimensional low frequency controlled source electro-magnetic (CSEM) problems. We apply the method to the marine controlled source electromagnetic (MCSEM) exploration situation where conductivity and permittivity are different from the known background medium. For 3D problems fast computational methods are relevant for both forward and inverse modeling studies. Since this problem involves a large number of unknowns, it has to be solved efficiently so that the results can be obtained in a timely manner, without compromising accuracy. For this reason, the Born approximation (BA), extended Born approximation (EBA) and iterative extended Born approximation (IEBA) are implemented and compared with the full solution of the conjugate gradient fast Fourier transformation method (CG-FFT). These methods are based on an electric field domain integral equation formulation. It is shown here how well the IEBA method performs in terms of both accuracy and speed with different configurations and different source positions. For forward modeling the solution at the sea bottom is of interest because that is where the receivers are usually located. But for inverse modeling, the accuracy of the solution in the target zone is important to be able to obtain reasonably accurate conductivity values from the inversion using this approximate solution method. Our modeling studies show that the IEBA method is suitable for both forward and inverse modeling.