A fast iterative approach to full vector three-dimensional forward scattering problems is discussed, where the unknown object is an assumed reservoir in the layered earth where conductivity and permittivity are different from the known background medium. Since this problem involves a large number of unknowns, it has to be solved effectively and efficiently so that the results can be obtained in a timely manner. To achieve this goal, approximations can give us reasonable results. Therefore Born approximation and Extended Born approximation are implemented and compared with the full solution of the CG-FFT method. The forward modeling is based on a domain integral equation formulated in terms of the electric contrast source. Integral Equation (IE) solver has several advantages such as separation of incident and scattered field which gives us a more accurate result, furthermore IE method requires the discretization of the domain of the reservoir only and not the entire of modeling domain, in addition because of the unique solution to the domain equation, the method is suitable for inverse modeling.


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