Method for efficient processing of controlled source electromagnetic data, whereby Maxwell's equations are solved [107] by numerical techniques [109] such as finite difference or finite element in three dimensions for each source location and frequency of interest. The Reciprocity Principle is used [103] to reduce the number of computational source positions, and a multi-grid is used [105] for the computational grid to minimize the total number of cells yet properly treat the source singularity, which is essential to satisfying the conditions required for applicability of the Reciprocity Principle. An initial global resistivity model [101] is Fourier interpolated to the computational multi grids [106]. In inversion embodiments of the invention, Fourier prolongation is used to update [120] the global resistivity model based on optimization results from the multi-grids.