1. A method for inverting measured data from a controlled-source electromagnetic survey of a subsurface region to generate a resistivity data volume representing the subsurface region, comprising: (a) selecting a discrete forward-modeling grid to represent at least a portion of the subsurface region; (b) determining geometry information for structural units of the subsurface region from seismic or other available data; (c) generating an inversion grid with a mesh based on the structural unit geometry, the inversion grid containing fewer cells than the forward modeling grid; (d) specifying an initial resistivity model of the portion of the subsurface region, said model having a value of resistivity for each cell in the inversion grid; (e) solving Maxwell's electromagnetic field equations on the forward-modeling grid at one or more frequencies for a plurality of source-receiver survey positions, said frequencies being selected from the frequency spectrum of the survey's source waveform, said solution using survey source-receiver geometry information and source parameters and resistivity values from the resistivity model; and (f) generating an adjusted resistivity model by comparing the computed electromagnetic field values to the measured survey data, said comparison including minimizing a selected objective function, thereby using differences between computed electromagnetic field values and measured survey data to determine resistivity model adjustments; wherein at least (e) and (f) are performed on a computer programmed to perform (e) and (f).