1. A method of geophysical exploration within a predetermined volume of the earth containing subsurface structural and stratigraphic features conducive to the generation, migration, accumulation, or presence of hydrocarbons, comprising the steps of: a. selecting a 3D seismic data set, wherein at least a portion of said 3D seismic data set images said at least a portion of said predetermined volume of the earth, and wherein said 3D seismic data set comprises a plurality of seismic traces; b. computing a partial Fourier transform of at least a portion of said seismic traces in said 3D seismic data set, thereby producing a transformed 3D seismic data set; c. choosing an initial subsurface model; d. using at least said initial subsurface model to calculate a 3D frequency domain forward propagated wave field by time domain forward modeling; e. calculating a residual volume between said 3D frequency domain wave field and said transformed 3D seismic data set; f. calculating a frequency domain back propagated wave field by 3D time domain forward modeling using at least said back propagated wave field; g. using at least said 3D frequency domain back propagated wave field and said 3D frequency domain forward propagated wave field to update said initial subsurface model, thereby producing an updated subsurface model; and, h. using said at least a portion of said updated subsurface model to explore for said subsurface structural and stratigraphic features conducive to the generation, migration, accumulation or presence of hydrocarbons within said predetermined volume of the earth.