Abstract: A method of spectrum restoring and broadening to produce high resolution seismic data from a plurality of shot records in a seismic survey is described. The method includes the steps of: dividing each shot record into a plurality of windows, in which each of the relevant variables is practically constant, and wherein each window contains one or more trace segments; forward modelling of spectral signatures for any ghost reflections in the shot records using a best estimate of all known parameters, such that every trace segment will have an observed and a (prior) modelled spectral signature; calculating an inverse operator to correct the spectral notches in every trace segment using a constrained set of final fitted values for all the relevant variables; and, recombining the processed trace segments to produce a final set of shot records whereby, in use, the deleterious effects of the ghost reflections in the shot records can be substantially eliminated.