1. A method for correcting measured data from a marine seismic survey to eliminate surface-related multiples, said measured data being pressure data either measured by pressure sensor receivers located in the water or calculated from measured particle velocity data, said method comprising: (a) using a computer to simulate the measured data (“simulated data”) with a forward model that includes a water propagation operator between source locations and receiver locations and a term representing primary impulse responses; (b) updating the primary impulse responses by iterative optimization to minimize a difference between the measured data and the simulated data; and (c) using the updated primary impulse responses to correct the measured data for multiple reflections, or for further processing to interpret for indications of hydrocarbon potential.