Computing device, computer instructions and method for estimating a broadband wavelet associated with a given seismic data set. The method includes receiving broadband seismic data; constructing and populating a misfit function; calculating the broadband wavelet based on the misfit function and the broadband seismic data; and estimating physical reservoir properties of a surveyed subsurface based on the broadband wavelet. The broadband wavelet is constrained, through the misfit function, by (1) an amplitude only long wavelet, and (2) an amplitude and phase short wavelet. The amplitude and phase short wavelet is shorter in time than the amplitude only long wavelet.