A method of seismic exploration above a region of the subsurface containing structural or stratigraphic features conducive to the presence, migration, or accumulation of hydrocarbons, wherein there is provided a blended source seismic survey containing at least two interfering seismic source excitations therein, and wherein there is a random time interval between each of said at least two interfering seismic source excitations and a lowest frequency of interest in said blended source seismic survey, and the length of said random time interval is chosen to be longer than a wavelength of said lowest frequency of interest in said blended seismic survey, comprising the steps of: (a) within a computer, accessing at least a portion of said blended source seismic survey; (b) selecting one of said at least two interfering seismic source excitations; (c) obtaining at least a time of activation and location coordinates for said selected one of said at least two interfering seismic source excitations; the method characterized by further comprising: (d) using at least said time of activation and said location coordinates for said selected one of said at least two interfering seismic source excitations separating said selected source excitation from said at least two interfering seismic source excitations using sparse inversion by solving the equation: Γ T d = Γ T ΓSm, for the matrix m thereby producing a single source gather, where m is said single source gather, d is a matrix representation of the recorded seismic data, S is a matrix or operator that describes the similarity between nearby shots, and Γ is a matrix that defines the blending or mixing of the individual sources, Γ T is the transpose of Γ; and (e) using said at least one single source gather to explore for hydrocarbons within said region of the subsurface. (a) within a computer, accessing at least a portion of said blended source seismic survey; (b) selecting one of said at least two interfering seismic source excitations; (c) obtaining at least a time of activation and location coordinates for said selected one of said at least two interfering seismic source excitations; (d) using at least said time of activation and said location coordinates for said selected one of said at least two interfering seismic source excitations separating said selected source excitation from said at least two interfering seismic source excitations using sparse inversion by solving the equation: Γ T d = Γ T ΓSm, for the matrix m thereby producing a single source gather, where m is said single source gather, d is a matrix representation of the recorded seismic data, S is a matrix or operator that describes the similarity between nearby shots, and Γ is a matrix that defines the blending or mixing of the individual sources, Γ T is the transpose of Γ; and for the matrix m thereby producing a single source gather, where m is said single source gather, d is a matrix representation of the recorded seismic data, S is a matrix or operator that describes the similarity between nearby shots, and Γ is a matrix that defines the blending or mixing of the individual sources, Γ T is the transpose of Γ; and (e) using said at least one single source gather to explore for hydrocarbons within said region of the subsurface.