A method for imaging non-specular seismic events as well as correlating non-specular events with physically measurable quantites in a volume of Earth's subsurface. Includes entering as input to a computer signals detected by a plurality of seismic sensors disposed above and/or within the volume in response to actuation of at least one seismic energy source above and/or within the volume. Parameter analysis is performed to populate the initial model with point-wise, best-fit wavefront travel-time approximations. Imaging is performed to obtain undifferentiated specular and non-specular representations of the volume. Specular boundaries are mapped using the imaged volume and using the boundaries to form a model of specular components of the volume. Beamforming is used to characterize seismic attributes associated with specular and non-specular reflections as separate and differentiated data sets.