Seismic scanning tunneling macroscope: Theory

We propose a seismic scanning tunneling macroscope (SSTM) that can detect the presence of sub-wavelength scatterers in the near-field of either the source or the receivers. Analytic formulas for the time reverse mirror (TRM) profile associated with a single scatterer model show that the spatial resolution limit to be, unlike the Abbe limit of /2, independent of wavelength and linearly proportional to the source-scatterer separation as long as the point scatterer is in the near-field region; if the sub-wavelength scatterer is a spherical impedance discontinuity then the resolution will also be limited by the radius of the sphere. Therefore, superresolution imaging can be achieved as the scatterer approaches the source. This is analogous to an optical scanning tunneling microscope that has sub-wavelength resolution. Scaled to seismic frequencies, it is theoretically possible to extract 100 Hz information from 20 Hz data by imaging of near-field seismic energy.