Multi-frequency borehole imager

An apparatus for imaging an earth formation, the apparatus including: a logging instrument configured to be conveyed through a borehole penetrating the earth formation; a source of acoustic waves disposed at the logging instrument, wherein the source is configured to emit first acoustic waves having at least a first frequency and to enable intermodulation of the first acoustic waves in a medium having a nonlinear acoustic property resulting in generating new acoustic waves that are transmitted to the earth formation, the new acoustic waves having a new frequency different from the at least first frequency; and a receiver of acoustic waves configured to receive the new acoustic waves reflected from the earth formation, wherein the received new acoustic waves provide an image of the earth formation.