Downhole Acoustic Mapping

A system comprising:

• a downhole tool for operation within a wellbore, wherein the downhole tool comprises:
• a first transmitter unit located at a first axial location of the downhole tool and operable to transmit a first acoustic signal at a first frequency that is less than 30 kilohertz;
• a first receiver unit located at a second axial location axially offset from the first axial location and operable to measure amplitude of the first acoustic signal;
• a second receiver unit located at a third axial location axially offset from the first and second axial locations and operable to measure amplitude of the first acoustic signal;
• a second transmitter unit comprising a plurality of transmitters azimuthally distributed around a longitudinal axis of the downhole tool at a fourth axial location axially offset from the first, second, and third axial locations, wherein each transmitter of the second transmitter unit is operable to transmit a second acoustic signal at a second frequency that is greater than 50 kilohertz;
• a third receiver unit comprising a plurality of receivers azimuthally distributed around the longitudinal axis and located at a fifth axial location axially offset from the first, second, third, and fourth axial locations, wherein each receiver of the third receiver unit is operable to measure amplitude of the second acoustic signal;
• and
• a fourth receiver unit comprising a plurality of receivers azimuthally distributed around the longitudinal axis and located at a sixth axial location axially offset from the first, second, third, fourth, and fifth axial locations, wherein each receiver of the fourth receiver unit is operable to measure amplitude of the second acoustic signal;
• and
• surface equipment disposed at a wellsite surface from which the wellbore extends, wherein one or both of the downhole tool and the surface equipment are individually and/or cooperatively operable to detect an empty space within cement behind a casing installed in the wellbore, based on the amplitude measurements obtained by one or more of the first, second, third, and fourth receiver units at two or more different azimuthal locations.