Method and apparatus for geophysical formation evaluation measurements behind casing

A system comprising:

• an acoustic logging tool having a receiver array and one or more directional acoustic or ultrasonic transmitters configured to sample different propagation paths between the one or more directional acoustic or ultrasonic transmitters and the receiver array, the acoustic logging tool configured to acquire a plurality of waveform data sets at a wellbore depth corresponding to a target subterranean formation zone adjacent to casing or tubing, wherein the plurality of waveform data sets comprises a first waveform data set corresponding to a first propagation path regime and a second waveform data set corresponding to a second propagation path regime;
• at least one processor in communication with the acoustic logging tool, wherein the at least one processor is coupled with a non-transitory computer-readable storage medium having stored therein instructions which, when executed by the at least one processor, causes the at least one processor to:
• determine a total wavefield across the receiver array of the acoustic logging tool at the wellbore depth;
• generate a first Green's function based on the first waveform data set and a second Green's function based on the second waveform data set, the first Green's function representing the first propagation path regime and the second Green's function representing the second propagation path regime;
• determine a noise wavefield by convolving the first Green's function, the second Green's function, a known transmitted pressure signal corresponding to the first waveform data set and a known transmitted pressure signal corresponding to the second waveform data set;
• and
• generate a reduced-noise wavefield by subtracting the noise wavefield from the total wavefield.