Frequency domain stacking of acoustic dipole LWD measurements

An acoustic logging while drilling tool comprising:

• a logging while drilling tool body;
• an acoustic transmitter deployed in the logging while drilling tool body;
• a directional acoustic receiver including a plurality of circumferentially spaced receiver arrays deployed in the logging while drilling tool body axially spaced from the acoustic transmitter;
• a controller deployed in the logging tool body and configured to:
• cause the acoustic transmitter and the direction acoustic receiver to make a plurality of directional sonic logging measurements while the logging while drilling tool rotates in a wellbore;
• identify a plurality of orthogonal pairs of measurements among the plurality of directional sonic logging measurements, wherein each of the plurality of orthogonal pairs includes a first measurement and a second measurement, wherein a measured angle of a transmitter firing direction of the first measurement is orthogonal with a measured angle of a transmitter firing direction of the second measurement within a predetermined tolerance;
• compile 4C component waveforms for each of the identified plurality of orthogonal pairs of measurements;
• rotate the compiled 4C component waveforms to align with predefined axes;
• transform selected ones of the rotated 4C component waveforms to a frequency domain;
• and
• stack the transformed rotated waveforms in the frequency domain to compute a median or average slowness at each of a plurality of frequencies.

A method for acoustic logging a wellbore, the method comprising:

• rotating a logging tool in a wellbore penetrating a subterranean formation, the logging tool including an acoustic transmitter and a directional acoustic receiver including a plurality of circumferentially spaced receiver arrays;
• making a plurality of directional sonic logging measurements while rotating the logging tool in the wellbore;
• retaining ones of the plurality of directional sonic logging measurements for which a monopole component is less than a threshold and discarding the remainder of the plurality of directional sonic logging measurements;
• rotating selected ones of the retained waveforms to align with predefine axes;
• stacking the rotated waveforms in the time domain;
• transforming the rotated waveforms to the frequency domain;
• and
• stacking the transformed rotated waveforms in the frequency domain to compute a median or average slowness at each of a plurality of frequencies.