Quadruple transmitter and methods to determine wave velocities of a downhole formation

A downhole acoustic tool, comprising:

• a quadrupole transmitter, comprising:
• at least two piezoelectric rings that alternatively contract and expand;
• and
• a windowed sleeve surrounding the at least two piezoelectric rings and having a first portion and a second portion adjacent to the first portion, wherein the first portion and the second portion are each formed from a plurality of window sections and adjacent covered sections that are positioned around different sections of the at least two piezoelectric rings to allow transmission of quadrupole acoustic signals when the at least two piezoelectric rings are simultaneously excited;
• and
• a receiver to receive signals of waves transmitted through a formation proximate the downhole acoustic tool.

A method to determine wave velocities of a downhole formation, comprising:

• deploying a quadrupole transmitter in a borehole of a well, the quadrupole transmitter comprising:
• a first piezoelectric ring;
• a second piezoelectric ring;
• and
• a windowed sleeve surrounding the first piezoelectric ring and the second piezoelectric ring and having a first portion and a second portion adjacent to the first portion,
• wherein the first portion and the second portion are each formed from a plurality of window sections and adjacent covered sections that are positioned around different sections of the first piezoelectric ring and the second piezoelectric ring to allow transmission of quadrupole acoustic signals when the first piezoelectric ring and the second piezoelectric ring are simultaneously excited;
• simultaneously exciting the first piezoelectric ring and the second piezoelectric ring to alternatively contract and expand in opposite radial directions to generate quadrupole acoustic signals;
• detecting the quadrupole acoustic signals that are transmitted through a formation proximate the quadrupole transmitter;
• and
• calculating wave velocities of the formation based on the detected quadrupole acoustic signals.