A compact array of transducers (110, 120) is employed as a downhole instrument for acoustic investigation of the surrounding rock formation. The array is operable to generate simultaneously a first acoustic beam signal (110) at a first frequency and a second acoustic beam signal (120) at a second frequency different than the first frequency. These two signals can be oriented through an azimuthal rotation of the array and an inclination rotation using control of the relative phases of the signals from the transmitter elements or electro-mechanical linkage. Due to the non-linearity of the formation (140), the first and the second acoustic beam signal (110, 120) mix into the rock formation where they combine into a collimated third signal (150) that propagates in the formation along the same direction than the first and second signals and has a frequency equal to the difference of the first and the second acoustic signals. The third signal is received either within the same borehole, after reflection, or another borehole, after transmission, and analyzed to determine information about rock formation.