An acoustic borehole logging system for generation and detection of multipole modes used to determine elastic properties of earth formations characterized as inhomogeneous anisotropic solids. The system concurrently generates and senses monopole, dipole, quadrupole and any higher order pole in the borehole/formation system in order to characterize the elastic properties and stress state of material penetrated by the borehole. Multipole modes of all orders are induced simultaneously without the need for separate transmitter and receiver systems. Performance of the logging system is not compromised due to eccentering of the axis of the tool in the borehole, tool tilt with respect to the axis of the borehole, or mismatch of response sensitivity of multiple receivers within the tool. The system comprises apparatus for generating and sensing acoustic signals in a borehole in an earth formation, and further comprises a processing method by which the sensor response signals are processed and analyzed to obtain desired formation parameters of interest.