An acoustic logging tool is disposed in a wellbore during an acidizing operation. Measurements are made using the acoustic logging tool on a region of a formation penetrated by the wellbore and being subjected to the acidizing operation. An acoustic anisotropic property of the formation is inferred at one or more depths of investigation within the region using the measurements, and a wormhole porosity and/or an orientation of one or more wormholes resulting from the acidizing operation is determined. Acidizing operation management decisions may be made based on the determined wormhole porosity and/or orientations of the wormholes. An acidizing operation management decision may be to maintain, increase, or decrease an acid injection rate. Measurements made may include the velocity of an acoustic wave propagating through the formation and the acoustic anisotropic properties of fast waves and slow waves. The acoustic anisotropic properties of the formation generally depend on rock stiffness.