Systems, devices, and methods for evaluating a volume of interest of an earth formation. Methods include estimating a parameter of interest of a volume of the formation using a value of a signal property (frequency amplitude) for a second harmonic mode signal component of a detected acoustic signal from the volume. Methods may include activating a transmitter to propagate an acoustic wave through the volume; producing the detected acoustic signal at a receiver responsive to the acoustic wave; and identifying the fundamental mode signal and the second harmonic mode signal associated with the detected acoustic signal. Methods include estimating an acoustic wave non-linearity parameter (β) for the volume using a relationship between the value of the signal property of the second harmonic mode signal component and a value of the signal property for a fundamental mode signal component of the detected acoustic signal.