Logical Inference for Model-Based Reconstruction of Ultrasonic Nonlinearity

Quantifying the constitutive nonlinearity parameter β in fluids is of key interest for understanding ultrasonic propagation and its wide implications in medical and industrial applications. However, current methods for ultrasonically measuring it show large limitations in that the signal is only valid at a reduced and unjustified spatial range away from the transducer. This is not consistent with the fact that β should be constant everywhere in the fluid and independently of the ultrasonic experimental setup. To overcome this, the nonlinear wave propagation equations are rigorously derived and the ensuing differential equation is numerically solved. As a second contribution, the experimental and model information sources are treated under the information theory context to probabilistically reconstruct β, providing not only its value, but also the degree of confidence on it given both sources of data. This method is satisfactorily validated testing the repeatability of β in water varying distances, energies, frequencies, and transducer setups, yielding values compatible with β = 3.5