Modelling of sound propagation in media with continuously changing properties towards a locally resolved measurement of sound velocity

A new method to measure sound velocity and distance in homogeneous media simultaneously had been developed. It works with only one transducer and needs no additional reflectors at known positions. Instead the echoes of moving scattering particles are analyzed to determine the focus position as a second piece of information. An annular array allows to move the focus along the acoustic axis of the transducer and so to measure locally resolved. To reach also high accuracy for media with continuously changing properties, the sound field of the transducer has to be calculated within these media. A first approach for simulation by using Fermat's principle is presented and compared to measurement results. It can be shown, that this model is not sufficient and that the wave equation with additional terms has to be derived and solved.