Time domain modeling of pulse propagation in non-isotropic dispersive media

Acoustic pulse propagation requires the inclusion of attenuation and its causal companion, dispersion when propagation is through a non-ideal fluid medium. For acoustic propagation in a linear medium, Szabo [T.L. Szabo, J. Acoust. Soc. Am., 96 (1994) 491–500] introduced the concept of a convolutional propagation operator that plays the role of a casual propagation factor in the time domain. The resulting modified wave equation is solved via the method of finite differences. One aspect of the acoustic field that is of interest to researchers is the monostatic-backscattered field. This field which by definition is small compared to the forward-propagated field is challenging to isolate. Since the numerical grid is of finite size, the received signal has the possibility of being contaminated with spurious reflections coming from the walls of the computational grid even if absorbing boundary conditions (ABCs) are imposed. Therefore, a robust highly accurate absorbing boundary condition is developed. In addition, the finite difference description of the modified wave equation is developed having fourth-order accuracy in both time and space.