The viscodynamics of a poroelastic material in the frequency domain has non-negligible dependence on frequency when it's higher than the 'critical' value. As a result, there is a time-convolution term (a.k.a. the memory term) in the time-domain equations. In this talk, we will take a closer look at this term and reveal its relation with the microstructure of the poroelastic material. We will see that it is just one example of the class of "causal" functions studied under the name of Nevanlinna-Stieltjes functions. The nice approximation structure of these functions can be utilized to design an effective time domain solver for the equations with memory terms. Numerical results will also be presented in this talk. The results presented in this talk is joint work with Hugo Woerdeman (Drexel U.), Jiangming Xie (Qinghua U., China) and Liwei Xu (Chengdu Tech, China).