Fractal mechanical network based time domain viscoacoustic wave equation

Seismic waves propagating in the Earth media exhibit an approximate constant-Q behavior in seismic frequency bands and can be parameterized by the frequency independent Q (constant-Q) model. The constant-Q model that is derived mathematically lacks a physical basis. In this study, we propose a fractal mechanical network model with alternating springs and dashpots to provide this mathematical model a physical motivation. With this, we derive a new time domain viscoacoustic wave equation where fractional Laplacian power terms are independent of the model heterogeneity. This equation can characterize the heterogeneous Q models accurately and computationally efficiently.