On effective characteristic of Rayleigh surface wave propagation in porous fluid-saturated media at low frequencies

• We obtain viscoelastic representation for Rayleigh wave in poroelastic media.
• We examine the validity and limitation of the representation at low frequencies.
• The media of high critical frequency fc can show better effective representation.
• The effective behaves provide an applicable way for poroelastic surface waves.

The analytical dispersion and waveform solutions of Rayleigh surface wave for the Biot fluid-saturated model are obtained at low frequencies for a homogeneous half space. The equivalent solution is also obtained by the equivalent-viscoelastic representation of the fluid-saturated model based on a single viscoelastic element for each wave modulus. The effective characteristics of the validations and limitations for the equivalent-viscoelastic model are analyzed by comparison of the numerical solutions of the fluid-saturated model and the equivalent model for the surface wave propagations. Our calculations show that the free boundary effects on the frequency dependent dispersion and time dependent dynamical waveforms of the surface wave in the Biot model are well fitted in a relative narrow low frequency band by the Zener elements in case of the frequency is much lower than the critical frequency fcfc of the porous material. The effective characteristics for air filled cases with a higher fcfc show a better result. Furthermore, if the critical frequency fcfc is low, always with high permeability κκ under near surface condition, at low frequencies (e.g. the seismic frequency band <200 Hz) the surface fluid drainage conditions influence Rayleigh-wave propagations obviously. The frequency range must hence be carefully checked for the viscoelastic representations. When the validated frequency range is defined, the viscoelastic elements can solve the transient surface wave propagation in porous media effectively. The convolution integral in wave modeling can be replaced by memory variables, which makes the field quantities calculated at every time step need not be stored. The effective representation saves the consumptions of computer time and storages, and supplies a more convenient approach to apply the surface wave considering poroelasticity.