Love Wave Propagation in Viscoelastic Media

Publication Date


Type of Culminating Activity


Degree Title

Doctor of Philosophy in Geophysics



Major Advisor

Paul Michaels, Ph.D.


Surface wave measurements have been used to compute dynamic soil properties for near surface site characterization and the dynamic design of foundations. Much of this work has been done with Rayleigh waves which are dependent on both the shear and compressive wave properties of the soil. Love waves, on the other hand, are sensitive only to the shear wave response of the soil. This shear only sensitivity greatly simplifies determining the damping and stiffness of a near surface soil profile. Further, the mechanism of damping can be related to purely inertial interactions of the soil frame and pore fluids, free from compressive factors.

Traditionally, soils have been represented by elastic models. While elastic models are adequate in representing dry or impermeable soils, they fail to account for observed body wave dispersion in permeable, water saturated soils. To overcome this limitation, a viscoelastic model can be used. In this work, representation of Love wave propagation is extended to viscoelastic media. This extension involves replacing classic Hooke's law by viscoelastic Hooke's law. This is done by introducing a shear strain rate term. As a result of this extension, Love wave phase velocity and motion-stress vectors become complex quantities.

A method is presented to solve for Love wave modes, combining a grid search with steepest descent search. The solution to this forward problem yields the dispersion and attenuation curves. Also computed are the complex motion-stress vectors for a vertically heterogeneous, viscoelastic medium, with shear viscosity as a specific material property. The viscoelastic constitutive model will lead to an improved representation of Love wave propagation in permeable, water saturated soils where the concept of effective viscosity becomes inappropriate.

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