In-situ measurement of damping ratio spectra from the inversion ofphase velocities of P and S waves in cross-hole seismic testing

Linear viscoelasticity is the simplest constitutive model able to capture the capacity exhibited by geomaterials to absorb and dissipate strain energy at low-strain dynamic excitations. An important result implied by this theory is the interdependency of phase velocity dispersion and damping ratio of P- and Swaves by the Kramers-Kronig dispersion relations which are nothing but a mathematical statement of the principle of physical causality. Recently obtained exact solutions of Kramers-Kronig relations establish a direct, functional relationship between material damping ratio and the speed of propagation of seismic waves which can be profitably used in experimental measurement of low-strain dynamic properties of geomaterials. Specifically, determination of material damping ratio spectra from phase velocity measurement of P - and S - waves through geophysical in-situ testing seems particularly attractive. This paper aims at providing a preliminary validation for an underway work of the authors whose ultimate goal is setting up a reliable methodology for the in-situ measurement of damping ratio from standard cross-hole seismic testing.