what is relationship between resonance frequency and s and p-wave velocities for a rock core sample?
Dear Zaheer, Goodafternoon and Fraternal greetings!
Thank you for your question and my answer is as follows
P-wave velocity test that can be carried out both in the laboratory and on-site is a common non-destructive testing method used in civil, geotechnical and mining projects.
The method is also commonly used for determination of rock weathering degree and rock
mass characterization. Thill and Bur (1969) stated that the P-wave velocity changes with
porosity and degree of saturation.
In a great variety of laboratory experiments over large intervals in stress, strain, and frequency, rocks display pronounced nonlinear elastic behavior. Two important features of nonlinear resonant behavior are a shift in resonant frequency away from the linear resonant frequency as the amplitude of the disturbance is increased and the harmonics in the time signal that accompany this shift. Generally, samples with resonant frequencies of approximately 0.5-1.5 kHz display resonant frequency shifts of 10% or more, over strain intervals of 10-7 to 10-6 and under a variety of saturation conditions and ambient pressure conditions. Resonant peak shift is not always observed, even at large drive levels; however, harmonics are always observed even in the absence of peak shift when detected strain levels exceed 10-7 or so.
Frequency dispersion has limited the use of the ultrasonically determined P- and S-wave velocity of fluid saturated rock sample to the seismic exploration. However, it has been a consensus that the bulk and shear modulus determined from laboratory measured P- and S-wave velocities on dry samples can be directly used in fluid substitution at seismic frequency. Based on the P- and S-wave velocity measurement on dry samples, the low frequency seismic velocities can be calculated from the effective bulk moduli (Keff) according to Gassmanís formula (Gassman 1951) assuming that the shear modulus is not changed by liquid saturation.
Dr D S Subrahmanyam