A simple demonstration of the frequency dependences of elastic moduli and the damping of stress waves at seismic frequencies

Abstract

Recognition of the frequency dispersion of seismic waves first arose from the study of the shapes of explosively generated pulses. Mathematically, the relevant dispersion relation has been derived with satisfying rigour, but the implied frequency dependences of elastic moduli have been difficult to demonstrate in a simple and convincing way. It is shown here that a torsional pendulum suffices to display the first order frequency dependence of the rigidity modulus for a hard plastic which is strongly dissipative, as represented by an anelastic Q factor of order 20. A similar direct demonstration for rocks is beset by the difficulty of reducing the strain amplitude to 10-6 or less, to bring the anelasticity into the linear range.