Seismic Q revisited

Abstract

This paper revisits the theories of Q (quality factor) as a measure of the attenuation and velocity dispersion of a wave field. Q is a dimensionless measure of energy loss per cycle, and a proper understanding is important in a variety of fields, from seismology, geophysical prospecting to acoustics of materials. Measurements for standing modes and propagating waves differ and yield the temporal and spatial Q, respectively. This distinction is largely ignored in the literature. The relationship between these Qs is investigated for a power-law stress–strain relation based on spatial fractional derivatives that describes the behavior of compressional waves when combined with the conservation of momentum equation. In addition, the relationship between the quality factors for low-loss media proposed by Knopoff et al. 60 years ago is verified.