Q: A Review

The quality factor Q is a dimensionless measure of the energy loss per cycle of a wave field, and a proper understanding of this factor is important in a variety of fields, from seismology, geophysical prospecting to electrical science. Here, the focus is on viscoelasticity. When interpreting experimental values, several factors must be taken into account, in particular the shape of the medium (rods, bars or unbounded media) and the fact that the measurements are made on stationary or propagating modes. From a theoretical point of view, the expressions of Q may differ due to different definitions, the spatial dimension and the inhomogeneity of the wave, i.e. the fact that the vectors of propagation (or wavenumber) and attenuation do not point in the same direction. We show the difference between temporal and spatial Q, the relationships between compressional and shear Q, the dependence on frequency, the case of poro-viscoelasticity and anisotropy, the effect of inhomogeneous waves and various loss mechanisms, and consider the analogy between elastic and electromagnetic waves. We discuss physical theories describing relaxation peaks, bounds on Q and experiments showing the behaviour of Q as a function of frequency, saturation and pore pressure. Finally, we propose an application example where Q can be used to estimate porosity and saturation.