Relative Seismic Attenuation Estimation

The end goal of any solid Earth study is to better constrain physical parameters of the Earth (e.g. viscosity, temperature, and mineral composition). As we are unable to directly measure many of these quantities, past a few kilometers in depth, we must content ourselves with indirect estimates by way of experiment and theory. Just as geochemists do this by way of compositional deviations from pyrolite [ZH86], seismologists do this by way of deviations from seismically measurable quantities such as velocity, attenuation, and density. All of these quantities play a crucial role in developing our ability to better understand the solid Earth [VDHWE97]. Constraints on Earth’s deviation from being perfectly elastic over short time scales [Nol08] has remained a challenging problem and seen relatively little progress compared to studies focusing on seismic velocity [Rom99]. However, seismic velocity can not be used to constrain estimates of the Earth’s internal temperatures, compositions, or melt contents alone [Kar08]. We give a formulation of seismic attenuation in terms of a viscoelastic material, yielding a frequency dependent definition of attenuation. We then discuss application of attenuation to solid Earth studies. Finally, we develop a method for measuring attenuation that does not make use of synthetic data. The outline of this paper is as follows: We first develop the seismic theory of waves in a viscoelastic material following [Ken01]. We then discuss applications of seismic attenuation to solid Earth studies by using attenuation along with seismic velocity to put constraints on mantle temperatures, compositions, and melt contents. We then develop a new technique for measuring body wave attenuation by way of relative spectral ratios and apply it to a data set from the TA Array.