Seismic, viscoelastic attenuation

Abstract

The intrinsic attenuation of seismic waves in the earth has been found to be consistent with loss mechanisms that are thermally activated. The observed regional and frequency dependences of seismic Q agree with the expected lateral variations in a geotherm having a rapid temperature increase in the upper 400 km of the mantle, followed by a slower vertical and lateral variation in the mid-and lower mantle. High velocities correlate with regions of low attenuation; low seismic velocities correlate with regions of high attenuation. Measurements are consistent with losses primarily in shear rather than bulk deformations. The existence of lateral heterogeneity in the elastic properties of the Earth complicates the measurement of viscoelastic properties. The longer scale lengths of heterogeneity can split modes of free oscillation and focus and defocus body waves and surface waves. Shorter scale lengths scatter seismic energy, broaden the waveforms of body waves, and redistribute energy into different time and angular windows. Observations that are useful for discriminating between the effects of scattering attenuation versus viscoelastic attenuation include the ratio of apparent P wave attenuation to apparent S wave attenuation, the rate of velocity dispersion within a frequency band, and the apparent viscoelastic modulus defect. The intensity of heterogeneity in percent fluctuation of velocities and densities is higher at shorter scale lengths at shallower depths in the Earth’s crust and upper mantle. There is still a need for experiments that determine finer details of how the distribution of heterogeneity changes with depth and lateral location in the Earth and its anisotropy of scale lengths. Many, if not most experiments, have not completely removed the effects of heterogeneity on the apparent attenuation, making their results an upper bound on the viscoelastic Q1. Laboratory experiments find a transition from linear to non-linear rheology at strains of the order of 106. The observed strain dependence of Q and its dependence on pressure in the shallow crust agree with a mechanism of frictional sliding of cracks. It is still unknown how and at what strain levels linear superposition begins to break down close to a seismic source. Although a consensus has been reached on the major features and thermal activation of intrinsic attenuation in most of the Earth’s upper mantle, this is less true of other deep regions of the Earth. Definitive experiments are still needed for the determination of Q1 in the lowermost 400 km of the mantle, where increased lateral heterogeneity exists across a broad spatial spectrum, complicating the separation of its effects from those of viscoelasticity. A concept unifying lateral variations in velocity, elastic anisotropy, scattering, and apparent attenuation in the uppermost inner core is needed (e.g., Calvet and Margerin, 2008).