Is there seismic attenuation in the mantle?

- We relate the scattered elastic energy to the power spectrum of the mantle heterogeneities.
- The power spectrum of mantle heterogeneities should vary as inverse wavenumber.
- This implies a frequency independent apparent attenuation.
- 6-9% rms heterogeneities would account for the mantle seismic attenuation.

The small scale heterogeneity of the mantle is mostly due to the mixing of petrological heterogeneities by a smooth but chaotic convection and should consist in a laminated structure (marble cake) with a power spectrum S(k) varying as 1/k, where k is the wavenumber of the anomalies. This distribution of heterogeneities during convective stirring with negligible diffusion, called Batchelor regime is documented by fluid dynamic experiments and corresponds to what can be inferred from geochemistry and seismic tomography. This laminated structure imposes density, seismic velocity and potentially, anisotropic heterogeneities with similar 1/k spectra. A seismic wave of wavenumber k0 crossing such a medium is partly reflected by the heterogeneities and we show that the scattered energy is proportional to k0S(2k0). The reduction of energy for the propagating wave appears therefore equivalent to a quality factor 1/Q∝k0S(2k0). With the specific 1/k spectrum of the mantle, the resulting apparent attenuation should therefore be frequency independent. We show that the total contribution of 6-9% RMS density, velocity and anisotropy would explain the observed S and P attenuation of the mantle. Although these values are large, they are not unreasonable and we discuss how they depend on the range of frequencies over which the attenuation is explained. If such a level of heterogeneity were present, most of the attenuation of the Earth would be due to small scale scattering by laminations, not by intrinsic dissipation. Intrinsic dissipation must certainly exist but might correspond to a larger, yet unobserved Q. This provocative result would explain the very weak frequency dependence of the attenuation, and the fact that bulk attenuation seems negligible, two observations that have been difficult to explain for 50 years.