An experimental ultrasonic method to determine a scattering quality factor, with application to earth's inner core

Seismic attenuation can be intrinsic or due to scattering. The relative role of each for Earth's inner core is uncertain. Whereas intrinsic attenuation depends primarily on the material, temperature, and pressure, scattering is primarily a function of microstructure, that is, grain size, shape, texture, as well as single-crystal elastic anisotropy. Here we studied experimentally scattering of ultrasonic compressional waves in a hexagonal close-packed (hcp) Zn-rich Sn alloy, for two microstructures that are likely relevant to the inner core: textured, large columnar dendritic crystals typical of directional solidification, and untextured, equiaxed, ‘fine-grained’ crystals that can result from diffusion creep. We also studied the wavelength/grain size dependence of scattering for these two microstructures. We used a Zn-rich Sn alloy not because we expect it to have intrinsic attenuation similar to Fe under inner core conditions, but because its hcp crystal structure is the likely phase of the Fe alloy in the inner core, making it suitable for understanding the role of microstructure on scattering in the inner core. For the purpose of scaling the experiments to the inner core, pressure and temperature affect scattering primarily through their effects on the elastic constants of Fe and inner core growth dynamics, both of which we account for.

We developed an algorithm using the pulse-echo technique to experimentally determine a scattering quality factor Q_Z. We set criteria to determine, and measured, the energy per cycle in the first echo T₁, which is a measure of the transmitted energy, and the energy per cycle that is reflected before the first echo R₁, which represents the scattered energy. In order to facilitate comparison with seismic quality factors we defined a scattering quality factor Q_Z = (R₁ + T₁)/R₁. Scaling Q_Z from the laboratory experiments to the inner core depends on the magnitude of the single-crystal wave speed anisotropy, which is known for Zn, but uncertain for Fe under inner core conditions, so we scaled the experimental results for single-crystal Fe elastic anisotropy between 5 and 20 %.

As expected, we found a directionally solidified microstructure has a highly anisotropic Q_Z, showing almost no scattering in the growth direction, whereas in the transverse directions scattering attenuation in the inner core may be comparable to intrinsic attenuation. Taking into account the anisotropy factor for scattering in polycrystalline, anisotropic material, our results predict randomly oriented, equiaxed 10 km-sized grains in the inner core would exhibit more scattering attenuation that the total inferred seismic attenuation, ruling out such a microstructure. However, Q_Z increases rapidly for randomly oriented, equiaxed grain sizes smaller than 10 km, suggesting that the large lateral variations in seismic quality factor Q_P are most likely due to variations in grain size in the 0.1–0.10 km range. The largest uncertainty in our algorithm to determine Q_Z is scattered energy that arrives after the first echo, which we attempt to quantify.