Seismic Wave Speeds Derived from Nuclear Resonant Inelastic X-ray Scattering for Comparison with Seismological Observations

Brent Delbridge,Miaki Ishii

doi:10.3390/min10040331

Brent Delbridge, Miaki Ishii

Open Access

https://doi.org/10.3390/min10040331

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Journal: Minerals	Publication Date: Apr 8, 2020
Citations: 2	License type: CC BY 4.0

Affiliation: Planetary Science Institute, Harvard University

Abstract

Nuclear resonant inelastic X-ray scattering (NRIXS) experiments have been applied to Earth materials, and the Debye speed is often related to the material’s seismic wave speeds. However, for anisotropic samples, the Debye speed extracted from NRIXS measurements is not equal to the Debye speed obtained using the material’s isotropic seismic wave speeds. The latter provides an upper bound for the Debye speed of the material. Consequently, the acoustic wave speeds estimated from the Debye speed extracted from NRIXS (Nuclear Resonant Inelastic X-ray Scattering) measurements are underestimated compared to the material’s true seismic wave speeds. To illustrate the differences, the effects of various assumptions used to estimate the Debye speed, as well as seismic wave speeds, are examined with iron alloys at Earth’s inner core conditions. For the case of pure iron, the variation of the crystal orientation relative to the incoming X-ray beam causes a 40 % variation in the measured Debye speed, and leads to 3% and 31% underestimation in the compressional and shear wave speeds, respectively. Based upon various iron alloys, the error in the inferred seismic shear wave speed strongly depends upon the strength of anisotropy that can be quantified. We can also derive Debye speeds based upon seismological observations such as the PREM (Preliminary Reference Earth Model) and inner core anisotropy model. We show that these seismically derived Debye speeds are upper bounds for Debye speeds obtained from NRIXS experiments and that interpretation of the Debye speeds from the NRIXS measurements in terms of seismic wave speeds should be done with utmost caution.

Highlights

Advances in instrumentation and experimental techniques are allowing for rapid improvement in the use of lattice dynamics to determine the elastic moduli of materials at high pressure (e.g., [1,2]).Inelastic scattering of synchrotron radiation is used to probe the mechanical properties of condensed matter
The seismic wave speeds of materials at high pressure and high temperature are often estimated from the partial phonon density of states obtained from nuclear resonant inelastic scattering experiments
This manuscript demonstrates that the Debye speeds extracted from these experiments are not equivalent to the Debye speed estimated from that material’s seismic wave speeds

Summary

Introduction

Advances in instrumentation and experimental techniques are allowing for rapid improvement in the use of lattice dynamics to determine the elastic moduli of materials at high pressure (e.g., [1,2]). The study highlights the difficulty of comparing NRIXS derived Debye speeds with seismically observed wave speeds This is demonstrated by showing the effects of the various approximations to the calculation of the Debye speed for the case of several iron alloys at inner core pressures and temperatures. These results are crucial for using NRIXS measurements of the Debye speed in geophysical applications, and a new methodology is derived that avoids the isotropic assumptions which are currently a large source of error in procedures which extract seismic wave speeds from NRIXS measurements

Theory

D 2 E D 2 E

Results and Discussion

Variations in the Debye Speed

Extracting Seismic Wave Speeds

Conclusions