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3 Seismic Wave Velocities in Earth’s Mantle from Mineral Elasticity
Johannes Buchen
Seismological Laboratory, California Institute of Technology, Pasadena, CA, USA
ABSTRACT
The propagation of seismic waves through Earth’s mantle is controlled by the elastic properties of the minerals that form mantle rocks. Changes in pressure, temperature, and chemical composition of the mantle as well as phase transitions affect seismic wave speeds through their impact on mineral elasticity. The elastic properties of minerals can be determined in experiments and by first-principle computations and be combined to model the elastic wave speeds of mantle rocks. Based on recent advances, I evaluate the uncertainties on modeled elastic wave speeds and explore their sensitivity to physical and chemical key parameters. I discuss the elastic properties of solid solutions and elastic anomalies that arise from continuous phase transitions, such as spin transitions and ferroelastic phase transitions. Models for rocks of Earth’s lower mantle indicate that continuous phase transitions and Fe‐Mg exchange between major mantle minerals can have significant impacts on elastic wave speeds. When viewed in context with other constraints on the structure and dynamics of the lower mantle, mineral-physical models for the elastic wave speeds of mantle rocks can help to separate thermal from compositional signals in the seismic record and to identify patterns of material transport through Earth's deep interior.
3.1 INTRODUCTION
Seismic waves irradiated from intense earthquakes propagate through Earth’s interior and probe the physical properties of materials that constitute Earth’s mantle. Analyzing travel times and wave forms of seismic signals allows reconstructing the propagation velocities of seismic waves in Earth’s interior. With the fast‐growing body of seismic data and improvements in seismological methods, such reconstructions reveal more and more details about Earth’s deep seismic structure. The propagation velocities of body waves, i.e., compressional (P) and shear (S) waves, are mainly controlled by the elastic properties of the mantle. The interpretation of seismic observations therefore requires a profound understanding of how pressure, temperature, and chemical composition affect the elastic properties of candidate materials. High‐pressure experiments and quantum‐mechanical calculations have been devised to sample thermodynamic and elastic properties of deep-earth materials by simulating the extreme conditions deep within Earth’s mantle. Their results serve as anchor points for thermodynamic models that allow predicting the elastic properties of mantle rocks for comparison with seismic observations.
The task of assessing the composition of Earth’s interior by comparing seismic velocities with elastic properties of candidate materials was pioneered by Francis Birch (Birch, 1964, 1952). Building on the work of Murnaghan (Murnaghan, 1937), Birch was also among the first to advance finite‐strain theory for describing the elastic properties of materials subjected to strong compressions (Birch, 1947, 1939, 1938). Further extensions and generalizations of finite‐strain formulations (Davies, 1974; Thomsen, 1972a) lead to widespread and successful applications of finite‐strain theory in modeling seismic properties of mantle materials (Bass & Anderson, 1984; Cammarano et al., 2003; Cobden et al., 2009; Davies and Dziewonski, 1975; Duffy & Anderson, 1989; Ita & Stixrude, 1992; Jackson, 1998; Stixrude & Lithgow‐Bertelloni, 2005). Today, compilations of finite‐strain and thermodynamic parameters for mantle minerals and dedicated software tools allow computing phase diagrams for typical rock compositions together with elastic properties (Chust et al., 2017; Connolly, 2005; Holland et al., 2013; Stixrude & Lithgow‐Bertelloni, 2011). Mineral‐physical databases have proven particularly useful in modeling the seismic properties of Earth’s mantle to depths of about 900 km (Cammarano et al., 2009; Cobden et al., 2008; Xu et al., 2008). To some extent, this success reflects current capabilities of high‐pressure experiments as most major minerals of the upper mantle and transition zone can be synthesized and their elastic properties be determined for relevant compositions and at realistic pressures and temperatures, limiting the need for far extrapolations.
For the lower mantle, however, the situation is different as information on the elastic properties of minerals and rocks at pressures and temperatures spanning those of Earth’s lower mantle is more challenging to retrieve, both from experiments and computations. This might be one reason why attempts to interpret the seismic structure of the lower mantle based on incomplete mineral‐physical data have led to contradicting conclusions about the composition and temperature profile of the lower mantle (Cobden et al., 2009; Khan et al., 2008; Matas et al., 2007; Mattern et al., 2005). In recent years, however, important progress has been made in constraining the elastic properties of lower-mantle minerals at high pressures and high temperatures, as for instance by experimental measurements on different bridgmanite compositions (Fu et al., 2018; Kurnosov et al., 2017; Murakami et al., 2012), on unquenchable cubic calcium‐silicate perovskite (Gréaux