Mantle Convection and Surface Expressions. Группа авторов

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СКАЧАТЬ 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 et al., 2019; Thomson et al., 2019), and on the calcium‐ferrite structured phase (Dai et al., 2013), as well as by better constraining thermoelastic parameters through experiments and computations (Gréaux et al., 2016; Murakami et al., 2012; Yang et al., 2016; Zhang et al., 2013). Similarly, experiments on single crystals (Antonangeli et al., 2011; Crowhurst et al., 2008; Marquardt et al., 2009c, 2009b; Yang et al., 2015), improved computational methods (Wu et al., 2013; Wu and Wentzcovitch, 2014), and measurements at seismic frequencies (Marquardt et al., 2018) have advanced our understanding of how the spin transition of ferrous iron affects the elastic properties of ferropericlase. Many of these and other achievements have not yet been incorporated into mineral‐physical databases, and the effects of spin transitions on mineral elasticity are not accounted for by commonly applied finite‐strain formalisms.

      This chapter aims to review recent advancements in experimental and computational mineral physics on the elastic properties of mantle minerals. A brief introduction to finite‐strain theory and to the elastic properties of minerals and rocks is followed by an overview of experimental and computational methods used to determine elastic properties of minerals at pressures and temperatures of Earth’s mantle. To assess the resilience and reliability of mineral‐physical models and their potential to explain seismic observations, I systematically evaluate how uncertainties on individual finite‐strain parameters impact computed elastic wave velocities for major mantle minerals and address the effect of inter‐ and extrapolating elastic properties across complex solid solutions. This analysis aims at revealing the leverages of finite‐strain parameters and extrapolations in chemical compositions on elastic wave velocities in order to guide future efforts to improve mineral‐physical models by reducing uncertainties on key parameters and compositions. With a particular focus on minerals of the lower mantle, I discuss the effect of continuous phase transitions on elastic properties, including ferroelastic phase transitions and spin transitions. A volume-dependent formulation for spin transitions is proposed that is readily combined with existing finite‐strain formalisms. To provide an up‐to‐date perspective on the elastic properties of Earth’s lower mantle, I combine most recent elasticity data and derive elastic wave velocities for a selection of potential mantle rocks, taking into account spin transitions in ferrous and ferric iron and the ferroelastic phase transition in stishovite. A comparison of scenarios for different assumptions about compositional parameters reveals persisting challenges in the mineral physics of the lower mantle.

3.2 ELASTIC PROPERTIES

When a seismic wave passes through a rock, the wave imposes stresses and strains on the rock and on the individual mineral grains that compose the rock. In Earth’s mantle, these stresses and strains are much smaller than those that arise from compression and heating of the rock to pressures and temperatures in the mantle. The mineral grains or crystals react to compression and heating as well as to seismic waves mainly by reversible elastic deformation. For each crystal grain in the rock, the small stresses and strains imposed by a seismic wave can be assumed to obey a linear relationship between the stress tensor σ_ij and the infinitesimal strain tensor e_ij (Haussühl, 2007; Nye, 1985):

      with the components of the elastic stiffness tensor c_ijkl and the elastic compliance tensor s_ijkl of the crystal.

      Large strains that arise from compression and thermal expansion can be described by the Eulerian finite‐strain tensor E_ij (Birch, 1947; Davies, 1974; Stixrude & Lithgow‐Bertelloni, 2005). For hydrostatic compression СКАЧАТЬ