Full-waveform tomography reveals iron spin crossover in Earth's lower mantle.

Three-dimensional models of Earth's seismic structure can be used to identify temperature-dependent phenomena, including mineralogical phase and spin transformations, that are obscured in 1-D spherical averages. Full-waveform tomography maps seismic wave-speeds inside the Earth in three dimensions, at a higher resolution than classical methods. By providing absolute wave speeds (rather than perturbations) and simultaneously constraining bulk and shear wave speeds over the same frequency range, it becomes feasible to distinguish variations in temperature from changes in composition or spin state. We present a quantitative joint interpretation of bulk and shear wave speeds in the lower mantle, using a recently published full-waveform tomography model. At all depths the diversity of wave speeds cannot be explained by an isochemical mantle. Between 1000 and 2500 km depth, hypothetical mantle models containing an electronic spin crossover in ferropericlase provide a significantly better fit to the wave-speed distributions, as well as more realistic temperatures and silica contents, than models without a spin crossover. Below 2500 km, wave speed distributions are explained by an enrichment in silica towards the core-mantle boundary. This silica enrichment may represent the fractionated remains of an ancient basal magma ocean.

Self-similar properties of avalanche statistics in a simple turbulent model.

In this paper, we consider a simplified model of turbulence for large Reynolds numbers driven by a constant power energy input on large scales. In the statistical stationary regime, the behaviour of the kinetic energy is characterized by two well-defined phases: a laminar phase where the kinetic energy grows linearly for a (random) time [Formula: see text] followed by abrupt avalanche-like energy drops of sizes [Formula: see text] due to strong intermittent fluctuations of energy dissipation. We study the probability distribution [Formula: see text] and [Formula: see text] which both exhibit a quite well-defined scaling behaviour. Although [Formula: see text] and [Formula: see text] are not statistically correlated, we suggest and numerically checked that their scaling properties are related based on a simple, but non-trivial, scaling argument. We propose that the same approach can be used for other systems showing avalanche-like behaviour such as amorphous solids and seismic events. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.

A multi-component lattice Boltzmann approach to study the causality of plastic events.

Using a multi-component lattice Boltzmann (LB) model, we perform fluid kinetic simulations of confined and concentrated emulsions. The system presents the phenomenology of soft-glassy materials, including a Herschel-Bulkley rheology, yield stress, ageing and long relaxation time scales. Shearing the emulsion in a Couette cell below the yield stress results in plastic topological re-arrangement events which follow established empirical seismic statistical scaling laws, making this system a good candidate to study the physics of earthquakes. One characteristic of this model is the tendency for events to occur in avalanche clusters, with larger events, triggering subsequent re-arrangements. While seismologists have developed statistical tools to study correlations between events, a process to confirm causality remains elusive. We present here, a modification to our LB model, involving small, fast vibrations applied to individual droplets, effectively a macroscopic forcing, which results in the arrest of the topological plastic re-arrangements. This technique provides an excellent tool for identifying causality in plastic event clusters by examining the evolution of the dynamics after 'stopping' an event, and then checking which subsequent events disappear. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

On interevent time distributions of avalanche dynamics.

Physical systems characterized by stick-slip dynamics often display avalanches. Regardless of the diversity of their microscopic structure, these systems are governed by a power-law distribution of avalanche size and duration. Here we focus on the interevent times between avalanches and show that, unlike their distributions of size and duration, the interevent time distributions are able to distinguish different mechanical states of the system. We use experiments on granular systems and numerical simulations of emulsions to show that systems having the same probability distribution for avalanche size and duration can have different interevent time distributions. Remarkably, these interevent time distributions look similar to those for earthquakes and, if different from an exponential, are indirect evidence of non trivial space-time correlations among avalanches. Our results therefore indicate that interevent time statistics are essential to characterise the dynamics of avalanches.

Sensitivity Kernels of PP Precursor Traveltimes and Their Limitations for Imaging Topography of Discontinuities.

We analyze the sensitivity of PP precursor traveltimes that are often used to infer lateral variation in the depths of the 410- and 660-km discontinuities in the mantle. Previous results were inconclusive due to complex wave phenomena, such as multiple energy conversions and focusing/defocusing, that hamper their interpretation. Using spectral-element synthetics and Fréchet derivatives calculated with adjoint methods, we compute sensitivity kernels for volumetric and boundary parameters in a 1-D model for representative epicentral distances of past studies, and a dominant period of 11-25 s. Our results indicate that the boundary sensitivity of PP precursors is low and that these phases are not coherently seen in exact synthetics. Our most important finding is the strong sensitivity to both shear and compressional wave speeds, indicating that wave interference and wave conversions are dominant. The PP precursor traveltimes appear more sensitive to structural parameters, that is, compressional and shear wave speed, than to the boundaries; therefore, they are unlikely sources for valuable insight into discontinuity topography.

Effects of Induced Stress on Seismic Waves: Validation Based on Ab Initio Calculations.

When a continuum is subjected to an induced stress, the equations that govern seismic wave propagation are modified in two ways. First, the equation of conservation of linear momentum gains terms related to the induced deviatoric stress, and, second, the elastic constitutive relationship acquires terms linear in the induced stress. This continuum mechanics theory makes testable predictions with regard to stress-induced changes in the elastic tensor. Specifically, it predicts that induced compression linearly affects the prestressed moduli with a slope determined by their local adiabatic pressure derivatives and that induced deviatoric stress produces anisotropic compressional and shear wave speeds. In this article we successfully compare such predictions against ab initio mineral physics calculations for NaCl and MgO.

The Collaborative Seismic Earth Model: Generation 1.

We present a general concept for evolutionary, collaborative, multiscale inversion of geophysical data, specifically applied to the construction of a first-generation Collaborative Seismic Earth Model. This is intended to address the limited resources of individual researchers and the often limited use of previously accumulated knowledge. Model evolution rests on a Bayesian updating scheme, simplified into a deterministic method that honors today's computational restrictions. The scheme is able to harness distributed human and computing power. It furthermore handles conflicting updates, as well as variable parameterizations of different model refinements or different inversion techniques. The first-generation Collaborative Seismic Earth Model comprises 12 refinements from full seismic waveform inversion, ranging from regional crustal- to continental-scale models. A global full-waveform inversion ensures that regional refinements translate into whole-Earth structure.

Insights on Upper Mantle Melting, Rheology, and Anelastic Behavior From Seismic Shear Wave Tomography.

In seismic tomography we map the wave speed structure inside the Earth, but we ultimately seek to interpret those images in terms of physical parameters. This is challenging because many parameters can trade-off with each other to produce a given wave speed. The problem is compounded by the convention of mapping seismic structures as perturbations relative to a 1-D reference model, rather than absolute wave speeds. Using a full waveform tomography model of Europe as a case study, we quantify the extent to which thermochemical and dynamic properties can be constrained using only S wave speed, expressed in absolute values. The wave speed distributions of this tomography model are compared with 4 million thermochemical models, whose seismic properties are computed via thermodynamic modeling. These models sample the full range of realistic mantle compositions, including variable water and melt contents, and mineral intrinsic anelasticity is taken into account. Intrinsic anelasticity causes waves to travel more slowly at higher temperatures, leading to seismic attenuation, but the sensitivity of the wave speed reduction to temperature is, in turn, controlled by the wave frequency. Global studies of surface waves indicate an anticorrelation between S wave speed and attenuation. We therefore only retain thermochemical models satisfying this anticorrelation. Our study indicates that the frequency dependence of anelasticity, α, depends on temperature or rheology, with α ≈ 0.1 being most appropriate in cold or lithospheric mantle and α ≈ 0.3 in warmer regions (i.e., the asthenosphere). Additionally, the slowest regions require specific compositions and/or a velocity-weakening mechanism, such as partial melting, elastically accommodated grain boundary sliding, or water.

Probabilistic tomography maps chemical heterogeneities throughout the lower mantle.

We obtained likelihoods in the lower mantle for long-wavelength models of bulk sound and shear wave speed, density, and boundary topography, compatible with gravity constraints, from normal mode splitting functions and surface wave data. Taking into account the large uncertainties in Earth's thermodynamic reference state and the published range of mineral physics data, we converted the tomographic likelihoods into probability density functions for temperature, perovskite, and iron variations. Temperature and composition can be separated, showing that chemical variations contribute to the overall buoyancy and are dominant in the lower 1000 kilometers of the mantle.

Robust normal mode constraints on inner-core anisotropy from model space search.

A technique for searching full model space that was applied to measurements of anomalously split normal modes showed a robust pattern of P-wave and S-wave anisotropy in the inner core. The parameter describing P-wave anisotropy changes sign around a radius of 400 kilometers, whereas S-wave anisotropy is small in the upper two-thirds of the inner core and becomes negative at greater depths. Our results agree with observed travel-time anomalies of rays traveling at epicentral distances varying from 150 degrees to 180 degrees. The models may be explained by progressively tilted hexagonal close-packed iron in the upper half of the inner core and could suggest a different iron phase in the center.

Global azimuthal anisotropy in the transition zone.

Surface wave dispersion measurements for Love wave overtones carry evidence of azimuthal anisotropy in the transition zone of Earth's mantle (400 to 660 kilometers deep). A Backus-Gilbert inversion of anisotropic phase velocity maps, with resolution kernels mainly sensitive to the transition zone, shows a robust long-wavelength azimuthally anisotropic velocity structure. This observation puts new constraints on the mineralogy and dynamics of the transition zone because this anisotropy may result from aligned minerals, tilted laminated structures, or even organized pockets of fluid inclusions.