Magmatic evolution of the material of the Earth’s lower mantle: Stishovite paradox and origin of superdeep diamonds (Experiments at 24–26 GPa)

The ultrabasic–basic magmatic evolution of the lower mantle material includes important physicochemical phenomena, such as the stishovite paradox and the genesis of superdeep diamonds. Stishovite SiO₂ and periclase–wüstite solid solutions, (MgO · FeO)_ss, associate paradoxically in primary inclusions of superdeep lower mantle diamonds. Under the conditions of the Earth’s crust and upper mantle, such oxide assemblages are chemically impossible (forbidden), because the oxides MgO and FeO and SiO₂ react to produce intermediate silicate compounds, enstatite and ferrosilite. Experimental and physicochemical investigations of melting phase relations in the MgO–FeO–SiO₂–CaSiO₃ system at 24 GPa revealed a peritectic mechanism of the stishovite paradox, (Mg, Fe)SiO₃ (bridgmanite) + L = SiO₂ + (Mg, Fe)O during the ultrabasic–basic magmatic evolution of the primitive oxide–silicate lower mantle material. Experiments at 26 GPa with oxide–silicate–carbonate–carbon melts, parental for diamonds and primary inclusions in them, demonstrated the equilibrium formation of superdeep diamonds in association with ultrabasic, (Mg, Fe)SiO₃ (bridgmanite) + (MgO · FeO)_ss (ferropericlase), and basic minerals, (FeO · MgO)_ss (magnesiowüstite) + SiO₂ (stishovite). This leads to the conclusion that a peritectic mechanism, similar to that responsible for the stishovite paradox in the pristine lower mantle material, operates also in the parental media of superdeep diamonds. Thus, this mechanism promotes both the ultrabasic–basic evolution of primitive oxide–silicate magmas in the lower mantle and oxide–silicate–carbonate melts parental for superdeep diamonds and their paradoxical primary inclusions.     

Solubility of hydrogen and carbon in reduced magmas of the early Earth’s mantle

The solubility of volatile compounds in magmas and the redox state of their mantle source are the main factors that control the transfer of volatile components from the planet’s interior to its surface. In theories of the formation of the Earth, the composition of gases extracted by primary planetary magmas is accounted for by the large-scale melting of the early mantle in the presence of the metallic Fe phase [1, 2]. The fused metallic Fe phase and the melted silicate material experienced gravitational migration that exerted influence upon the formation of the metallic core of the planet. The large-scale melting of the early Earth should have been accompanied by the formation of volatile compounds, whose composition was controlled by the interaction of H and C with silicate and metallic melts, a process that remains largely unknown as of yet.     

Low‐frequency wave propagation in periodically layered media

In this paper, we consider wave propagation in a layered medium. Using the Baker‐Campbell‐Hausdorff series, we expand the logarithm of a propagator matrix in series of frequency. The series coefficients allow us to extend the effective Backus medium for low frequencies. The proposed technique is applied to vertical propagation in a periodically layered and binary medium as well as for a gradient medium. The velocity dispersion equations are derived for these media. We also consider the layered medium with monoclinic anisotropy. We illustrate the accuracy of the proposed method on synthetic and well‐log data.     

A unified approach to self-calibration of terrestrial laser scanners

In recent years, the method of self-calibration widely used in photogrammetry has been found suitable for the estimation of systematic errors in terrestrial laser scanners. Since high correlations can be present between the estimated parameters, ways to reduce them have to be found. This paper presents a unified approach to self-calibration of terrestrial laser scanners, where the parameters in a least-squares adjustment are treated as observations by assigning appropriate weights to them. The higher these weights are the lower the parameter correlations are expected to be. Self-calibration of a pulsed laser scanner Leica Scan Station was performed with the unified approach. The scanner position and orientation were determined during the measurements with the help of a total station, and the point clouds were directly georeferenced. The significant systematic errors were zero error in the laser rangefinder and vertical circle index error. Most parameter correlations were comparatively low. In part, precise knowledge of the horizontal coordinates of the scanner centre helped greatly to achieve low correlation between these parameters and the zero error. The approach was shown to be advantageous to the use of adjustment with stochastic (weighted) inner constraints where the parameter correlations were higher. At the same time, the collimation error could not be estimated reliably due to its high correlation with the scanner azimuth because of a limited vertical distribution of the targets in the calibration field. While this problem can be solved for a scanner with a nearly spherical field-of-view, it will complicate the calibration of scanners with limited vertical field-of-view. Investigations into the influence of precision of the scanner position and levelling on the adjustment results lead to two important findings. First, it is not necessary to level the scanner during the measurements when using the unified approach since the parameter correlations are relatively low anyway. Second, the scanner position has to be known with a precision of about 1 mm in order to get a reliable estimate of the zero error.     

Weak‐anisotropy approximation for P‐wave reflection coefficient at the boundary between two tilted transversely isotropic media

Existing and commonly used in industry nowadays, closed‐form approximations for a P‐wave reflection coefficient in transversely isotropic media are restricted to cases of a vertical and a horizontal transverse isotropy. However, field observations confirm the widespread presence of rock beds and fracture sets tilted with respect to a reflection boundary. These situations can be described by means of the transverse isotropy with an arbitrary orientation of the symmetry axis, known as tilted transversely isotropic media. In order to study the influence of the anisotropy parameters and the orientation of the symmetry axis on P‐wave reflection amplitudes, a linearised 3D P‐wave reflection coefficient at a planar weak‐contrast interface separating two weakly anisotropic tilted tranversely isotropic half‐spaces is derived. The approximation is a function of the incidence phase angle, the anisotropy parameters, and symmetry axes tilt and azimuth angles in both media above and below the interface. The expression takes the form of the well‐known amplitude‐versus‐offset “Shuey‐type” equation and confirms that the influence of the tilt and the azimuth of the symmetry axis on the P‐wave reflection coefficient even for a weakly anisotropic medium is strong and cannot be neglected. There are no assumptions made on the symmetry‐axis orientation angles in both half‐spaces above and below the interface. The proposed approximation can be used for inversion for the model parameters, including the orientation of the symmetry axes. Obtained amplitude‐versus‐offset attributes converge to well‐known approximations for vertical and horizontal transverse isotropic media derived by Rüger in corresponding limits. Comparison with numerical solution demonstrates good accuracy.