Kinematic parameters of pure‐ and converted‐mode waves in elastic orthorhombic media

I derive the kinematic properties of single‐mode P, S1, and S2 waves as well as converted PS1, PS2, and S1S2 waves in elastic orthorhombic media including vertical velocity, two normal moveout velocities defined in vertical symmetry planes, and three anelliptic parameters (two of them are defined in vertical symmetry plane and one parameter is the cross‐term one). I show that the azimuthal dependence of normal moveout velocity and anellipticity is different in phase and group domains. The effects on‐vertical‐axis singularity and on‐vertical‐axis triplication are considered for pure‐mode S1 and S2 waves and converted‐mode S1S2 waves. The conditions and properties of on‐vertical‐axis triplication are defined in terms of kinematic parameters. The results are illustrated in four homogeneous orthorhombic models and one multilayered orthorhombic model with no variation in azimuthal orientation for all the layers.     

The modified generalized moveout approximation: a new parameter selection

Non‐hyperbolic generalised moveout approximation is a powerful tool to approximate the travel‐time function by using information obtained from two rays. The standard approach for parameter selection is using three parameters defined from zero‐offset ray and two parameters obtained from a reference ray. These parameters include the travel time and travel‐time derivatives of different order. The original parameter selection implies more fit at zero offset compared with offset from a reference ray. We propose an alternative approach for parameter selection within the frame of generalised moveout approximation by transferring more fit from the zero offset to a reference ray by changing in parameter selection. The modified approximation is tested against the original one in few analytical model examples, including the multi‐layered model.     

Preserved travel‐time smoothing in orthorhombic media

Certain degree of smoothness of velocity models is required for most ray‐based migration and tomography. Applying conventional smoothing in model parameters results in offset‐dependent travel‐time errors for reflected events, which can be large even for small contrasts in model parameters between the layers. This causes the shift in both the depth and residual moveout of the migrated images. To overcome this problem in transversely isotropic medium with a vertical symmetry axis, the preserved travel‐time smoothing method was proposed earlier. We extend this method for orthorhombic media with and without azimuthal variation between the layers. We illustrate this method for a single interface between two orthorhombic layers and show that the smoothing‐driven errors in travel time are very small for practical application.     

Low-frequency layer-induced dispersion in a weak-contrast vertically heterogeneous orthorhombic medium

In this paper, we consider wave propagation in a periodically layered medium with orthorhombic symmetry. The weak-contrast approximation is utilized to derive the low-frequency dispersion in effective properties for P, S1 and S2 waves. We show that the dispersion term for all effective properties is controlled by the second-order contrasts in elastic properties from the layers. We also compute the sensitivity matrices for second- and fourth-order coefficients from eigenvalues of frequency-dependent system matrix associated with kinematic parameters for individual wave modes.     

Impacts as sources of the exosphere on Mercury

Chemical processes associated with meteoroid bombardment of Mercury are considered. Meteoroid impacts lead to production of metal atoms as well as metal oxides and hydroxides in the planetary exosphere. By using quenching theory, the abundances of the main Na-, K-, Ca-, Fe-, Al-, Mg-, Si-, and Ti-containing species delivered to the exosphere during meteoroid impacts were estimated. Based on a correlation between the solar photo rates and the molecular constants of atmospheric diatomic molecules, photolysis lifetimes of metal oxides and SiO are estimated. Meteoroid impacts lead to the formation of hot metal atoms (0.2-0.4 eV) produced directly during impacts and of very hot metal atoms (1-2 eV) produced by the subsequent photolysis of oxides and hydroxides in the exosphere of Mercury. The concentrations of impact-produced atoms of the main elements in the exosphere are estimated relative to the observed concentrations of Ca, assumed to be produced mostly by ion sputtering. Condensation of dust grains can significantly reduce the concentrations of impact-produced atoms in the exosphere. Na, K, and Fe atoms are delivered to the exosphere directly by impacts while Ca, Al, Mg, Si, and Ti atoms are produced by the photolysis of their oxides and hydroxides. The chemistry of volatile elements such as H, S, C, and N during meteoroid bombardment is also considered. Our conclusions about the temperature and the concentrations of impact-produced atoms in the exosphere of Mercury may be checked by the Messenger spacecraft in the near future and by BepiColombo spacecraft some years later.