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In the ultrahigh-pressure metamorphic (UHPM) Kokchetav massif (northern Kazakhstan), diamond-bearing clinozoisite gneisses of the western Barchi-Kol' area display three particular types of reaction textures involving melts: (1) kyanite + silicate-carbonaceous melt = clinozoisite-quartz symplectite + CO₂; (2) rutile + silicate-carbonaceous melt = titanite + CO₂; (3) silicate-carbonaceous melt = calcite + quartz + graphite. Recent experimental work provided constraining evidence on melt-carbonate interaction under UHP conditions and produced a clinozoisite-bearing rock at the interface between metacarbonates and metapelites. These results corroborate well our petrographic observations, illustrating silicate-carbonaceous melt formation under UHPM conditions. Since the amount of partial melts in pelitic material increases when carbonate is available, the carbonate-rich western part of the Kokchetav massif has endured a more extensive weakening. The melting under UHPM conditions induced rheological weakening and thus influenced the exhumation evolution of the UHPM Kokchetav massif.

In situ dating of zircon domains with a Sensitive High Resolution Ion Microprobe (SHRIMP) has been proved to be the best way to determine the age of peak metamorphic conditions in the diamondiferous, deeply subducted Kokchetav rocks. Three independent studies obtained within error-consistent results, providing evidence for peak metamorphic conditions at about 530 Ma. These studies demonstrated through mineral inclusions that the dated zircon crystals formed under peak metamorphic conditions, within the diamond stability field. Mineral inclusions indicate that zircon formed not only at the metamorphic peak, but also during the retrograde evolution under granulite- to amphibolite-facies conditions. The ages of the retrograde zircon domains are within error not distinguishable from the age of peak metamorphism. This provides evidence for very fast exhumation rates of minimum 1.8 cm/yr from diamond to granulite-facies metamorphism and high cooling rates > 40

Study of a series of samples of homogeneous and inhomogeneous (banded) calc-silicate rocks with contrasting diamond contents from the Kumdy-Kol' deposit of metamorphic diamonds (northern Kazakhstan) has shown an extremely wide diversity of compositions of pyrope-grossular garnets in association with dolomite, Mg-calcite, magnesite, diopside with up to 1.5 wt.% K₂O, forsterite, Ti-clinohumite, and phlogopite. Perovskite as an inclusion in forsterite has been discovered in these rocks for the first time. In some samples of complex composition interbeds with and without diamond alternate. Garnet forms a series of compositions with wide variations of Mg# [100 · Mg/(Mg + Fe)] from 70 to 95 and Ca# [100 · Ca/(Ca + Mg + Fe + Mn)] from 42 to 85, which has first been found for these rocks. Wide variations in garnet zoning have been revealed, with a decrease in Ca# towards the rims. Relict Mg-rich garnets which were firstly recognized under natural conditions persistently occur as light irregular spots, with uniquely low amounts of FeO, within 1-2 wt.% (Mg# is 92-95 and Ca# is 60-66). These relics make up 5 to 70 vol.% of the respective grain surfaces in thin section and are revealed only by cathodoluminescence (CL) approximately in only 10-20% of garnet grains for each sample. Thus, these unusual relics are typical of the diverse samples under study, and their composition is relatively homogeneous. The outer zones of most of these garnets completely correspond to typical well-studied compositions with Mg# of 70-80 and Ca# of 40-55. Supposedly, these relics are the earliest garnets formed under the conditions corresponding to the maximum of ultrahigh-pressure metamorphism. These garnets are often surrounded by reactionary rims irregularly developed around the grains made up of clinopyroxene and spinel symplectite. Occasionally, sapphirine and corundum are found in these rims. The symplectite paragenesis was formed as a result of retrograde metamorphism, in the early stages of exhumation, and is direct evidence of the granulite facies conditions, probably, at 1.8 GPa and about 900

The use of integral reflection and transmission operators to account for boundary conditions follows from the theory of wave scattering at curved interfaces in layered inhomogeneous media obtained in our previous studies. In this respect it appears practical to investigate the possibility of applying these operators instead of plane-wave reflection and transmission coefficients to describe high-frequency wavefields by Kirchhoff-type surface singular integrals common in forward and inverse seismic problems. We compare the integral reflection operator and reflection coefficient approaches in numerical experiments for single scattering of a spherical wave at a curved interface. We show that the use of the integral reflection operator allows eliminating artefacts associated with the use of the reflection coefficient and ensures including head waves.

A numerical-analytical solution for seismic and acoustic-gravity wave propagation is applied to a heterogeneous `Earth-atmosphere' model. Seismic wave propagation in elastic earth is described by a system of first-order dynamic equations of the elasticity theory and propagation of acoustic-gravity waves in the atmosphere by the linearized Navier-Stokes equations. The solution algorithm combines the time-domain integral Laguerre transform, the finite integral Bessel transform along the radial coordinate, and the FD solution of the reduced problem along the vertical coordinate. The suggested algorithm is tested with numerical experiments for the heterogeneous `Earth-atmosphere' model for different source locations.

Particle motion of homogeneous and inhomogeneous time-harmonic plane waves propagating in unbounded viscoelastic anisotropic media is generally elliptical. Exception is linear polarization of P and S waves propagating along some specific directions. A typical example is a linear polarization of SH waves propagating in a plane of symmetry of a viscoelastic anisotropic medium. Two most important characteristics of the particle motion are the orientation of the axes of the polarization ellipse and its eccentricity. They both usually vary considerably with the direction of wavefront propagation, and with varying strength of inhomogeneity of the considered plane wave. The orientation of the P -wave polarization ellipse generally differs from the direction of wavefront propagation, and it is usually closer to the direction of the energy flux. The orientation of the polarization ellipses of S waves often differs from the direction perpendicular to the wavefront propagation, and it is usually closer to the direction perpendicular to the direction of the energy flux. The eccentricity of the polarization ellipse depends particularly strongly on the inhomogeneity of the plane wave. For homogeneous plane waves, the particle motion is usually nearly linear, i.e., polarization ellipses have large eccentricity, and the eccentricity decreases with increasing inhomogeneity of the wave. For strongly inhomogeneous plane waves, the polarization ellipse becomes nearly circular, eccentricity being very small. The eccentricity of the polarization ellipse usually also decreases in the vicinity of singular directions.

A new method for estimating the quality of geoelectrical data inversion implies formalization of the concepts for horizontal and vertical resolution and equivalence. Various aspects of the suggested approach are illustrated by examples.

Amplitude versus offset (AVO) or amplitude versus angle (AVA) curves are nowadays regularly extracted from seismic data for various purposes of reservoir studies and characterization. After adequate processing, these curves represent the variation of the reflection coefficients with respect of offset or angle at points of key target reflectors, such as, for example, the top of a reservoir. Besides the information that can be obtained merely from their shape, AVO/AVA curves can also be used to invert more quantitative attributes, such as the intercept and the gradient of the reflection coefficient or, even better, the elastic-parameter contrasts. For a common-midpoint gather, the AVA curve is generally derived from its AVO counterpart by means of a well-known expression that relates the reflection angle to offset. It is to be noted that a successful inversion of the sought-for attributes is strongly dependent on the approximations of the reflection coefficient that are considered.
The recently introduced reflection impedance concept provides an attractive approximation of the elastic PP-reflection coefficient as a function of the ray parameter. In this sense, that approximation can be of value when amplitude versus ray parameter (AVP) curves are available from seismic data. It is to be noted that an AVP curve tend to be more reliable that its AVA counterpart. This is because the ray parameter, as a function of offset, depends on the RMS-velocity only, as opposed to the incidence angle, which also depends on the (more unstable) interval velocity.
In this paper, we propose an algorithm to invert elastic-parameter contrasts from AVP curves using the reflection impedance approximation of the PP-reflection coefficient. First results shown on synthetic data indicate that the procedure may offer a promising alternative to existing methods of inverting reservoir attributes from AVO/AVA curves.

For a horizontally layered medium with isotropic layers with constant velocity gradient, it is possible to estimate the velocity function (gradient and velocity at the top of the layer) and thickness of each layer. From large-offset PP seismic reflections one can estimate three traveltime parameters: the zero-offset two-way traveltime, the NMO velocity and a heterogeneity coefficient, using the shifted hyperbola approximation or a fractional approximation. From the estimated traveltime parameters at the top and bottom of a layer, it is possible to compute the thickness and velocity function of the layer. It is necessary to solve a simple nonlinear equation which also can be solved approximately. There are two solutions, corresponding to a positive and negative velocity gradient. Therefore, the sign of the velocity gradient must be chosen. When there is one solution, the velocity gradient in the layer is zero, and the result is the standard Dix equations.

The paper addresses traveltime processing for 2D models with laterally inhomogeneous layers and curved interfaces in shallow subsurface. Analytical equations are derived to approximate the relation between shallow velocity anomalies and NMO velocity as a basis for traveltime inversion to obtain an initial-approximation velocity model. The new approach is applied to real field data from regions with shallow velocity anomalies.