Source–receiver two‐way wave extrapolation for prestack exploding‐reflector modelling and migration

Most modern seismic imaging methods separate input data into parts (shot gathers). We develop a formulation that is able to incorporate all available data at once while numerically propagating the recorded multidimensional wavefield forward or backward in time. This approach has the potential for generating accurate images free of artiefacts associated with conventional approaches. We derive novel high‐order partial differential equations in the source–receiver time domain. The fourth‐order nature of the extrapolation in time leads to four solutions, two of which correspond to the incoming and outgoing P‐waves and reduce to the zero‐offset exploding‐reflector solutions when the source coincides with the receiver. A challenge for implementing two‐way time extrapolation is an essential singularity for horizontally travelling waves. This singularity can be avoided by limiting the range of wavenumbers treated in a spectral‐based extrapolation. Using spectral methods based on the low‐rank approximation of the propagation symbol, we extrapolate only the desired solutions in an accurate and efficient manner with reduced dispersion artiefacts. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach.     

A fast algorithm for 3D azimuthally anisotropic velocity scan

The conventional velocity scan can be computationally expensive for large‐scale seismic data sets, particularly when the presence of anisotropy requires multiparameter scanning. We introduce a fast algorithm for 3D azimuthally anisotropic velocity scan by generalizing the previously proposed 2D butterfly algorithm for hyperbolic Radon transforms. To compute semblance in a two‐parameter residual moveout domain, the numerical complexity of our algorithm is roughly as opposed to of the straightforward velocity scan, with N being the representative of the number of points in a particular dimension of either data space or parameter space. Synthetic and field data examples demonstrate the superior efficiency of the proposed algorithm.     

Stratigraphic coordinates: a coordinate system tailored to seismic interpretation

In certain seismic data processing and interpretation tasks such as spiking deconvolution, tuning analysis, impedance inversion, and spectral decomposition, it is commonly assumed that the vertical direction is normal to reflectors. This assumption is false in the case of dipping layers and may therefore lead to inaccurate results. To overcome this limitation, we propose a coordinate system in which geometry follows the shape of each reflector and the vertical direction corresponds to normal reflectivity. We call this coordinate system stratigraphic coordinates. We develop a constructive algorithm that transfers seismic images into the stratigraphic coordinate system. The algorithm consists of two steps. First, local slopes of seismic events are estimated by plane‐wave destruction; then structural information is spread along the estimated local slopes, and horizons are picked everywhere in the seismic volume by the predictive‐painting algorithm. These picked horizons represent level sets of the first axis of the stratigraphic coordinate system. Next, an upwind finite‐difference scheme is used to find the two other axes, which are perpendicular to the first axis, by solving the appropriate gradient equations. After seismic data are transformed into stratigraphic coordinates, seismic horizons should appear flat, and seismic traces should represent the direction normal to the reflectors. Immediate applications of the stratigraphic coordinate system are in seismic image flattening and spectral decomposition. Synthetic and real data examples demonstrate the effectiveness of stratigraphic coordinates.     

Galactic cosmic rays—clouds effect and bifurcation model of the Earth global climate. Part 2. Comparison of theory with experiment

The solution of energy-balance model of the Earth global climate and the EPICA Dome C and Vostok experimental data of the Earth surface palaeotemperature evolution over past 420 and 740 kyr are compared.In the framework of proposed bifurcation model (i) the possible sharp warmings of the Dansgaard-Oeschger type during the last glacial period due to stochastic resonance is theoretically argued; (ii) the concept of climatic sensitivity of water in the atmosphere, whose temperature instability has the form of so-called hysteresis loop, is proposed, and based on this concept the time series of global ice volume over the past 1000 kyr, which is in good agreement with the time series of δ¹⁸O concentration in the sea sediments, is obtained; (iii) the so-called “CO₂ doubling” problem is discussed.     

On utility of triangular C-grid type discretization for numerical modeling of large-scale ocean flows

Ocean circulation models based on triangular C-grid discretization are frequently employed to simulate coastal ocean dynamics on unstructured meshes. It is shown that on time and space scales dominated by slow geostrophic dynamics, this discretization tends to exhibit checkerboard noise in the field of horizontal velocity divergence and vertical velocity, respectively. The noise is linked to the geometry of triangular C-grid and is amplified in regimes that are close to geostrophic balance through the particular structure of the Coriolis operator. It can be partly suppressed in some cases but remains a problem in a general case and makes the triangular C-grid a suboptimal choice for large-scale ocean modeling.     

Precision Analytical Calculation of Geodynamical Effects on Satellite Motion

A new analytical method for calculating satellite orbital perturbations due to different disturbing forces is developed. It is based on the Poincaré method of small parameter but takes advantages of modern high-performance computers and of the tools of computer algebra. All perturbations proportional up to and including the 5th-order of small parameters are obtained. The method can precisely calculate the effects of all geodynamical forces on satellite motion given by the most up-to-date IAU and IERS models, such as non-central Earth gravity potential, precession and nutation of the geoequator, polar motion and irregularities in the Earth's rotation, effect of ocean and solid Earth tides, pole tide, and secular variations of gravity coefficients.Numerical tests prove the method's accuracy to be equivalent to 1–2 cm when calculating positions of high altitude geodetic satellites (like ETALON), and/or of GLONASS navigational spacecraft. The accuracy is stable over 1 year at least and comparable to that of the best tracking measurements of satellites.Positions of low altitude geodynamical satellites (like STARLETTE) by the analytical method are calculated to an accuracy of about 70cm over a month's interval. The method is developed for future use in GLONASS/GPS on-board ephemeris computation where it can improve the current scheme of their flight control.This revised version was published online in October 2005 with corrections to the Cover Date.     

Hydrogeochemistry of the permafrost zone in the central part of the Yakutian diamond-bearing province,Russia

The hydrogeochemical characteristics and zonation of the permafrost zone in the central part of the Yakutian diamond-bearing province formed mainly under the influence of cryogenic processes that occurred in the late Cenozoic. On the basis of field and experimental studies, conclusions were formulated that the perennial cryogenesis of the sedimentary cover in this region resulted in increasing the concentration of carbonate and sulfate compounds in groundwaters as well as increasing the concentration of easily soluble compounds (sodium, magnesium, and calcium chlorides).

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Resumen Las características hidrogeoquímicas y la zonación del permafrost existente en el centro de la provincia de Yakutia, rica en diamantes, se formaron fundamentalmente bajo la influencia de procesos criogénicos durante el tramo final del Cenozoico. Con base en estudios de campo y experimentales, se ha concluido que la criogénesis perenne de la cubierta sedimentaria de la región ha provocado un aumento de la concentración de compuestos de carbonato y sulfato en las aguas subterráneas, además de incrementar la concentración de compuestos solubles, como el sodio, magnesio y cloruros de calcio.

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Résumé Les caractéristiques hydrogéochimiques et la zonation de la région de permafrost dans la partie centrale de la province diamantifère de Yakoutie ont été acquises principalement sous l'influence des processus cryogéniques qui existent depuis la fin du Tertiaire. Sur la base d'études expérimentales et de terrain, on conclut que la cryogenèse permanente de la couverture sédimentaire de cette région a provoqué un accroissement de la concentration des composés carbonatés et sulfatés dans les eaux souterraines, en même temps que celui de composés facilement solubles, comme les chlorures de sodium, de magnésium et de calcium.

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