Errors due to the anisotropic-common-ray approximation of the coupling ray theory

The common-ray approximation eliminates problems with ray tracing through S-wave singularities and also considerably simplifies the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies. It is thus of principal importance for numerical applications to estimate the errors due to the common-ray approximation applied. The anisotropic-common-ray approximation of the coupling ray theory is more accurate than the isotropic-common-ray approximation. We derive the equations for estimating the travel-time errors due to the anisotropic-common-ray (and also isotropic-common-ray) approximation of the coupling ray theory. The errors of the common-ray approximations are calculated along the anisotropic common rays in smooth velocity models without interfaces. The derivation is based on the general equations for the second-order perturbations of travel time.     

中国大陆及邻区海域地壳上地幔各向异性研究

利用分别由Love波和Rayleigh波得到的S波速度结构的差值（VSH-VSV）对中国大陆及邻区海域（70°E～145°E，15°N～55°N）地壳上地幔中的偏振各向异性进行研究.初步研究结果表明，各向异性在空间分布上存在不均匀性：（1）在小于150 km的深度范围内，VSH>VSV的各向异性体占主导地位，反映出在地球的浅部岩石圈内的水平应力作用及软流圈顶部物质的水平向流动对各向异性的形成起主导作用.在大陆地区，各向异性的强度随深度有显著变化.上地壳和上地幔盖层中的各向异性普遍较弱，而在流变性较强的下地壳和软流圈存在较大范围的各向异性.这一现象说明下地壳在岩石圈变形中可能有解耦作用.（2）在大于200 km深度的软流圈下部主要表现为VSH<VSV的各向异性，说明地幔物质垂直运动相对占优势地位.（3）在中国大陆东部可以看出一个大致趋势：在构造比较稳定的地区，岩石圈中VSH>VSV的各向异性比较显著，而软流圈中VSH<VSV的各向异性较弱；在构造活动比较强烈的地区，软流圈中VSH<VSV的各向异性占主导地位.（4）印度板块低角度向青藏高原下俯冲影响了中国大陆西部地区各向异性的特征.印度板块向北运动水平挤压中国西部大陆，使得物质定向重结晶，从而在岩石圈下部产生显著的VSH>VSV各向异性.     

Seismic identification of channel sandbodies in the Fuyang oil layer in North Songliao Basin, China

The Fuyang oil-layer in North Songliao Basin is characterized by thin interbedded sands and shales, strong lateral variation, strong reservoir heterogeniety, and so on. The thickness of individual sand layers is generally 3 - 5 m. Identifying the channel sand-bodies of the Fuyang oil layer using seismic techniques is very difficult due to the low seismic resolution. Taking the GTZ area as an example, we discuss the genetic characteristics of the channel sand-bodies and point out the real difficulty in using seismic techniques to predict the channel sand-bodies. Two methods for the identification of channels are presented： frequency spectrum imaging and pre-stack azimuthal anisotropy. Identifying the channel sand-bodies in Fuyu oil-layer using the two seismic methods results in a success rate up to 80% compared with well data.     

Interpretation of a two-point flux stencil for skew parallelogram grids

Control-volume formulations for elliptic equations often use two-point flux stencils, even for skew grids. Any two-point flux stencil may be interpreted as a multipoint flux stencil. This yields a definition of the permeability (or conductivity) tensor. Formulas for calculating the permeability tensor, based on the user-specified quantities in the two-point flux stencil, are given. Numerical test examples demonstrate the validity of the derivation.      

Utilisation of the image analysis method for the detection of the morphological anisotropy of calcite grains in marble

This paper presents the development and utilisation of an automated image processing algorithm for detection and analysis of grains. Using optical polarising microscopy, a set of colored images are collected from an area on a thin section. A filtering operation, using rotation of a morphological alternating sequence filter (based on a structuring element), is used to remove twinning features within individual grains. Filtering is followed by the watershed segmentation technique to determine grain boundaries. The method is used for the identification of calcite grains in marble and the subsequent analysis of morphological anisotropy.     

橄榄石的晶格优选定向、含水量与地震波各向异性:对大陆俯冲带变形环境的约束

橄榄石在不同热动力学条件下形成的晶格优选定向是认识上地幔塑性变形与地震波各向异性的基础。本文通过总结橄榄石的晶格优选定向、含水量与地震波各向异性的研究进展,探讨大陆俯冲带的变形环境。绝大部分天然变形橄榄岩中的橄榄石都发育了[100](010)组构:[100]轴近平行于线理,(010)面平行或近平行于面理,使橄榄岩的最快P波速度近平行于线理,最大S波分裂平行面理并垂直线理。但来自超高压变质带的石榴石橄榄岩可发育[001](100)组构,使橄榄岩的最快P波速度和最小S波分裂方向垂直面理。近年来的变形实验与理论计算表明:超高压和低温是橄榄石组构从[100](010)向[001](100)转变的关键因素,而水对橄榄石流变行为的影响还有待进一步研究。对170个天然橄榄石结构水含量的统计结果表明:橄榄石含水量变化很大(0～170×10~(-6)H_2O),玄武岩中橄榄岩包体的橄榄石比较贫水,而所有富水橄榄石均来自克拉通金伯利岩中的石榴石橄榄岩。因此,除了水在上地幔的不均匀分布,橄榄岩折返过程中氢的扩散会强烈影响橄榄石的含水量。苏鲁芝麻房橄榄岩提供了以超高压、低温、贫流体为特征的大陆俯冲带中[001](100)橄榄石组构的实例。在俯冲的大陆板片中,橄榄石组构在120～220 km从[100](010)向[001](100)的转变可导致地震波各向异性突然降低,而且最快P波速度垂直于俯冲方向。     

Quasi-isotropic approximation of ray theory for anisotropic media

Wave propagation in weakly anisotropic inhomogeneous media is studied by the quasi-isotropic approximation of ray theory. The approach is based on the ray-tracing and dynamic ray-tracing differential equations for an isotropic background medium. In addition, it requires the integration of a system of two complex coupled differential equations along the isotropic ray.
The interference of the qS waves is described by traveltime and polarization corrections of interacting isotropic S waves. For qP waves the approach leads to a correction of the traveltime of the P wave in the isotropic background medium.
Seismograms and particle-motion diagrams obtained from numerical computations are presented for models with different strengths of anisotropy.
The equivalence of the quasi-isotropic approximation and the quasi-shear-wave coupling theory is demonstrated. The quasi-isotropic approximation allows for a consideration of the limit from weak anisotropy to isotropy, especially in the case of qS waves, where the usual ray theory for anisotropic media fails.     

Three-dimensional image of the anisotropic bodies beneath central Honshu, Japan

Shear-wave splitting from local deep earthquakes is investigated to clarify the volume and the location of two anisotropic bodies in the mantle wedge beneath central Honshu, Japan. We observe a spatial variation in splitting parameters depending on the combination of sources and receivers, nearly N–S fast in the northern region, nearly E–W fast in the southern region and small time delays in the eastern region. Using forward modelling, two models with 30 and 10 per cent anisotropy are tested by means of a global search for the locations of anisotropic bodies with various volumes. The optimum model is obtained for 30 per cent anisotropy, which means a 5 per cent velocity difference between fast and slow polarized waves. The northern anisotropic body has a volume of 1.00° (longitude) × 0.5° (latitude) × 75 km (depth), with the orientation of the symmetry axis being N20°E. The southern anisotropic body has a volume of 1.25° × 1.25° × 100 km with the symmetry axis along N95°E. Our results show that the anisotropic bodies are located in low-velocity and low- Q regions of the mantle. This, together with petrological data and the location of volcanoes in the arc, suggests that the possible cause of the anisotropy is the preferred alignment of cracks filled with melt.