Practical VTI approximations: a systematic anatomy

Transverse isotropy (TI) with a vertical symmetry axis (VTI) often provides an appropriate earth model for prestack imaging of steep-dip reflection seismic data. Exact P-wave and SV-wave phase velocities in VTI media are described by complicated equations requiring four independent parameters. Estimating appropriate multiparameter earth models can be difficult and time-consuming, so it is often useful to replace the exact VTI equations with simpler approximations requiring fewer parameters. The accuracy limits of different previously published VTI approximations are not always clear, nor is it always obvious how these different approximations relate to each other. Here I present a systematic framework for deriving a variety of useful VTI approximations. I develop first a sequence of well-defined approximations to the exact P-wave and SV-wave phase velocities. In doing so, I show how the useful but physically questionable heuristic of setting shear velocities identically to zero can be replaced with a more precise and quantifiable approximation. The key here to deriving accurate approximations is to replace the stiffness a₁₃ with an appropriate factorization in terms of velocity parameters. Two different specific parameter choices lead to the P-wave approximations of Alkhalifah (Geophysics 63 (1998) 623) and Schoenberg and de Hoop (Geophysics 65 (2000) 919), but there are actually an infinite number of reasonable parametrizations possible. Further approximations then lead to a variety of other useful phase velocity expressions, including those of Thomsen (Geophysics 51 (1986) 1954), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Harlan (Stanford Exploration Project Report 89 (1995) 145), and Stopin (Stopin, A., 2001. Comparison of v(θ) equations in TI medium. 9th International Workshop on Seismic Anisotropy). Each P-wave phase velocity approximation derived this way can be paired naturally with a corresponding SV-wave approximation. Each P-wave or SV-wave phase velocity approximation can then be converted into an equivalent dispersion relation in terms of horizontal and vertical slownesses. A simple heuristic substitution also allows each phase velocity approximation to be converted into an explicit group velocity approximation. From these, in turn, travel time or moveout approximations can also be derived. The group velocity and travel time approximations derived this way include ones previously used by Byun et al. (Geophysics 54 (1989) 1564), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Tsvankin and Thomsen (Geophysics 59 (1994) 1290), Harlan (89 (1995) 145), and Zhang and Uren (Zhang, F. and Uren, N., 2001. Approximate explicit ray velocity functions and travel times for P-waves in TI media. 71st Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 106–109).     

论构造耦合作用

构造耦合作用是一种普遍存在的地质现象。现今东、西太平洋的构造差异及古太平洋和现今太平洋大陆边缘构造差异与俯冲的洋壳板块性状有关,即:①俯冲角度;②俯冲角度的改变;③俯冲速率;④俯冲速率的改变;⑤俯冲深度;⑥俯冲板块前缘与海沟间的水平距离;⑦俯冲板块在670km上、下地幔界线处的构造形态;⑧俯冲板块的位移及位移方向。这种深部构造活动对浅部构造形成的制约和影响,是活动大陆边缘构造耦合现象的具体表现。中国西北部的盆山耦合现象是大陆内部的构造耦合作用,印度板块与欧亚板块碰撞产生的远距离效应,导致中亚地区产生陆内A型俯冲,A型俯冲是造成盆地消亡、山系形成的重要因素。     

岩石断裂作用的复杂性和混沌动力学

断裂是一个复杂的动力学体系,受到岩石结构、反应、流体迁移、应力、岩石变形和力学等多种地质因素和过程的耦合控制。本文建立了断裂体系的反应-输运-力学耦合动力学模型并编制了模拟程序。以湖南水口山矿区为例,通过动力学模拟表明不同地层岩性的断裂渗透率大小和演化特征存在显著差异,断裂作用促使岩石渗透率的空间非均匀性增强,从而有利于流体的局部汇聚和矿体的形成。断裂中压力随时间呈现出非周期振荡变化,反映了断裂演化的混沌特征。     

Computational study of tetrahedral Al–Si and octahedral Al–Mg ordering in phengite

 As part of a wider study of the nature and origins of cation order–disorder in micas, a variety of computational techniques have been used to investigate the nature of tetrahedral and octahedral ordering in phengite, K₂ ^[6](Al₃Mg)^[4](Si₇Al)O₂₀(OH)₄. Values of the atomic exchange interaction parameters J _n used to model the energies of order–disorder were calculated. Both tetrahedral Al–Si and octahedral Al–Mg ordering were studied and hence three types of interaction parameter were necessary: for T–T, O–O and T–O interactions (where T denotes tetrahedral sites and O denotes octahedral sites). Values for the T–T and O–O interactions were taken from results on other systems, whilst we calculated new values for the T–O interactions. We have demonstrated that modelling the octahedral and tetrahedral sheets alone and independently produces different results from modelling a whole T–O–T layer, hence justifying the inclusion of the T–O interactions. Simulations of a whole T–O–T layer of phengite indicated the presence of short-range order, but no long-range order was observed. Received: 8 August 2002 / Accepted: 14 February 2003 Acknowledgements The authors are grateful to EPSRC (EJP) and the Royal Society (CIS) for financial support. Monte Carlo simulations were performed on the Mineral Physics Group's Beowulf cluster and the University of Cambridge's High Performance Computing Facility.     

Global thermal and dynamical perturbations due to Cretaceous mantle avalanche

The numerical models of mantle convection agree to depict avalanches behaviour according to the level of endothermicity of the spinel → perovskite phase change. Their potential effects on the global thermal and dynamical states of the mantle have been computed thanks to a numerical code, which takes into account both the 400-km exothermic and the 660-km endothermic phase changes. The cycle followed by the avalanches is: local layering, destabilization of the 660-km thermal layer, travelling and spreading on the core, and reappearing of the local layering. Therefore, mantle convection is characterized by quiet periods of partial layering embedded in catastrophic events. During the avalanche, the amplitude of the surface velocity is multiplied by two, which would imply an enhanced plate tectonic and ridge activities. The global thermal effects of the avalanche are compatible with a high mantle temperature and an acceleration of Earth's rotation during the Cretaceous. They also offer a coherent explanation to locate the origin of mantle plumes both within the CMB and just below the transition zone.     

地震前地表重力场变化的一种可能解释——应力-损伤耦合效应

文中运用损伤力学研究方法 ,提出孕震过程中引起地壳破坏的应力 -损伤耦合效应。利用应变等效性假设 ,推导了地壳体的应力 -损伤耦合效应与地表重力变化之间的理论关系。根据岩石力学实验的不同加载途径 ,模拟了 1976年唐山 7 8级地震和 2 0 0 1年昆仑山口西 8 1级地震重力演化的不同特征 ,结果与实际情况符合较好 ,表明应力 -损伤耦合效应可以作为地震前地壳重力变化的一种物理解释     

偏心结构非线性地震反应分析的一种简化方法

本文建立了基于结构状态方程和偏心结构体系的层剪力-扭矩等效屈服EYST面概念的求解平扭耦联非线性地震反应的分离-予估-修正递推算法，编制了相应的计算程序。通过与三个单层偏心结构模型的破坏性地震模拟试验结果的对比，验证了小变形阶段平-扭耦联地震反应算法的实用性和可靠性。算例表明，该程序数据处理量小，运算快捷，便于应用。     

考虑空间效应的非线性结构主共振分析

本文针对考虑空间效应非对称刚度的单层结构，利用能量法得到了结构水平侧移和扭转相耦合的振动方程，采用多尺度法研究了侧移刚度和扭转刚度之间有某一关系时的主共振，分析了结构主共振的定常解并且讨论了其稳定性，通过算例分析得到了考虑空间效应时结构的一些有益的结论。     

储液罐液—固—土耦合非线性翘离振动分析

本文考虑液固耦联及底板几何非线性与土壤弹性，建立了液－固－土耦合的储液罐翘离分析力学模型。算例表明，恢复力矩与翘离角之间的关系可以表达为分段线性，翘离将使地震响应增大。     

确定精密重力仪相位滞后方法的研究

从系统辨识的原理出发,给出了确定精密重力仪相位滞后的一种方法,即记录精密重力仪在阶跃信号作用下的输出数据,利用这些数据对仪器的传递函数进行辨识,从而确定重力仪对各潮汐波产生的相位滞后角度.用这种方法对ET-21地潮重力仪进行了相位滞后的确定,并给出这台仪器对15个主要潮汐波的相位滞后角度.