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).     

Explosion seismic reflections from the Earth’s core

Recent seismological studies have presented evidence for the existence of a layer with ultra-low seismic velocities at the core-mantle boundary at ca. 2900 km depth. We report high-amplitude, high-frequency, and laterally coherent seismic arrivals from three nuclear explosions in Siberia. With recording station intervals of 15 km, the seismic phases are readily correlated and show the presence of a thin, ultra-low velocity zone in a region where it was not previously reported. The duration and complexity of the arrivals are inconsistent with a simple core-mantle boundary and require a hitherto unidentified, kilometre-scale, fine structure in the ultra-low velocity zone. The observations may be explained by a ca. 7 km thick, two-layer, ultra-low velocity zone with exceptional low velocities, which indicate the presence of high percentages of melt (>15%), in particular in the lower part of the zone. Waveform variation implies lateral change in the thickness and physical properties of the ultra-low velocity zone with a wavelength of less than 100 km.     

变参考慢度Born近似傅氏偏移

针对常规Born近似傅氏偏移方法对于剧烈横向变速介质不能精确成像的状况而提出了变参考慢度Born近似傅氏偏移，理论上解决了任意速度变化地质模型的偏移成像问题。此外，为进一步提高复杂地层的成像精度和波场延拓算子的稳定性，对散射波场的计算公式作了改进。将改进的方法运用于盐丘模型的正演和偏移试验，并与常规Born近似偏移方法相比较，可明显看出变参考慢度Born近似傅氏偏移方法在效果上要优于后者，其处理速度横向变化的能力大大增强。     

Velocity structure of uppermost mantle beneath North China from Pn tomography and its implications

20301 Pn arrival time data are collected from the seismological bulletins of both national and regional seismic networks. Pn travel time residuals are tomographically inverted for the Pn velocity structure of uppermost mantle beneath North China. The result indicates that the average Pn velocity in North China is 7.92 km/s, and the velocity varies laterally from ?0.21 to +0.29 km/s around the average. The approximately NNE trending high and low velocity regions arrange alternatively west-eastward. From west to east we can see high velocity in the middle Ordos region, the Shanxi graben low, the Jizhong depression high, the west Shandong uplift and Bohai Sea low, and the high velocity region to the east of the Tanlu fault. In the southern boundary zone of the North China block, except for the high velocity in the Qingling Mountains region, the velocity is generally lower than the average. Obvious velocity anisotropy is seen in the Datong Cenozoic volcanic region, with the fast velocity direction in NNE-SSW. Notable velocity anisotropy is also seen around the Bay of Bohai Sea, and the fast velocity directions seem to show a rotation pattern, possibly indicating a flow-like deformation in the uppermost mantle there. The Pn velocity variations show a reversed correlation with the Earth's heat flow. The low Pn velocity regions generally show high heat flow, e.g., the Shanxi graben and Bohai Sea region. While the high Pn velocity regions usually manifest low heat flow, e.g., the region of Jizhong depression. This indicates that the Pn velocity variation in the study region is mainly aroused by the regional temperature difference in the uppermost mantle. Strong earthquakes in the crust tend to occur in the region with the abnormal low Pn velocity, or in the transition zone between high and low Pn velocity regions. The earthquakes in the low velocity region are shallower, while that in the transition zone are deeper.     

高温高压下含水矿物脱水对斜长岩纵波速度的影响

在1GPa、室温至880℃条件下对斜长岩的纵波速度进行了测量，并对实验产物进行了鉴定分析，讨论了含水矿物脱水对岩石纵波速度的影响。实验结果表明，在680℃左右，由于斜长岩中的含水矿物绢云母和黝帘石开始脱水，矿物脱水产生的流体及其所引起岩石结构的变化可使岩石纵波速度降低10％左右。这意味着通过矿物脱水这一机制可以形成壳内低速层。     

ADV measurements of velocity distributions in a gravel‐bed flume

Velocity measurements carried out by an acoustic doppler velocimeter (ADV) in a rectangular laboratory ?ume having a gravel bed are presented. The velocity pro?les are measured in six verticals of the channel cross‐section having an increasing distance (from 4 to 38·5 cm) from the ?ume wall. The experimental runs are carried out for ?ve different bed arrangements, characterized by different concentrations of coarser elements, and for the two conditions of small‐ and large‐scale roughness. For both hydraulic conditions, the velocity measurements are ?rst used to test the applicability of the Dean pro?le and of the logarithmic pro?le corrected by a divergence function proposed in this paper. Then, for each value of the depth sediment ratio h/d₈₄, the non‐dimensional friction factor parameter is calculated by integration of the measured velocity distributions in the different verticals of the cross‐section. Finally a semi‐logarithmic ?ow resistance equation is empirically deduced. Copyright © 2003 John Wiley & Sons, Ltd.     

Formation of Concentric Rings Around Sources

Zones of increased concentration formed by a solvent flowing from a source are considered. A matehmatical model for forming such zones is proposed. It takes into account that such a zone is composed of a set of independent particles. Hence the distribution of a substance around the source can be explained by movement of an individual particle. In the model this movement is a continuous semi-Markov process with terminal stopping at some random point in space. Parameters of the process depend on the velocity field of the flow. Forward and backward partial differential equations for the distribution density of a random stopping point of the process are derived. The forward equation is investigated for the centrally symmetric case. Solutions of the equation demonstrate either a maximum or a local minimum at the source location. In the latter case a concentric ring around the source is formed. If different substances vary in their absorption rates, they can form separable concentration zones as a family of concentric rings.     

农田生态系统大气硫沉降通量的观测研究

1998年 11月～ 1999年 10月间在中国科学院红壤站 (江西鹰潭 )农田小气候站进行了大气二氧化硫 (SO2 )、硫酸盐粒子 (SO2 -4)浓度采样和雨水样本收集 ,利用阻力模式和全年逐时气象资料计算 SO2 和 SO2 -4的干沉降速度 ,估算干沉降通量 ,利用降水资料和雨水中硫酸根离子浓度估计大气硫的湿沉降 ,从而定量研究大气硫沉降输入农田生态系统的通量 ,结果表明 :农田下垫面上 SO2 和 SO2 -4干沉降速度的年平均值分别是 0 .373± 0 .170 cm· s-1(月均值 0 .16 1～ 0 .5 45 cm·s-1)、0 .198± 0 .12 3cm· s-1(月均值 0 .15 2～ 0 .2 6 9cm· s-1)。农田下垫面硫年总沉降量为 10 .3g· m-2 ,其中干沉降占总沉降的 83.3%。硫的干沉降又以 SO2 的干沉降为主 ,占年干沉降总量的 92 .2 %。大气硫沉降输入占农田生态系统输入总量的 90 %以上 ,是农田生态系统获取硫素的一个重要途径     

实验速度场测量技术及对流边界层特征研究

在对流槽中对对流边界层(CBL)温度场实验研究的基础上,进一步尝试通过实验技术测量速度场并分析研究CBL中的速度场特征。在应用PIV测量技术时选用铝粉作示踪粒子。实验证明了在混合层中速度分布明显具有对流边界层热泡特性;混合层顶部的速度分布很好地反应出夹卷层的结构特征;湍流速度特征量的垂直分布合理,与野外实测结果和类似的对流槽实验结果接近;误差分析表明示踪粒子的跟随性良好,粒子速度的测量结果能真实地反应流体的运动特征,从而得证了分析结果的可靠性。     

松潘-甘孜造山带地壳速度结构

位于川西地区的奔子栏——唐克深地震测深剖面以NNE走向穿越松潘——甘孜造山带．根据人工地震记录分析得到的震相走时和相关的振幅信息，确定了该剖面二维P波地壳速度结构．剖面的地壳结构可分为5层，其中第1，2，3层为上地壳；第4，5层为下地壳．上地壳中部普遍存在低速异常带，但龙日坝以北，这一低速带与其上覆的低速基底合为一体．同时，沿剖面的地壳速度结构具有较强的横向变化．据此，可将剖面分为4段，即甘孜——理塘断裂以南、甘孜——理塘断裂至鲜水河断裂、鲜水河断裂至龙日坝断裂和龙日坝断裂以北. 这与区域构造划分基本一致． 地壳厚度沿测线从南西向北东逐渐减薄，即从金沙江畔的62 km减小到黄河附近的52 km． 根据PmP震相分析，莫霍界面深度在鲜水河断裂两侧没有明显变化．全剖面的地壳平均速度较低，为6.30 km/s．奔子栏——唐克剖面揭示了该地区的造山带型地壳上地幔结构特征．鲜水河断裂带位于剖面的中部，该地区的上地壳速度为正异常，而下地壳和上地幔顶部存在负异常．笔者认为，这是一类有利于强震孕育和发生的深部构造环境．