Complex Rays and Wave Packets for Decaying Signals in Inhomogeneous,Anisotropic and Anelastic Media

Diffraction and anelasticity problems involving decaying, evanescent or inhomogeneous waves can be studied and modelled using the notion of complex rays. The wavefront or eikonal equation for such waves is in general complex and leads to rays in complex position-slowness space. Initial conditions must be specified in that domain: for example, even for a wave originating in a perfectly elastic region, the ray to a real receiver in a neighbouring anelastic region generally departs from a complex point on the initial-values surface. Complex ray theory is the formal extension of the usual Hamilton equations to complex domains. Liouville's phase-space-incompressibility theorem and Fermat's stationary-time principle are formally unchanged. However, an infinity of paths exists between two fixed points in complex space all of which give the same final slowness, travel time, amplitude, etc. This does not contradict the fact that for a given receiver position there is a unique point on the initial-values surface from which this infinite complex ray family emanates. In perfectly elastic media complex rays are associated with, for example, evanescent waves in the shadow of a caustic. More generally, caustics in anelastic media may lie just outside the real coordinate subspace and one must trace complex rays around the complex caustic in order to obtain accurate waveforms nearby or the turning waves at greater distances into the lit region. The complex extension of the Maslov method for computing such waveforms is described. It uses the complex extension of the Legendre transformation and the extra freedom of complex rays makes pseudocaustics avoidable. There is no need to introduce a Maslov/KMAH index to account for caustics in the geometrical ray approximation, the complex amplitude being generally continuous. Other singular ray problems, such as the strong coupling around acoustic axes in anisotropic media, may also be addressed using complex rays. Complex rays are insightful and practical for simple models (e.g. homogeneous layers). For more complicated numerical work, though, it would be desirable to confine attention to real position coordinates. Furthermore, anelasticity implies dispersion so that complex rays are generally frequency dependent. The concept of group velocity as the velocity of a spatial or temporal maximum of a narrow-band wave packet does lead to real ray/Hamilton equations. However, envelope-maximum tracking does not itself yield enough information to compute synthetic seismograms. For anelasticity which is weak in certain precise senses, one can set up a theory of real, dispersive wave-packet tracking suitable for synthetic seismogram calculations in linearly visco-elastic media. The seismologically-accepiable constant-Q rheology of Liu et al. (1976), for example, satisfies the requirements of this wave-packet theory, which is adapted from electromagnetics and presented as a reasonable physical and mathematical basis for ray modelling in inhomogeneous, anisotropic, anelastic media. Dispersion means that one may need to do more work than for elastic media. However, one can envisage perturbation analyses based on the ray theory presented here, as well as extensions like Maslov's which are based on the Hamiltonian properties.     

Site effects in Mexico City: Constraints from surface wave inversion of shallow refraction data

In order to understand and simulate site effects on strong ground motion records of recent earthquakes in Mexico City, it is fundamental to determine the in situ elastic and anelastic properties of the shallow stratigraphy of the basin. The main properties of interest are the shear wave velocities and Q-quality factors and their correlation with similar parameters in zones of the city. Despite population density and paved surfaces, it is feasible to gather shallow refraction data to obtain laterally homogeneous subsoil structures at some locations. We focused our analysis in the Texcoco Lake region of the northeastern Mexico City basin. This area consists of unconsolidated clay sediments, similar to those of the lake bed zone in Mexico City, where ground motion amplification and long duration disturbances are commonly observed. We recorded Rayleigh and Love waves using explosive and sledgehammer sources and 4.5 Hz vertical and horizontal geophones, respectively. Additionally, for the explosive source, we recorded three-component seismograms using 1 Hz seismometers. We obtained phase velocity dispersion curves from ray parameter-frequency domain analyses and inverted them for vertical distribution of S wave velocity. The initial model was obtained from a standard first-break refraction analysis. We also obtained an estimation of the Q_S shear wave quality factor for the uppermost stratigraphy. Results compare well with tilt and cone penetrometer resistance measurements at the same test site, emphasizing the importance of these studies for engineering purposes.     

北半球不同纬度臭氧层系统混沌吸引子的特征研究

将TOMS测量的北半球不同纬度各纬向平均逐日O。总量作为无规序列,利用时滞方法重构序列的相空间吸引子,计算其系统状态演化过程中形成的整体结构特征.结果表明,各纬度O₃层系统吸引子都具有非整数分维结构；此外,在完整的Lpapunov指数谱中,所有指数分量之和均为负值,且最大指数分量总是正值.反映出O₃层系统相空间总体上是收缩的,同时提供了存在奇怪吸引子的证据,表征O₃层系统的演化是一种耗散混饨运动.这对于进一步应用非线性动力系统理论和方法,深入研究O₃层系统的动力学特征具有重要意义.     

天山及其邻区地壳上地幔S波速度结构的接收函数与面波频散联合反演

根据天山及其邻近区域88个宽频带地震台站的接收函数和欧亚大陆的基阶瑞利波群速度图像, 联合反演了这些台站下的地壳上地幔一维S波速度结构. 在这些速度模型的基础上, 利用线性各向同性变差克里金空间插值技术得到了该区域的地壳上地幔三维S波速度模型. 通过在垂向不同深度上的切片和横向上剖面投影的方式, 显示和分析了天山及其邻区地壳上地幔的剪切波速度特性与构造特性之间的关系. 结果表明, 天山及其邻区的地壳结构垂向上分为上、 中、 下3层, 每层的界面大致位于20, 40和50 km, 并且这些界面的起伏随不同块体的构造差异而变化. 天山地区和塔里木盆地隆起区的上地壳表现为高速特征, 而沉积盆地大部分地区和山前坳陷区的上地壳则表现为低速特征. 东、 西天山之间下地壳存在的近南北向低速带以及上地幔高速盖层在深度上的差异均说明东、 西天山在构造活动和形变上有明显的差别, 这种差别可能是由于印度板块与欧亚大陆的碰撞对它们产生的不同影响而造成的.     

三峡数字台网地震目录与地震报告的编辑

长江三峡数字遥测地震台网地需求目录与地震报告的编辑，是当每天地震交切定位后，存放到总库中，月底编辑、修改、整理形成地震目录和地震报告。本文主要对三峡数字遥测地震台网地震目录与地震报告的编辑进行阐述。     

Modeling of Wave Dispersion Using Continuous Wavelet Transforms

In the estimate of dispersion with the help of wavelet analysis considerable emphasis has been put on the extraction of the group velocity using the modulus of the wavelet transform. In this paper we give an asymptotic expression of the full propagator in wavelet space that comprises the phase velocity as well. This operator establishes a relationship between the observed signals at two different stations during wave propagation in a dispersive and attenuating medium. Numerical and experimental examples are presented to show that the method accurately models seismic wave dispersion and attenuation.     

Mantle structure from inter-station Rayleigh wave dispersion and its tectonic implication in western China and neighboring regions

We processed more than 3000 inter-station great circle paths to determine the phase velocity for the fundamental mode of Rayleigh wave, and finally arrived at 110 paths of high quality dispersion data, which show good spatial coverage in western China and neighboring regions. Rayleigh wave phase velocity dispersion model WChina1D was obtained and compared with previous global and regional models. Phase velocity maps from 15 to 120 s were inverted and the maps of 20, 40, 80, and 120 s are presented in this paper. Checkerboard tests show the average lateral resolution in our area of interest is about 7°. Our tomographic results corroborate a prominent low-velocity anomaly lying mainly in the lower crust and uppermost mantle in the Chang Thang terrane. The apparent low-velocity anomaly also appears in the wide area of northeastern Tibet in the crust and upper mantle. The low-velocity area around southeastern Tibet may be created by the southeastern migration of the low-velocity mass of the Tibetan plateau. The eastern Tarim shows structure with higher velocities relative to that of central Tarim. A large-scale low-velocity anomaly is clearly seen in central and western Mongolia. Our high quality measurements were also used to evaluate the CUB global shear velocity model [Shapiro, N., Ritzwoller, M., 2002. Monte-Carlo inversion for a global shear-velocity model of the crust and upper mantle. Geophys. J. Int. 151, 88-105] of the crust and upper mantle. The 40 s Rayleigh phase velocity map predicted from CUB model shows an apparent discrepancy with our measurements in western China and western Mongolia, which implies a higher estimated (about +1-2%) phase velocity model in these regions, probably due to the Gaussian smoothing condition in their tomography inversion.     

Earthquake source nucleation as self organization process

The theory of an earthquake source nucleation is discussed. Based on the assumption that self organization of damage process takes place in the zone of an earthquake source nucleation the theory incorporates the damage rheology framework of Lyakhovsky et al. and the approach of phenomenology theory of second-order phase transition. Namely, the free energy governing the process of an earthquake source nucleation depends on two collective variables α and φ in addition to the strain tensor ε_ij. The variable α quantifies the fracture of the medium and the variable φ quantifies the interaction effect of cracks. The region Ω_S is associated with a potential source of an earthquake if the damage variable α exceeds the critical value α_cr⁽¹⁾ inside Ω_S. The important feature of a potential source is that interaction of fractures causes acceleration of damage process inside the region of potential source and the material should lose stability primarily in this region. Interaction of fractures results also in occurrence of a residual stress caused by nonuniformity of fracture density. The appearance and development of the potential source result in increase of intensity of damage process not only in the region of potential source but also in a certain neighborhood of the last. It is compatible with such observed effects as acceleration of seismic energy release and growth of correlation length of weak seismicity before large earthquake. Transition of potential source to the stage of avalanche-unstable fracturing is associated with instability generated by explosive increase of interaction of fractures when the damage variable α exceeds the second critical value α_cr⁽²⁾ inside Ω_S.     

周边地区对北京地面SO2影响的初步研究

采用Lagrangian传输、扩散、沉降模式计算了1994年9、10月份(非采暖期)、1995年1月和2000年1月(采暖期)北京地区SO2的变化规律,并分别计算了北京市不同类型的排放源以及周边地区污染源对平均地面SO2浓度的贡献.计算结果与实际观测资料对比表明,模式能够较好地模拟北京地区SO2的浓度量级和逐日变化趋势.北京地区地面SO2浓度受天气条件的影响较大.采暖期,北京当地排放源的影响相对较大;但在大气条件有利输送的背景下,来自周边地区污染排放源的影响不容忽视.     

涡旋相互作用及其对强度和路径的影响

研究一个台风涡旋和一个低压涡旋之间的相互作用。该相互作用使低压涡旋强度 衰减的速率显著变慢，使低压涡旋滞留在初始位置附近的时间显著加长。在低压涡旋强度 演化和路径变化的过程中，显示出清楚的临界点现象。