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.     

基于F-K偏移和反偏移的地震道插值方法研究

野外采集的地震数据经常存在空道或者坏道的情况,为了满足地震数据处理精度的要求,就必须首先进行插值.本文提出了一种新的地震数据插值方法：F-K偏移和反偏移插值法,该方法是通过F-K偏移和反偏移的串联使用来实现的.与其他的插值方法相比,这种插值方法的优点在于计算速度快,没有经过近似处理,精度高.F-K偏移/反偏移能够实现道插值的原理和Kirchhoff偏移/反偏移插值方法类似,也是由于数据是有限带宽的原因引起的.通过对模型的试算,可以看到F-K偏移和反偏移插值方法有着比较好的插值效果,是一种高效、准确、可行的方法.     

Analytical study of the effect of the geometrical parameters during the interaction of regular wave-horizontal plate-current

The present work is an analytical study of the influence of geometrical parameters, such as length, thickness and immersion of the plate, on the reflection coefficient of a regular wave for an immersed horizontal plate in the presence of a uniform current with the same direction as the propagation of the incident regular wave. This study was performed using the linearized potential theory with the evanescent modes while searching for complex roots to the dispersion equation that are neither pure real nor pure imaginary. The results show that the effects of the immersion and the relative length on the reflection coefficient of the plate are accentuated by the presence of the current, whereas the plate thickness practically does not have an effect if it is relatively small.     

基于传输线的单负材料双层结构的隧穿性质

通过传输线方法实现了负介电常数(ENG)和负磁导率(MNG)材料,并在实验上研究了由两种单负材料组成的双层结构(ENG-MNG)的电磁隧穿性质.结果表明,两种单负材料均不支持电磁波的传播,然而ENG-MNG双层结构在结构的平均介电常数和平均磁导率分别为零的条件下,具有完全隧穿模,并且这一隧穿模不随着结构尺度的改变而改变.在隧穿频率点,通过对ENG-MNG双层结构中电场分布的模拟与测量,实验上观察到了倏逝场的指数放大.