井孔声场计算中的黎曼叶选择

针对耗散介质地层模型和双相介质地层模型，给出频率-波数域井孔声场函数Φ1(r,ω，k）在k实轴上满足辐射条件的单值定义，确定在积分围道上和围道内Φ1(r，ω,k)所在的黎曼叶．同时，澄清了首波分析中的一些概念．

充液井孔声场的路径积分估值中的极点分布(英文)

深入研究了充液井孔中声场积分所涉及到的变极点在 4个主要黎曼面上的分布 .给出了井孔中声场的积分表示 ,在柯西定理的基础上 ,利用复波数平面上不同的路径积分方法来表示井孔中的纵波势函数 ,计算了 4个主要黎曼面的极点位置 .

Single-valued definition of the multivalued function for borehole acoustic waves in transversely isotropic formations

It is useful to extract all components, including compressional, shear, and guided waves, from the full waveforms when we investigate the acoustic log data. The component waves can be simulated by calculating the contributions from poles and branch points of the borehole acoustic function according to Cauchy’s theorem. For such an algorithm to be implemented, the multivalued function for the borehole wave field in the frequency-axial-wavenumber domain has to be rendered single-valued first. Assuming that the borehole axis is parallel to the symmetry axis of transverse isotropy, this paper derives the branch points of the borehole acoustic function. We discover that the number and the locations of those branch points are determined by the relation among the formation parameters c33, c44, ε, and δ. Thus the single-valued definitions in the acoustic-wave computation are sorted into two different cases. After building the Riemann surface related to each radial wavenumber, we give the single-valued definition of the borehole acoustic function inside and on the integration contour based on the radiation condition. In a formation with δ 】 ε + c44/2c33, if we choose the integration contour and the single-valued definition of the acoustic function in the way used in isotropic cases, the simulation results of component waves will be wrong.

Accurate evaluation of Green's functions in a layered medium by SDP-FLAM

Based on local Taylor expansions on the complex plane, a method for fast locating all modes （FLAM） of spectral-domain Green＇s Functions in a planar layered medium is developed in this paper. SDP-FLAM, a combination of FLAM with the steepest descent path algorithm （SDP）, is employed to accurately evaluate the spatial-domain Green＇s functions in a layered medium. According to the theory of complex analysis, the relationship among the poles, branch points and Riemann sheets is also analyzed rigorously. To inverse the Green＇s functions from spectral to spatial domain, SDP-FLAM method and discrete complex image method （DCIM） are applied to the non-near field region and the near filed region, respectively. The significant advantage of SDP-FLAM lies in its capability of calculating Green＇s functions in a layered medium of moderate thickness with loss or without loss. Some numerical examples are presented to validate SDP-FLAM method.

Acoustic mode waves and individual arrivals excited by a dipole source in fluid-filled boreholes

An approach of separating individual wave arrivals for a dipole logging is presented. The branch points are treated as a type of logarithm and the Riemann surface structure of the multivalued function is studied, that is, the displacement potential within the borehole. Based on the theoretical analysis, the complex poles contributing to the wave field on various Riemann sheets are investigated in detail for the case of a fast formation. It is shown that poles on Riemann sheet (0,0) are real and form branches of modes with dispersion. Mathematically, it is demonstrated that the flexural mode has no cutoff frequency, which is different from the traditional point of view. Poles on other relevant Riemann sheets are complex and form many branches on the complex frequency-wavenumber plane. Further investigation on the pole and branch cut contributions indicates that the vertical branch cut integration method has limitations in separating wave arrivals. By properly taking into account the complex poles on various Riemann sheets together with branch cut integrations, wave arrivals are separated from the full wave-forms effectively for both the fast and slow formation models. Specially, there are complex poles on Riemann sheet (0,-1) in the vicinity of the compressional branch cut for a slow formation with a large Poisson's ratio, which have small imaginary parts and contribute a lot to the p-wave arrival.

A novel fractional order controller design algorithm for a class of linear systems

In this paper,a novel fractional order controller design algorithm is proposed for a class of linear systems.The proposed control algorithm is developed by employing Riemann principal sheet stability criterion.Oustaloup recursive approximation(ORA)method is used to implement the controller.The proposed controller is implemented in simulation.The results show that the proposed fractional order controller provides better results than the existing controllers in the literature work.