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为了认识井孔声波的传播规律,有效地从声波测井信号中提取地层纵波、横波和模式波信息,在模拟和分析声测井信号时,通常将轴向波数域的实轴积分转换成围道积分以及围道内极点留数之和.为实现这一运算过程,必须将多值的频率-轴向波数域井孔声场函数单值化.针对对称轴平行于井轴的横向各向同性地层,推导了井孔声场函数全部支点的表达式.我们发现,就井孔声场函数的支点个数及分布位置而言,可按各向异性系数ε,δ以及弹性系数c33,c44之间的大小关系,将横向各向同性地层分成两类.通过构造径向波数的黎曼面,分别针对这两类情况,给出了积分围道上及围道内满足辐射条件的井孔声场函数的单值定义.算例表明:对于参数满足δ>ε+c44/2c33的地层,在分波计算中如果依然选用各向同性情况下的积分围道以及声场函数单值定义,所得到的波场模拟结果就是错误的.
In order to understand the propagation rule of borehole acoustic wave, the information of formation longitudinal wave, shear wave and mode wave is extracted effectively from the acoustic logging signal. When simulating and analyzing the acoustic logging signal, the real axis of the axial wave number domain is usually converted into the circumference Track integral and the number of poles in the enclosure.In order to realize this operation process, the multi-valued frequency-axial wave number field well field sound field function must be singularized.For a transverse isotropic formation with symmetry axis parallel to the well axis , We derive the expressions of the full fulcrum of the well field sound field function.We find that according to the number and location of the fulcrum of the sound field function of the well bore, the anisotropy coefficient ε, δ and the elastic coefficient c33, c44 , The transverse isotropic stratigraphy is divided into two categories. By constructing the radial wave number Riemannian surface, the single value definition of the wellbore sound field function is given respectively for the two types of situations The example shows that for the strata whose parameters satisfy δ> ε + c44 / 2c33, if the integral channel and the single value of the sound field function are still selected in the calculation of the wavefronts, the wave field simulation result is error .