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在分析井孔特征函数黎曼面结构的基础上,给出了分析泄漏模式对声场贡献的方法,研究了泄漏模式对声场的贡献随井孔内外参数的变化.数值算例表明泄漏模式对纵波头波的影响大小与(-1,-1)和(0,-1)黎曼叶上的复极点在频率-波数域的分布有关.快速地层中泄漏模式对声场的贡献几乎可以忽略,但是在泊松比较大的慢速地层中存在虚部较小且靠近纵波支点的复极点,因此对某些声源频率泄漏模式的贡献较大;泄漏模式对头波的贡献随源距的增加逐渐衰减,大致与源距的平方成反比.
Based on the analysis of the Riemannian surface structure of the wellbore feature, a method of analyzing the contribution of the leakage mode to the sound field is presented, and the contribution of the leakage mode to the sound field varies with the internal and external parameters of the wellbore. Numerical examples show that the leakage mode affects the longitudinal wave The size of the first wave is related to the distribution of complex poles on the (-1, -1) and (0, -1) Riemannian leaves in the frequency-wavenumber domain. The contribution of the leak mode in the fast formation to the sound field is almost negligible, however The existence of complex poles near the fulcrum of the P wave in the relatively large slow-velocity formations with large Poisson’s amplitudes contributes more to some modes of sound source frequency leakage. The contribution of the leakage mode to the head wave decays gradually with the increase of the source distance , Roughly inversely proportional to the square of the source distance.