VTI地层井孔模式波理论频散计算时伪极点的影响

波的频散特征在声波测井中有着十分关键的作用.VTI地层下井孔模式波的理论频散曲线可根据频散方程求解.本文首先采用常用的耦合位移势函数对应的频散方程进行了VTI地层斯通利波理论频散曲线的求解.结果发现,在一定各向异性强度范围内,会得到两种计算结果:一条常规斯通利波频散曲线和一条非频散曲线.这是频散矩阵行列式在该模型下存在两个零点导致的.进一步采用一种对称形式的位移势函数推导的对称频散矩阵时分析发现,非频散曲线对应的零点k^2-q^2p=0为频率-波数响应函数的一个伪极点.经分析,在横波速度范围内,满足伪极点存在的Thomsen参数γ有一定范围,通常在弱各向异性地层中存在.且满足伪极点存在的Thomsen参数γ范围与地层泊松比成负相关,泊松比越小,满足伪极点存在的γ范围越大.在计算理论频散曲线时应消除k^2-q^p这一公因式的影响,避免得到错误的计算结果,进而影响各向异性反演等计算结果.

Effect of pseudo-poles on the theoretical dispersion calculation of borehole mode waves in VTI formation

Due to the stratification of formation, anisotropic formation is a very common media in the oil and gas industry. Generally, a Transverse Isotropic(TI) model with a symmetric axis is used to simulate the wave propagation in anisotropic media. When the the symmetric axis of formation coincides with the borehole axis, we call it VTI(Vertical Transversely Isotropy) formation. Obtaining the anisotropy accurately is crucial to the accuracy of seismic imaging processing results. Wave dispersion characteristics play very important role in VTI anisotropy inversion. The theoretical dispersion curve of the borehole mode wave in VTI formation can be solved according to the dispersion equation. In this paper, firstly the commonly used dispersion equation corresponding to the coupled displacement potential function was applied to solve the theoretical dispersion curve of Stoneley wave in VTI formation. It is found that within a certain range of anisotropic strength, two results can be obtained: a conventional Stoneley wave dispersion curve and a non-dispersion curve. This is caused by the existence of two zero solutions in the determinant of the coupled dispersion matrix. The form of coupled dispersion matrix is very complicated, and it is difficult to analyze the causes of multiple solutions. Further analysis of the dispersion matrix corresponding to the displacement potential function in a symmetrical form reveals that the zero point k^2-q^2p=0, which is corresponding to the non-dispersion curve, is a pseudo-pole of the frequency-wavenumber response function. Found by the research, in the range of shear wave velocity, the Thomsen parameter γ which satisfies the existence of the pseudo pole has a certain range, it is usually in weak anisotropic formation. And γ which satisfies the existence of the pseudo pole is negatively correlated with the Poisson’s ratio of the formation, that is to say, the smaller the Poisson’s ratio is, the larger the γ range satisfying the pseudo-solution is. In the calculation of the theoretical dispersion curve, the influence of this common factor k^2-q^p should be removed to avoid erroneous calculation results, which in turn affect the calculation results such as anisotropic inversion.