用传播矩阵法研究层状交错地层中的多分量感应测井

为了实现交错沉积等复杂环境中的电磁场数值模拟，本文在常规横向同性模型的基础上引入了电导率主轴坐标系相对地层坐标系的层理方位角和倾角，建立了交错地层模型.并利用传播矩阵法建立了一维层状交错地层模型中的多分量感应测井仪器响应的正演模拟算法.首先将频率-波数域中的电磁场分解为上行和下行模式波，给出了任意朝向的磁偶极子在无限大地层中模式波的解析解.进一步通过引入地层界面上的透射、局部反射以及广义反射系数矩阵，推导了一维层状地层中的模式波表达式.在此基础上，利用二维Gauss-Legendre积分实现了Fourier逆变换，得到了可用于多分量感应测井模拟的频率-空间域磁场并矢格林函数.最后，通过多个数值模拟结果考察了井眼倾角、层理方位角和倾角变化对多分量感应测井响应的影响.

Study of multi-component induction logging in layered crossbedding formation using the propagation matrix method

The purpose of this work is to simulate the electromagnetic (EM) field in complicated media such as crossbedding deposits. We consider a crossbedding model by introducing the bedding azimuth angle and the bedding dip angle of the principal conductivity coordinate with respect to the formation coordinate on the basis of the conventional transversely isotropic (TI) model. The propagation matrix method (PMM) is applied to establish the forward modeling for responses of multiple-component induction logging (MCIL) in 1D layered crossbedding formation. Firstly, the EM field in the frequency-wavenumber domain is decomposed into upward and downward mode-waves. Then, we derive the basic solutions of the mode-waves induced by an arbitrarily oriented transmitter in an infinite homogeneous medium. Based on this, we further obtain the expressions of mode-waves in the 1D layered formation by introducing the transmission matrices and both local and generalized reflection matrices. Next the 2D Gauss-Legendre quadrature is used to calculate inverse Fourier transformation and the magnetic Green's function in the frequency-space domain which permits to simulate the MCIL response. Finally, we investigate the influences of borehole dip angle, bedding azimuth angle and dip angle on MCIL responses by several numerical simulations.