双轴各向异性介质多分量感应测井响应快速计算

为研究双轴各向异性介质多分量感应测井响应特征,本文基于三重傅里叶变换,推导任意方向偶极子源的谱域电磁场解析式;采用围线积分方法,自适应截断积分区间,结合谱域电磁场周期特性,实现三重傅里叶变换的精确快速积分;进而,针对双轴各向异性倾斜地层,模拟研究不同纵横向各向异性条件多分量感应测井响应特征.结果表明:利用谱域内电磁场在周向的周期特性简化解析式,可将计算速度提高4倍;自适应截断积分区间方法保证了计算精度,并极大地减少了积分节点数.对于倾斜双轴各向异性介质,倾角较大时,共面分量可反映地层横向各向异性,同轴分量可反映地层纵向各向异性;倾角较小时,同轴分量可反映地层横向各向异性,共面分量可反映地层纵向各向异性.

Analytical solution of multicomponent induction logging response in biaxial anisotropic medium

To figure out the response characteristics of multicomponent induction logging in homogeneous biaxial anisotropic formation, analytical solution of electromagnetic (EM) field irradiated by arbitrary directed magnetic dipole is derived in spectral domain by using triple Fourier transform. Then, taking advantage of contour integration, adaptive integral interval truncation technique and periodicity property of EM field in spectral domain, fast and accurate integral of triple Fourier transform is readily available. Finally, the responses of multicomponent induction logging in dipping biaxial formations are simulated and the effects of transverse and longitudinal anisotropy are investigated. Numerical results show that analytical equations in spectral domain are simplified because of the periodicity of spectral domain EM field along angular direction, which can accelerate the integral up to four times. By introducing an adaptive integral interval truncation method, nodes of Gauss-Legendre quadrature are reduced without losing calculating precision. In dipping biaxial anisotropic media, while the dip angle is large, the transverse anisotropy of the formation will be reflected by the coplanar components, and the longitudinal anisotropy of the formation will be reflected by the coaxial component. When the dip angle is small, the transverse anisotropy of the formation will be reflected by the coaxial component, and the longitudinal anisotropy of the formation will be reflected by the coplanar components.