Recursive Algorithm for Electromagnetic Fields from Magnetic Dipole in Layered Triaxial Anisotropic Medium and Its Application

In order to quickly and accurately simulate the response of electromagnetic (EM) wave logging in complex triaxial anisotropic media, a pseudo-analytical recursive algorithm for the EM fields generated by magnetic dipole was developed, which was suitable for horizontal layered strata. By using the dual Fourier transform technique, the algorithm transformed the forward modeling of the three-dimensional EM field into a series of solutions of a one-dimensional spectral field. The upper and lower boundary positions were introduced into the general expressions of the spectral field, which avoided the numerical overflow problem in traditional algorithms. The propagation matrix method was then adopted to recursively derive the amplitude coefficients at each boundary. To handle the strong oscillation of the integral kernel function, a dual sine/cosine numerical filtering integral technique was developed to achieve the accurate and fast conversion between EMs from the spectral domain to the spatial domain. The simulation results show that the existence of triaxial anisotropy makes the electrical logging response more complex, and the traditional anisotropic electrical logging interpretation model is no longer applicable. The new recursive algorithm is the basis of complex anisotropic reservoir logging response analysis and provides a forward modeling method for accurate extraction of electrical parameters and accurate geosteering.