A 2.5D finite-difference(FD)algorithm for the modeling of the electromagnetic(EM)logging-whiledrilling(LWD)tool in anisotropic media is presented.The FD algorithm is based on the Lebedev grid,which allows for the disc...A 2.5D finite-difference(FD)algorithm for the modeling of the electromagnetic(EM)logging-whiledrilling(LWD)tool in anisotropic media is presented.The FD algorithm is based on the Lebedev grid,which allows for the discretization of the frequency-domain Maxwell's equations in the anisotropic media in 2.5D scenarios without interpolation.This leads to a system of linear equations that is solved using the multifrontal direct solver which enables the simulation of multi-sources at nearly the cost of simulating a single source for each frequency.In addition,near-optimal quadrature derived from an optimized integration path in the complex plane is employed to implement the fast inverse Fourier Transform(IFT).The algorithm is then validated by both analytic and 3D solutions.Numerical results show that two Lebedev subgrid sets are sufficient for TI medium,which is common in geosteering environments.The number of quadrature points is greatly reduced by using the near-optimal quadrature method.展开更多
文摘A 2.5D finite-difference(FD)algorithm for the modeling of the electromagnetic(EM)logging-whiledrilling(LWD)tool in anisotropic media is presented.The FD algorithm is based on the Lebedev grid,which allows for the discretization of the frequency-domain Maxwell's equations in the anisotropic media in 2.5D scenarios without interpolation.This leads to a system of linear equations that is solved using the multifrontal direct solver which enables the simulation of multi-sources at nearly the cost of simulating a single source for each frequency.In addition,near-optimal quadrature derived from an optimized integration path in the complex plane is employed to implement the fast inverse Fourier Transform(IFT).The algorithm is then validated by both analytic and 3D solutions.Numerical results show that two Lebedev subgrid sets are sufficient for TI medium,which is common in geosteering environments.The number of quadrature points is greatly reduced by using the near-optimal quadrature method.
