Efficient 1D modeling of triaxial electromagnetic logging in uniaxial and biaxial anisotropic formations using virtual boundaries and equivalent resistivity schemes

Abstract We introduce an efficient simulation method for triaxial electromagnetic (EM) logging in 1D uniaxial anisotropic (UA) and biaxial anisotropic (BA) formations. The foundation of this method is a set of compact formulas for EM fields in UA media, which transforms field computation into solving three decoupled amplitude pairs at each bed boundary. A virtual boundary scheme is proposed to ensure all formation boundaries within source-free layers, enabling a concise continuous equation at the source point. Subsequently, a modified propagator coefficient (MPC) algorithm is devised for calculating these amplitudes without complex matrix operations. Moreover, it reuses one-third of reflection coefficients, boosting the computational efficiency. For BA formations, this approach rapidly approximates scattered fields by leveraging solution multiplicities. Instead of direct computation, we invert equivalent UA models that yield identical responses, allowing us to compute the scattered fields with our efficient MPC algorithm. Numerical results confirm the stability and efficiency of 1D algorithm, demonstrating its capability for all UA formations and a 10-fold speed increase over traditional methods for BA formations. This advancement not only enhances simulation techniques for multilayered anisotropic formations but also facilitates the inversion of EM logging data.