A Robust Forward Modeling for Ultradeep Azimuthal Resistivity Logging in 3-D Well Trajectory

Electromagnetic (EM) forward modeling with analytical method in a planar-stratified transverse isotropic (TI) formation is the groundwork for electrical logging. However, there is little literature presenting the complete solution process despite it being a classic item for electrical logging. In this study, we present a complete framework of solving for EM field caused by triaxial magnetic dipole and apply it to simulate the response of ultradeep azimuthal resistivity (UDAR) logging tool. The complete framework consists of three parts such as solving for the direct fields in a homogeneous TI medium, deriving the field propagation in layered formation, and calculating the numerical integral of the field from the spectral domain to spatial domain. Each part is organically connected together, and the formulas are reformulated with an innovate approach. The field propagation is described using the coefficient propagator matrix method (CPMM), which is more efficient than the general reflection/transmission method because there is no iterative relationship. Over 400 filter coefficients are adopted to increase the efficiency and robustness of the Sommerfeld integral. Finally, an EM coupling algorithm for arbitrary azimuthal antennas is presented to simulate UDAR responses in 3-D well trajectory.