A Fast Hybrid Analytical-Numerical Method for Borehole Dipole Acoustic Remote Detection

Extensive forward modeling of dipole remote detection is essential for analyzing scattered wavefields and serves as the basis for advanced imaging and inversion of geological structures around boreholes. This study proposes a hybrid analytical-numerical method to address the computational efficiency challenges of conventional 3-D numerical methods. The method couples analytical and finite-difference time-domain (FDTD) solutions through the total-field/scattered-field (TF/SF) technique and uses the reciprocity principle, avoiding full-space discretization and reducing the overall computational cost. Numerical tests illustrate that the method improves computational efficiency by an order of magnitude and nearly halves memory requirements while maintaining high accuracy. This computational advantage enables efficient 3-D forward modeling for dipole array acoustic logging with various far-field objects. The resulting receiver array waveforms at varying depths indicate that the reflection features can well identify the distance, azimuth, and distribution of geological objects far away from the borehole. The proposed efficient forward modeling algorithm has the potential to investigate wave propagation and reflection characteristics in complex 3-D geological structures.