Quantitative imaging of fractures around a borehole using linear slip theory and elastic least-squares migration

Single-well reflection imaging using sonic logging data successfully locates fine-scale structures around a borehole including fractures. In order to achieve accurate and quantitative estimation of fracture properties with high resolution, we propose to couple least-squares migration with linear slip theory. The proposed least-squares migration solves linearized waveform inversion where the wavefield is approximated using a Born operator incorporating a linear slip boundary condition. Representing a fracture as a linear slip interface is advantageous in accurate seismic wave modeling and efficient estimation of fracture properties. We derive conventional elastic least-squares migration for imaging perturbations in elastic constants, and new elastic least-squares migration for imaging fracture compliances. The two formulations are tested using numerical modeling where a dipping fracture is embedded in random background medium. The results show that least-squares migration generally produces higher resolution images for both SH and P-SV wavefields than using adjoint operators. Furthermore, it shows the potential of quantitative estimation of fracture compliances which can be further used in interpreting fracture properties, e.g., fracture infill material and surface condition. The proposed approach, therefore, will be crucial in fracture characterization around a borehole.