Quantitative fracture imaging using least-squares migration and linear-slip model: theory and application to single-well reflection imaging

Characterizing subsurface fractures is a key to developing hydrocarbon and geothermal fields, as well as providing fundamental information on fracture system relevant to regional seismotectonics. Seismic characterization of fractures has generally been based on the effective medium theory, which considers seismically invisible small fractures. Therefore, there is a considerable scale gap between the fracture properties obtained by seismic methods and those from borehole logging. Recent studies of single-well reflection imaging using acoustic borehole logging data show the potential of filling the scale gap by providing fracture properties around the borehole up to a few tens of meter away from the borehole location. In the context of reflection imaging of individual fractures, in this study, we develop least-squares migration (LSM) coupled with linear-slip model. LSM solves the linearized waveform inversion to provide high-resolution quantitative images. Linear-slip model can describe wave reflection at a fracture accurately. We show numerical modelling examples of the proposed approach considering a vertical fracture with coupling compliances, and acoustic dipole measurements of a dipping fracture embedded in a background random velocity distribution. The results show that the proposed LSM provides higher resolution images than reverse-time migration, and more accurate images than the conventional LSM without linear-slip model.