Near-Borehole Formation Acoustic Logging Imaging: A Full Waveform Inversion Algorithm in Cylindrical Coordinates

Acoustic logging is essential for probing formations surrounding a borehole. However, conventional logging signal processing methods cannot process inhomogeneous formation structures. Inspired by seismic full waveform inversion (FWI), this study proposed a novel borehole imaging algorithm called borehole full-waveform inversion (BFWI) to probe the near-formation properties surrounding boreholes. To implement BFWI, we modified the original form of the elastic wave equations in cylindrical coordinates. We then derived the adjoint equations and gradient expressions in a pure form, avoiding the calculation of spatial derivatives and reducing the complexity of the program implementation. Simultaneously, we added a gradient preconditioning step to the BFWI to suppress the strong gradients generated by the guide waves. In addition, a multiscale inversion strategy was used to accommodate the initial model without prior structural information surrounding the borehole. The inversion results of the five test examples showed interface and velocity properties coincident with those of the true models, proving the validity and accuracy of the proposed algorithm. BFWI is not constrained by the formation structure and has wider applicability than traditional methods, showing considerable potential for near-borehole formation imaging.