Abstract: The measurement of acoustic moveout is affected by both hole diameter enlargement and lithological change. A sand/shale profile model was designed with different hole diameters and lithologies. The propagation path of slide wave generated by compensated sonic logging is analyzed. Then, Fermat minimum time principle is used to deduce the compensation formula by considering the effect of both hole diameter and lithology. The compensation value of acoustic moveout calculated by classical parameters is coinciding with the actual data read from logging curve.