DAS depth calibration with multi-gauge length interrogation

A method for determining a calibrated vertical seismic profile (VSP) with a distributed acoustic sensing (DAS) system in a borehole, comprising:

• obtaining a density log and an acoustic slowness log for the borehole, wherein each log comprises a value recorded at a plurality of locations common to the density log and the acoustic slowness log;
• determining a first impedance, a DAS impedance from well log (DIL) curve, from the density log and the acoustic slowness log;
• obtaining a VSP dataset in the borehole, wherein the VSP dataset comprises a plurality of acoustic signals generated by a seismic source and recorded with the DAS system for a plurality of gauge lengths;
• for each of the plurality of gauge lengths:
• determining a second impedance, a DAS impedance from vibrations (DIV) curve, from the VSP dataset for the plurality of gauge lengths, and
• determining a fit between DIV curves and the DIL curve by using a misfit functional for each of a plurality of depth adjustments;
• determining the calibrated VSP by applying a preferred depth adjustment to the VSP dataset;
• forming, using a seismic processing system, a seismic image based, at least in part, on the calibrated VSP;
• planning, using a well planning system, a sidetrack borehole trajectory based, at least in part, on the seismic image;
• and
• drilling, using a drilling system, a sidetrack borehole guided by the sidetrack borehole trajectory.