A depth positioning method to position a production logging tool (1) and a measurement log in a hydrocarbon well (3) in production obtained by means of the tool, the depth positioning method comprises: generating (S1, S2, S3, S1′, S2′, S3′, S11, S12, S13) a set of magnetic measurements (MAG1, MAG) of a depth portion of the hydrocarbon well from a first passive magnetic sensor along the depth portion of the hydrocarbon well, the set of magnetic measurements comprising magnitude and/or direction measurements of the magnetic field that forms a characteristic magnetic field pattern representative of a surrounding magnetic environment of the hydrocarbon well all along the depth portion; comparing (S4, S4′, S14) the set of magnetic measurements (MAG1, MAG) to another set of magnetic measurements (MAG_R, MAG2), the other set of magnetic measurements being a reference set of magnetic measurements generated either by a same or similar passive magnetic sensor deployed and run in the hydrocarbon well earlier, or by a second passive magnetic sensor spaced from the first passive magnetic sensor from a defined distance (DS) deployed and run in the hydrocarbon well simultaneously; and determining (S4, S4′, S14) the maximum of correlation between the set of magnetic measurements (MAG1, MAG) and the reference set of magnetic measurements (MAG_R, MAG2), the maximum being related to identifiable characteristic magnetic field pattern over a part of the depth portion.