Palaeoclimate and sea-level studies commonly rely on interpretations based on depth. The location and quantity of core recovered during a drilling expedition has direct implications for subsequent applications of core measurements. A key objective of Integrated Ocean Drilling Program (IODP) Expedition 310 is to establish the course of postglacial sea-level rise for Tahiti in the South Pacific, for which assigning the correct depth to recovered core is fundamental. By convention, core is placed at the top of the core barrel run from which it was collected. Unless core recovery is 100%, this results in depth errors that are inversely proportional to the recovery. The difficulties of locating core are compounded for the Tahiti boreholes, where primary cavities in the carbonate reef successions are frequently present. Only through the integration of core with continuous geophysical measurements of the borehole can accurate depth positioning be achieved. High-resolution optical and acoustic images of the borehole wall allow effective visual correlation of the core and logging datasets. The final integrated depths form the underlying framework for all subsequent scientific analyses of recovered core employing evaluations that rely on depth. Furthermore, the integration process allows true core recoveries to be accurately estimated.