Dynamic Depth Alignment of Well Logs: A Continuous Optimization Framework for Enhanced Petrophysical and Rock Physics Interpretation

Two well logs from the same section of a well often have an unknown depth shift between them. If the well logs are corrected for this depth shift, the correlation between the logs will increase. We formulate an optimization problem that maximizes the correlation between the logs, while maintaining a physically reasonable depth shift. We implement a solver for this optimization problem and test it on real well logs from the Norwegian Continental Shelf. We demonstrate that changing the trade-off between the correlation term and the smoothness term in our cost function also changes the trade-off between correlation and smoothness in the resulting estimated depth shift. The automatically estimated depth shifts were confirmed by expert opinion to be similar to the depth shift that would have been estimated by an expert on data from 12 real wells, illustrated in Appendix 1.