Well-log correlation is a crucial step to construct cross sections in estimating structures between wells and building subsurface models. Manually correlating multiple logs can be highly subjective and labor intensive. We have developed a weighted incremental correlation method to efficiently correlate multiple well logs following a geologically optimal path. In this method, we first automatically compute an optimal path that starts with longer logs and follows geologically continuous structures. Then, we use the dynamic warping technique to sequentially correlate the logs following the path. To avoid potential error propagation with the path, we modify the dynamic warping algorithm to use all the previously correlated logs as references to correlate the current log in the path. During the sequential correlations, we compute the geologic distances between the current log and all of the reference logs. Such distances are proportional to Euclidean distances, but they increase dramatically across discontinuous structures such as faults and unconformities that separate the current log from the reference logs. We also compute correlation confidences to provide quantitative quality control of the correlation results. We use the geologic distances and correlation confidences to weight the references in correlating the current log. By using this weighted incremental correlation method, each log is optimally correlated with all the logs that are geologically closer and are ordered with higher priorities in the path. Hundreds of well logs from the Teapot Dome survey demonstrate the efficiency and robustness of the method.