For a geoscientist, the Relative Geologic Time (RGT) is an important tool to perform chronostratigraphic analysis. However, automatically estimate an RGT image from a seismic image can be a challenging task where we have to respect seismic features, the deposit orders and to deal efficiently with unconformities such as erosions, progradating systems, etc. To this end, approaches have been proposed formulating the estimation problem in a regularized convex optimization problem. However none of these fully address efficiently all issues. In this paper, we propose a new regularization term based on an asymmetric and adaptive weight function. The asymmetric behavior focuses on the ill-posed problem while the adaptive process is used to deal with unconformities by modulating the strength of the regularization if necessary. Moreover, to increase the robustness of the approach, we propose variants of the method in terms of l(1)-norm instead of l(2)-norm that corresponds to potentially too smooth solutions. For evaluating the relevance of our proposals, experimentations have been conducted on both synthetic and real seismic images. (C) 2018 Elsevier B.V. All rights reserved.