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Crossing conjugate faults are difficult to incorporate into an earth model due to complex fault interactions and the limitations of fault modeling methods to handle these fault relationships. Y or lambda faults often require special handling, not only in the fault modeling stage but also when creating the horizon model and the reservoir grid. Correctly modeling half-Y or half-lambda faults - created by overlapping convergent or divergent conjugate faults - is even more problematic. These faults have truncation characteristics of Y or lambda faults along part of their length, but are not truncated in other sections. Previous methods of fault modeling, based on pillars or on binary trees, do not provide the flexibility necessary for modeling the complex truncations present in these situations. Our method not only provides a simple solution to modeling Y and lambda faults, but also to the more complex problem of the half-Y or half-lambda, including fault modeling, horizon modeling, and reservoir gridding. The inclusion of these faults in the framework not only results in a more accurate representation of the structure, but also improves the subsequent workflow. Volume calculations, well planning, reservoir gridding, and property modeling all benefit from the improved structural framework.