We describe the use of a novel mathematical data model, the sheaf data model, to support management and integration of diverse data sources and modeling tools used in the process of subsurface interpretation. We first introduce a simple abstract framework for the interpretation process. We follow with a review of the notion of data model and the requirements a data (meta-)model must meet to effectively support data integration in geoscience applications. We introduce the sheaf model and give a mostly non-mathematical overview of the principle features of the model, showing how it meets the requirements and how it can be used to make the abstract interpretation framework operational. We then describe the application of the framework and model to several specific interpretation topics. We finish by comparing the framework presented here to two existing frameworks.