Geological Objects and Physical Parameter Fields in the Subsurface: A Review

International audience; Geologists and geophysicists often approach the study of the Earth using different and complementary perspectives. To simplify, geologists like to define and study objects and make hypotheses about their origin, whereas geo-physicists often see the earth as a large, mostly unknown multivariate parameter field controlling complex physical processes. This paper discusses about some strategies to combine both approaches. In particular, I review some practical and theoretical frameworks associating petrophysical heterogeneities to the geometry and the history of geological objects. These frameworks open interesting perspectives to define prior parameter space in geophysical inverse problems, which can be consequential in under-constrained cases.