  Scientific curiosity, exploration of georesources and environmental concerns
are pushing the geoscientific research community toward subsurface
investigations of ever-increasing complexity. This review explores various
approaches to formulate and solve inverse problems in ways that effectively
integrate geological concepts with geophysical and hydrogeological data. Modern
geostatistical simulation algorithms can produce multiple subsurface
realizations that are in agreement with conceptual geological models and
statistical rock physics can be used to map these realizations into physical
properties that are sensed by the geophysical or hydrogeological data. The
inverse problem consists of finding one or an ensemble of such subsurface
realizations that are in agreement with the data. The most general inversion
frameworks are presently often computationally intractable when applied to
large-scale problems and it is necessary to better understand the implications
of simplifying (1) the conceptual geological model (e.g., using model
compression); (2) the physical forward problem (e.g., using proxy models); and
(3) the algorithm used to solve the inverse problem (e.g., Markov chain Monte
Carlo or local optimization methods) to reach practical and robust solutions
given today's computer resources and knowledge. We also highlight the need to
not only use geophysical and hydrogeological data for parameter estimation
purposes, but also to use them to falsify or corroborate alternative geological
scenarios.
