The methods of integrated interpretation of multiphysics geophysical data have been advanced considerably in recent years. One widely used approach is based on imposing so-called structural constraints. The concept itself and its numerical implementation, known as the cross-gradient inversion, have been introduced in seminal paper by Gallardo and Meju (2003a). For a recent review we refer to Moorkamp et al. (2016). The method and its numerous variants possess some limitations, such as non-uniqueness, non-linearity of the resulting model functional and difficulties to extend this approach to more than two physical properties. For these reasons, we develop another approach to the joint inversion based on the Gramian constraints (Zhdanov et al, 2012). This approach uses a very general mathematical formulation, which makes it possible to impose different types of constraints on the jointly inverted model parameters, including the structural constraint as a special case. One important advantage of this approach over the cross-gradient method is that, it results in a quadratic model functional that can be readily generalized on any number of physical domains.