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In water resources management, correct identification of bedrock characteristics, such as type, depth and structure is useful and various geophysical methods are used for this purpose. In geophysical and subsurface investigations, solving inverse problems using physics of the problem in partial differential equation (PDE) system is very important. Inverse modeling is one of the useful solutions which creates a logical model between observed and measured values. The limitations and ambiguity of individual techniques can be significantly reduced by adopting joint inversion schemes. Using inversion approaches which combine two or more geophysical methods, allows substantial improvements in modeling processes. The joint inversion of different electromagnetic and resistivity data sets in hydrogeology, structural geology and mining has been used in some studies but the gravity method is less used in hydrogeological investigations. One example of using gravity method in previous studies is an algorithm for joint inversion of gravity and resistivity data, where the interfaces corresponding to changes in the bulk density were interpreted as interfaces of porosity and water content changes, i.e. interfaces of electrical resistivity changes. In this paper, we present a framework for joint inversion of gravity and geoelectric data solving under-determined inverse problems. It can be used in a wide range of physical systems governed by PDEs. The integrated approach is based on the connection between density and resistivity of a sedimentary sequence through the porosity. Also, we present a general adjoint state formulation which may be used in this framework. It increases the calculation speed of sensitivity matrices in a variety of commonly encountered under-determined problems. There are two steps in this research. First, 2D joint inversion of gravity and geoelectric data is run and validated in COMSOL multi-physics software using one synthetic model and synthetic data in a forward modeling process. Afterwards, using real gravity and geoelectric data surveyed along a cross-section in part of the Qotrum plain in the SE Yazd, the lateral structure of bedrock is estimated. Because Qotrum basin is already well surveyed, it offers opportunities for evaluation of accuracy and reliability in joint inversion approaches. Fifty-one gravity stations and eleven vertical electrical soundings were carried out across the central part of this basin to apply the proposed joint inversion. The results indicated that gravity-geoelectric joint inversion is more accurate than the individual interpretation of each of these methods and significantly improves the solution by decreasing the ambiguity of models. Furthermore, this method, while high in computational speed, can be used in modeling of a wide range of geophysical, hydrogeological and physical systems governed by the partial differential equation laws. [ABSTRACT FROM AUTHOR]