A new seismic and gravitational method for the decompacted zones detection in crystalline basement, based on a multi-crack-cavernous pore (gas or oil saturated) model of crystalline reservoir is proposed. To estimate the capabilities of the proposed method mathematical modeling of effective elastic and acoustic properties of granite reservoir rocks with different pore space structure is realized. The algorithm and software for solving the problem of joint inversion of seismic and gravimetric data based on Born's approximation for the space-time Green's function with root mean square background velocity for the horizontally-layered medium has been developed and tested. It has been determined that the most reliable estimation of density and seismic velocity can be obtained by joint inversion. Convincingly is illustrated on an example of the Prykerch shelf model that the presence of decompacted oil or gas saturated zone in granite basement can be confidently identified based on results of seismic and precise gravity observations.