Reconstruction of the history of the movement of layered geostructures: Inverse problem of gravitational stability
A time-inverse problem of gravitational (Rayleigh-Taylor) stability of a layered system is to reconstruct positions of its layers to their earlier stages. The Stokes equation, equations for transfer of density and viscosity, and equations of motion for interfaces between layers are solved numerically for negative time. We ignore thermal effects due to viscous dissipation. Under this assumption, the solution of the inverse problem is possible. A numerical approach is based on the Galerkin-spline finite-element method with interface tracking and a stripping-off method. A viscous material filling a model rectangular box is divided into layers by advected boundaries, across which physical parameters (density and viscosity) change discontinuously. The model approximates a stratified geological medium. The evolution of diapiric structures is restored by stripping off and decompacting sediments and by calculating material flows under the effect of gravity. An applicability of the suggested technique is demonstrated by reconstructions of upbuilt and downbuilt diapirs. The method is well suited for reconstructing diapiric structures.