3D deflection of a lithospheric plate with a variable flexural rigidity and under a variable sedimentary load for 3D backstripping: preliminary tests

To study the stratigraphic and morphological evolution of sedimentary basins and continental margins through time, sequential backstripping is commonly used to reconstruct their past geometries. On seismic images, the present geometry of preserved strata is different from its depositional morphology due to the effects of thermal subsidence, compaction, sediment loading and tectonics. The aim of backstripping is to undo the effects of these deformations and determine improved estimates of the past bathymetry and stratigraphy at different time slices. These calculations are generally performed along 2-D cross-sections but most continental margins are highly 3-D structures. Deltaic sediment lobes, oblique structures and sediment packages, deep sea fans, etc limit the accuracy of 2-D calculations. In addition, the flexural rigidity commonly varies from the continent, across the margin and into the oceanic basin. In order to perform 3-D backstripping, flexural unloading has to be considered as the deflection of a plate with a 3-D variable sedimentary loads and a spatially variable flexural rigidity. The global form of the equation is : \nabla²(D(\nabla²w)) - T\nabla²w + w = P, where D is the flexural rigidity, w is the deflection of the surface, T is the tension in the plate and P is the load. Formulating the equation in terms of the bending moments, M, leads to a set of four coupled 2nd-order equations. This theoretical problem leads, in practice, to a complex sparse matrix of the finite-difference approximation which must be solved numerically. First results will be shown (1) to estimate the validity of the approach prior to application to real data set, such as the Golfe du Lion passive margin and (2) to discuss the estimates and influence of the various parameters.