New analytical solution for estimation of flexural rigidity

In the frame of a PHD-work in the subproject F1/F4 of the Collaborative Research Center "Deformation processes in the Andes" (SFB 267) the analytical solution for estimation of the flexural rigidity (equivalent the elastic thickness) of the lithosphere based on given topography and moho undulations e.g. taken from a 3D density model or computed by an inversion from gravity data, was developed. The flexural rigidity is the parameter that governs the flexural response of the lithosphere in the meaning of a theoretical thin plate flexure model. This proposed analytical solution is an alternative methode to the widely used calculation of admittance of topography and gravity and the coherence methode, with some good advantages. Instabilities of the numerical admittance evaluation in wavenumber domain with low spectral energy of topography are overcome. The analysis can be made over an area which is much smaller than 350 km comparable to the coherence methode. The proposed methode allows a higher space resolution of elastic thickness than any other spectral methode. Instead of calculating the admittance function using spectral analysis, a set of point-load response functions is used in order to retrieve the optimal flexure parameter. Essential for the modeling is furthermore the isostatic flexure model, which is evaluated in terms of a convolutional approach (Braitenberg), thus overcoming the problems connected with a spectral analysis. This convolution methode was successfully applied in South China Sea and the Eastern Alps. Now the analytical solution is included within this convolution approach and was for the validation compared with the FFT-solution after Vening-Meinesz. This new methode has been applied in the SFB 267 working area of the Central Andes (15-$33\deg$S) and Southern Andes (36-$42\deg$S). Based on this Database the gravity field over the Andes has been used to construct 3D density models (IGMAS, Schmidt and Götze) from which the crustal thickness variations are obtained. Constraining data of this density models come from results of other projects of the SFB 267 e.g. the crust-mantle interface depth values recovered from seismic studies, reciever function study and the shipborne bathymetry measurements. The computation of spatial variations of the flexural rigidity leads us to understand the differences between the northern and the southern part of the Andes and to distinguish e.g. some tectonical provinces. The analytical computed flexure model and the gravity model of moho depth variations agree very well over all the areas.