Models of Lithospheric Flexure and Outer Trench Wall Fracturing using an Iterative Spectral Method

We have developed and tested an iterative spectral solution technique for flexure of thin elastic plates having continuously varying rigidity in both horizontal directions. This novel method was used to model oceanic lithosphere bending seaward of deep-sea trenches. In our formulation, the various mechanical loads that lead to plate flexure are simulated as applied bending moments and vertical forces acting on an arbitrary trench planform. Another input required by our model is a grid of flexural rigidity covering the plate domain laterally. We developed a procedure for estimating the rigidity from the plate age and curvature. With the loading and rigidity as input, the iterative spectral method gives the plate deflection as output. The plate curvature is then recalculated to obtain updated values of the rigidity, from which a new deflection grid is produced. These computations proceed iteratively until convergence is achieved. For our parameter estimation problem, we sought to find values of applied moments and vertical loads that produce a plate deflection surface which matches the seafloor bathymetry from ship soundings and marine gravity from satellite altimetry. By referring to a yield strength envelope formulation, we can take the modeled deflection surface and predict the lateral distribution of brittle failure at the bent areas of the plate. If we consider optimally-oriented faults according to an assumed value of the friction coefficient, we find that the upper layer of the plate undergoing brittle failure deepens with increasing proximity to the trench. We conducted tests for our modeling approach on an outer rise region adjacent to the South American Trench. Our preliminary results suggest a correspondence between the prevalence of surface fractures observed in high-resolution bathymetry with model predictions of brittle failure extending more than 10 kilometers deep into the plate.