Constraining the rheology of the lithosphere through joint geodynamic and gravity inversion

Understanding the physics of lithospheric deformation and continental collision requires good constraints on lithospheric rheology. Typically, rheology is determined from laboratory experiments on small rock samples, which are extrapolated to geological conditions - an extrapolation over 10 orders of magnitude in deformation rates. These laboratory experiments generally show that small changes in the composition of the rocks, such as adding a bit of water, can dramatically change its viscosity. Moreover, it is unclear which rock type gives the best mechanical description of, for example, the upper crust and whether a small sample is even appropriate to describe the large scale mechanical behavior of the crust. So the viscosity of the lithosphere is probably the least constrained parameter in geodynamics. Ideally, we thus need a new independent method that allows constraining the effective rheology of the lithosphere directly from geophysical data, which is the aim of this work. Our method uses the fact that the geodynamically controlling parameters of lithospheric deformation are its effective viscosity and density structure. By appropriately parameterising the rheological structure of the lithosphere we perform instantaneous forward simulations of present-day lithospheric deformation scenarios with a finite element method to compute the gravity field and surface velocities. The forward modelling results can be compared with observations such as Bouguer anomalies and GPS-derived surface velocities. More precisely, we automatize the forward modelling procedure with a Monte Carlo method, and in fact solve a joint geodynamic and gravity inverse problem. The resulting misfit can be illustrated as a function of rheological model parameters and a more detailed analysis allows constraining probabilistic parameter ranges. For a simplified setup with linear viscous rheologies we can demonstrate mathematically that a joint geodynamic-gravity inversion approach results in a unique solution as opposed to inverting for gravity alone. This is shown to work as well in combination with 3D forward models of salt tectonics on an upper crustal scale. Yet, the lithosphere has nonlinear rheologies that can be plastic or temperature-dependent powerlaw creep depending on stresses. As the thermal structure of the lithosphere is in general poorly constrained, and only affects the dynamics of the lithosphere in an indirect manner, we developed a parameterized rheology that does not include temperature but includes other nonlinearities (such as stress-dependent viscosity). To test the accuracy of this method we perform lithospheric-scale collision forward models that incorporate a temperature-dependent viscoelastic-plastic rheology to create synthetic gravity and surface velocities data. In a second step, we deploy these synthetic data sets to perform the joint inversion, using our simplified parameterized rheology. Results show that we can recover the rheology of the lithosphere reasonably well, provided that lithospheric layers contribute to the large-scale dynamics. In addition, we will show an application of our method to 2D cross-sections of the India-Asia collision system. Acknowledgements Funding was provided by the ERC under the European Community's Seventh Framework Program (FP7/2007-2013) / ERC Grant agreement #258830