Geodynamic inversion to constrain the non-linear rheology of the lithosphere

Abstract

One of the main methods to determine the strength of the lithosphere is by estimating it's effective elastic thickness. This method assumes that the lithosphere is a thin elastic plate that floats on the mantle and uses both topography and gravity anomalies to estimate the plate thickness. Whereas this seems to work well for oceanic plates, it has given controversial results in continental collision zones. For most of these locations, additional geophysical data sets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere as this also requires knowledge of the rheology of the lithosphere. Laboratory experiments suggest that rocks deform in a viscous manner if temperatures are high and stresses low, or in a plastic/brittle manner if the yield stress is exceeded. Yet, the experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent method is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. The goal of this paper is to discuss such an approach. Our method relies on performing numerical thermomechanical forward models of the present-day lithosphere with an initial geometry that is constructed from geophysical data sets. We employ experimentally determined creep-laws for the various parts of the lithosphere, but assume that the parameters of these creep-laws as well as the temperature structure of the lithosphere are uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology, we first perform a geodynamic inversion of a synthetic forward model of intraoceanic subduction with known parameters. This requires solving an inverse problem with 14–16 parameters, depending on whether temperature is assumed to be known or not. With the help of a massively parallel direct-search combined with a Markov Chain Monte Carlo method, solving the inverse problem becomes feasible. Results show that the rheological parameters and particularly the effective viscosity structure of the lithosphere can be reconstructed in a probabilistic sense. This also holds, with somewhat larger uncertainties, for the case where the temperature distribution is parametrized. Finally, we apply the method to a cross-section of the India–Asia collision system. In this case, the number of parameters is larger, which requires solving around 1.9 × 106 forward models. The resulting models fit the data within their respective uncertainty bounds, and show that the Indian mantle lithosphere must have a high viscosity. Results for the Tibetan plateau are less clear, and both models with a weak Asian mantle lithosphere and with a weak Asian lower crust fit the data nearly equally well.