Estimating the lithospheric flexure of a plate with non-uniform flexural rigidity: a quantitative modelling approach

Abstract

Lithospheric deformation is a fundamental process in plate tectonics. It is, therefore, critical to determine how the lithosphere responds to geological loads to better understand tectonic processes. The lithosphere can be modelled as the flexure of a thin, elastic plate over long-term (> 105 yr) geological timescales. The partial differential equation for the flexure of an orthotropic plate is used indirectly to calculate theoretical admittance and coherence, which are then compared against the observed admittance and coherence to invert for the non-uniform flexural rigidity (or effective elastic thickness, Te) of the plate. However, the process for accurately recovering variable lithospheric flexure remains unresolved, as the classical lithospheric model may overestimate the deflection of the plate. Here we adopt the classic lithospheric model with applied external and internal loads at the surface and Moho, respectively, and assume that the compensation material is denser than the mantle material beneath the Moho. The lithospheric flexure errors are derived mainly from the Te and Moho recovery errors in this lithospheric model. Synthetic modelling is then performed to analyse the influence of the Te and Moho errors. The analysis of synthetic modelling shows that: (1) the Te error-induced flexure errors exhibit a rippling pattern, and the rippling pattern is broader in high Te regions; (2) the Moho error-induced flexure errors mainly occur in the low Te regions, and applying Airy isostasy theory in low Te regions may still greatly overestimate the lithospheric deformation amplitude; and (3) the lithospheric flexure errors are dominated by the Te and Moho errors in the high and low Te regions, respectively.