Lithospheric flexure and deformation‐induced gravity changes: effect of elastic compressibility and gravitation on a multilayered, thick‐plate model

SUMMARY An approach is formulated by which the theoretical admittance can be evaluated for the flexure of a multi‐layered elastic plate overlying an inviscid fluid. The multi‐layered elastic and compressible plate is subjected to well‐posed boundary conditions. Gravitational body force, elastic compressibility and elastic coupling at the interfaces with elastic modulus contrast are fully accounted for. The elastic field solution was obtained by the propagator matrix technique. The contribution to gravity change from local density perturbation within the compressible plate is also included. Our calculation shows that the density perturbation component is smaller than the Bouguer component by at least an order of magnitude over the compensated waveband. The thin‐plate approximation can be used with an effective flexural rigidity evaluated from the thickness‐averaged values of the elastic moduli. If there is significant elastic coupling between the crust and the mantle, the discrepancy between our results and the incompressible, thick‐plate model can be quite appreciable due to the different isostatic compensation mechanisms operative within the crust. Preliminary calculations show that similar conclusions would apply to the response functions for the sub‐surface loading case. Our technique can also be used to compute the stress distribution in a multilayered plate. The numerical results show that the stresses can be appreciably different from that in a homogeneous plate.