Decoupling of Modes for the Elastic Wave Equation in Media of Limited Smoothness

Valeriy Brytik, Maarten V. de Hoop, Hart F. Smith, Gunther Uhlmann
2011 Communications in Partial Differential Equations  
We establish a decoupling result for the P and S waves of linear, isotropic elasticity, in the setting of twicedifferentiable Lamé parameters. Precisely, we show that the P ↔ S components of the wave propagation operator are regularizing of order one on L 2 data, by establishing the diagonalization of the elastic system modulo a L 2 -bounded operator. Effecting the diagonalization in the setting of twice-differentiable coefficients depends upon the symbol of the conjugation operator having a particular structure.
doi:10.1080/03605302.2011.558554 fatcat:ekhbeaean5gntceyig74vk3svq