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

Abstract

We establish a decoupling result for the P and S waves of linear, isotropic elasticity, in the setting of twice-differentiable 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.

Keywords:

• Diagonalization
• Elastic waves
• Mode decoupling
• Smoothness

Mathematics Subject Classification:

• Primary 35L52
• Secondary 35B65, 74J05

Acknowledgments

The research of Brytik, de Hoop, and Uhlmann was supported in part under NSF CMG grant EAR-0724644; Uhlmann was also partly supported by a Walker Family Endowed Professorship. The research of Smith was supported under NSF grant DMS-0654415.