Variational principle for Rayleigh wave ellipticity

SUMMARY Rayleigh wave ellipticity has high sensitivity to shallow depth and contains complementary information to phase and group velocity data whose sensitivity extends to deeper region. The inversion of this parameter has often been conducted by using numerically derived depth sensitivity kernels. We present compact formulas based on a variational principle which includes both volumetric seismic velocity perturbations and boundary perturbations. Use of this formula can speed up the inversion process considerably.