## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Extension of proofs of Fermat’s principle

We extended proofs of Fermat’s principle of stationary traveltime to generally anisotropic inhomogeneous media.

Our proofs are based on the relation between Hamilton and Lagrange mechanics.

In contrast to the isotropic case, there are restrictions due to singularities of the Legendre transformation.

In presented theorems, we quantify these restrictions.

Thus, a seismologist invoking this principle, which is a common approach in applied seismology, ensures the reliability of resulting imaging and interpretation.

Bucataru, I., Slawinski, M.A. (2005) Generalized orthogonality between rays and wavefronts in anisotropic inhomogeneous media. Nonlinear analysis: Series B Real-world applications 6, 111–121

Antonelli, P.L., Bóna, A., Slawinski, M.A. (2003) Seismic rays as Finsler geodesics . Nonlinear analysis: Series B Real-world applications 4(5), 711–722

Bóna, A., Slawinski, M.A. (2003) Fermat’s principle for seismic rays in elastic media. Journal of Applied Geophysics 54, 445–451