## 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

## Fréchet-derivative approach as a ray-theory concept

We presented proofs that place the Fréchet-derivative approach as a ray-theory concept.

Our proofs are based on properties of the Cauchy problem of partial differential equations.

Presently, as a part of ray theory, the so-called finite-frequency approach benefits from the wealth of theoretical methods.

Prior to this work, it was commonly stated that the recently developed finite-frequency approach was a fundamental generalization of ray theory.

This approach, however, neither generalizes nor supplants ray theory; it is precisely a consequence of that theory.

Bos, L.P., Slawinski, M.A. (2013) On the relationship between ray theory and the banana-doughnut formulation. International Journal on Geomathematics 4(1), 55–65

Bos, L.P., Slawinski, M.A. (2011) Proof of validity of first-order seismic traveltime estimates. International Journal on Geomathematics 2(2), 255–263

Bos, L.P., Slawinski, M.A. (2010) Elastodynamic equations: Characteristics, wavefronts and rays. The Quarterly Journal of Mechanics and Applied Mathematics 63(1), 23–37