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

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