Geodesic
Continuation of elastic waves in reverse time
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 3, pp. 341-350.

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Methods based on the inverse continuation of the oscillation field have received a wide use in the processing of multi-channel seismic prospecting data. Physically, the idea of this approach is clear: a wave field observed on some surface is continued into the medium and backward in time. Mathematically, all continuation algorithms that are used are based on a scalar model of the wave equation describing sufficiently well the wave nature of oscillations of individual types, but not taking into account the vector nature of these oscillations. It is well known that a system of equations of the dynamic elasticity theory (Lame equations) is a more adequate model for the description of seismic oscillations. In this paper, continuation of the field of elastic oscillations in an inhomogeneous isotropic medium is considered. 
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G. M. Tsybul'chik. Continuation of elastic waves in reverse time. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 3, pp. 341-350. http://geodesic.mathdoc.fr/item/SJVM_2009_12_3_a8/

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