Extrapolation of vector (elastic) displacements by displacement potential field continuation
Extrapolating recorded elastic displacement data from the surface downwards is the first step of a two-step elastic migration scheme. The second step is the image formation condition. Although an elastic (vector) reverse time migration can extrapolate elastic displacement data downwards, the subsurface reflections and the loss of energy due to the use of the two-way wave equations are unavoidable. The elastic Kirchhoff-Helmholtz type integrals can not be used to extrapolate elastic displacement data downwards in media in which the velocity changes in both the x-direction and the z-direction. The present method attempts to first obtain the P- and S-wave displacement potentials near the surface...
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