A View on Migration

The notion that migration collapses diffraction is derived from Huygens' principle in that migration integrates over the secondary source wavefront for all points and places the result at the apex of the hyperbola. Huygens' principle unifies acoustic wave propagation theory in that all wave types (reflection and diffraction) are derived from a single mechanism. However, this leads to thought that 3-0 resolution depends on diffraction. Wave propagation can also be broken into components of pure diffraction (Fraunhofer diffraction) and specular reflection by representing a reflector as a series of planar segments. Fraunhofer diffraction from an edge discontinuity, asymmetric and hyperbolic. represents the difference between specular reflection from an infinite plane and a planar segment. In the limit of reduction of a segment to a "point", Fresnel diffraction is seen to have encoded in it components of Fraunhofer (pure) diffraction and specular reflection. The explanation of migration in terms of segments shows that it is a dtscrtmtnator responsive only to reflection energy. To have a non-zero result, seismic energy must be coherent (tn-phase) along the (hyperbolic) path of integration. This occurs if S!llil only if the path is somewhere tangent to reflection energy, where the apex of the path coincides with a point on the reflector in its true position. Fraunhofer diffraction is a coincident hyperbola. but. because it is an asymmetric function. the integration result is zero. Integration that obliquely crosses coherent energy is statistically zero because the section taken of the energy is not coherent. Integration over random noise is statistically zero. Migration removes diffraction, and resolution depends on the 3-0 source wavelet. This description does not refute ideas based on Huygens' principle. Both models are actually mutually dependent. Fraunhofer diffraction and reflection can tie derived in terms of Fresnel diffraction and vice versa. What may appear to be a paradox is only a difference in Viewpoint. The hope is that the result is enlightening.