Kirchhoff integral formula for reverse-time wave equation migration

Let us consider some hypothetical wave traveling upwards to the surface of observation with its front coinciding in space at a certain moment of time (say at t = 

according to Claerbout, the process of migration includes two elements  

1) backward extrapolation of the scattered wavefields (i.e. continuation of the waves in the direction opposite to that of their actual propagation) and 2) synthesis of the medium image as a snapshot (at time t = 0) of the spatial structure of the wavefield produced by backward extrapolation. These principles form the foundation of the majority of algorithms of time section migration (Berkhout, 1980, 1984 Claerbout, 1985 Kozlov, 1986 Gardner, 1985). 

As we see from the previous discussion, the key element of this approach is the process of backward continuation of the scattered wavefield. The diversity of available migration algorithms is related mostly to the differences in the numerical 

A similar result takes place in the frequency domain. Substituting the Green s function (r r a ) in equation (13.197) with its complex conjugate, (r lr w), which satisfies the radiation condition for convergent waves, we arrive at the following migration formula in the frequency domain  

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