Rietveld et al. (1992) and Berkhout (1992) proposed a target-oriented wavefront synthesis for illuminating reflectors under a complex velocity overburden more clearly. Using the unitary property of the wavefield extrapolation operator, they generate a synthesis operator for a wave stack whose wavefront has a predefined shape at a certain subsurface location.
Suppose that we want to have a downgoing wavefield at depth zn. This wavefield can be obtained by propagating a certain wavefield at the surface, ,to the depth level zn.
If we assume each shot gather, U(w,x,z0|xs), is due to an impulse at xs, the response of the areal shot can be synthesized by using the convolution formula as
The imaging is performed in the same manner as profile imaging with as the upcoming wave and as the downgoing wave.