Analysis of stationary condition for Virtual Reflection signals

The “Virtual Reflector” (VR) method provides virtual seismic signals by processing real seismic traces. This technique is essentially based on cross-convolution of the recorded traces and subsequent integration in the receiver (or source) space. Under proper receiver (source) coverage conditions, the method allows obtaining the Green's function of virtual reflection wavefields as if at the position of the receivers (or sources) there was an ideal reflector, even if a real reflector is not present at said position. In this paper we analyze the stationary-phase conditions for virtual reflection signals, to determine the location of the virtual reflection point created at the receiver (source) line. The analysis does not need the knowledge of the subsurface velocity model, and provides reflection-angle conditions for rays propagating between source and receiver points that satisfy the stationary reflection conditions.