WAVE-EXTRAPOLATION EQUATIONS

A wave-extrapolation equation is an expression for the derivative of a wavefield (usually in the depth z direction). When the wavefield and its derivative are known, extrapolation can proceed by various numerical representations of  

$$P (z \,+\, \Delta z ) \eq P(z) \ + \ \Delta z \ {dP \over dz }$$ (1)

Extrapolation is moving information from z to $z+\Delta z$and what we need to do it is a way to find dP/dz. Two theoretical methods for finding dP/dz are the original transformation method and the newer dispersion-relation method.