DMO processing for mode-converted waves in a medium with a linear increase in velocity with depth
Shaowu Wang, John C. Bancroft, Donald C. Lawton
Dip moveout (DMO) processing for converted-waves (P-SV) differs from that for either P- or S-waves only because of the asymmetry of down-going and up-going raypaths, even in an isotropic and homogeneous medium and with a zero-dip reflector. This makes the kinematics more complicated than that for P-waves or S-waves. Previous work on DMO processing for a depth-variable velocity medium has been concerned with DMO processing for either P- or S-waves.
In this paper, an analytical expression for the P-SV DMO operator in a medium with a vertical, linear velocity gradient is derived. The differences between DMO operators in constant velocity medium and a linear velocity gradient medium are discussed. Finally, an approximate operator for a linear velocity gradient medium is proposed, and we show that this operator fits the accurate operator very well, making the P-SV DMO processing in a depth-variable velocity medium practical.