Relationships between Offset Domain/Angle Domain Common Image Gathers and Migration Velocity

In order to probe the relationships between wave equation offset domain common image gathers (ODCIGs) /angle domain common image gathers (ADCIGs) with migration velocity, we quantitatively derive the changes of ODCIGs and ADCIGs along with migration velocity on the assumption of uniform velocity medium with a horizontal reflector. We come to conclusion that ODCIGs are hyperbolas with half offset; on the contrary, they are ellipses. Combined with the results of depth focusing analysis, we find the apparent incident angles in ADCIGs are larger than the real incident angles when the migration velocity is larger than the true one and vice versa. With lower migration velocity, the residual moveout (RMO) on ADCIGs is an ellipse with the tangent of apparent incident angle; otherwise, it′s a hyperbola. In the valid seismic incident angle, ADCIGs are much more sensitive to the higher migration velocity. As to migration velocity analysis (MVA), it is suggested to start with a little higher initial velocity.