We analyze the kinematic properties of offset-domain common image gathers (CIGs) and angle-domain CIGs (ADCIGs) computed by wavefield-continuation migration. Our results are valid regardless of whether the CIGs were obtained by using the correct migration velocity. They thus can be used as a theoretical basis for developing migration velocity analysis (MVA) methods that exploit the velocity information contained in ADCIGs.
We demonstrate that in an ADCIG cube, the image point lies on the normal to the apparent reflector dip that passes through the point where the source ray intersects the receiver ray. The image-point position on the normal depends on the velocity error; when the velocity is correct, the image point coincides with the point where the source ray intersects the receiver ray. Starting from this geometric result, we derive an analytical expression for the expected movements of the image points in ADCIGs as functions of the traveltime perturbation caused by velocity errors. By applying this analytical result and assuming stationary raypaths (i.e., small velocity errors), we then derive two expressions for the residual moveout (RMO) function in ADCIGs. We verify our theoretical results and test the accuracy of the proposed RMO functions by analyzing the migration results of a synthetic data set with a wide range of reflector dips.
Our kinematic analysis leads also to the development of a new method for computing ADCIGs when significant geological dips cause strong artifacts in the ADCIGs computed by conventional methods. The proposed method is based on the computation of offset-domain CIGs along the vertical-offset axis and on the “optimal” combination of these new CIGs with conventional CIGs. We demonstrate the need for and the advantages of the proposed method on a real data set acquired in the North Sea.