Image-Domain Least-Squares Migration for RTM Surface-Offset Gathers

Recent development of reverse time migration allows us to produce surface-offset gathers (SOGs) and opens the opportunity for amplitude-verse-offset analysis with a wave-equation-based migration method instead of traditional ray-based migration. We formulate an image-domain least-squares migration for surface-offset gathers to correct for limited acquisition aperture, geometric spreading, and velocity complexity. To approximate the Hessian, we start with a distribution of point scatterers in the model space, generate synthetic diffraction data with Born modelling, and migrate the data to produce corresponding point-spread functions in the form of surface-offset gathers. An image-domain inversion is then performed with these point-spread functions, as an approximate to the Hessian inverse. Numerical examples of the 3D synthetic elastic data are shown to illustrate the benefits of our method. After inversion, the SOGs clearly show consistent amplitudes to further offsets and better resolutions after compensating for acquisition aperture, geometric spreading, and velocity complexity.