Generalized differential semblance optimization

This paper inverts space-lags in the suboffset-domain CIGs instead of time-lags for velocity estimate. As a reminder, the conventional DSO is an image-domain method for wave-equation tomography, where the essence of this method is to focus the image at zero suboffset and minimize the image at nonzero suboffset. At each iteration, the velocity model is updated by smearing the image on the nonzero sub- offset along wavepath. The space-lag is used as a penalty operator which annihilates the image energy at nonzero lags, where this space-lag is independent of the velocity model. This new method, denoted as generalized DSO, treats the space-lag as a function of velocity model. It is an extension of the conventional DSO except it updates the velocity model not only by smearing the image on the nonzero suboffset as in conventional DSO but also by smearing the nonzero suboffset along the wavepath. The former minimizes the image in the nonzero suboffset and the latter minimizes the nonzero suboffset of the image. Both methods aim to focus the image energy at zero suboffset. The mathematical derivation and numerical examples are presented to demonstrate its effectiveness in velocity inversion.