Double-difference constrained reflection tomography in two-dimensional elastic media

The inverted velocity model obtained from the reflection tomography based on the angle domain common-image gathers has a certain fuzziness. The inverted velocity model's stratigraphic interface is always not clear enough in areas with complex stratigraphic structure. In order to improve the accuracy and resolution of the inverted velocity model, a double-difference constraint condition is added on the basis of minimizing the absolute travel-time residual at the subsurface imaging points. This constraint makes the inverted velocity model local structure information more refined by minimizing the differential travel-time residual at adjacent imaging points (i.e. closely spaced points within the same layer) and makes the variation of velocity model information within a certain range more accurate. The method in this paper is based on angle domain common-image gathers, the tomography inversion equation is established by using the ray tracing method, and the conversion relationship between the traveltime residual and the residual curvature of the angle domain common-image gathers. Then, by adding differential constraint and double-differential constraint conditions and using the least squares QR decomposition method to solve the set of equations, the inverted velocity model can be obtained through multiple iterations, which provides a high-precision velocity field for the migration and improves the accuracy of seismic imaging. Numerical experiments on both one typical model and a field data example demonstrate the effectiveness of the proposed double-difference constrained elastic reflection tomography in generating high-precision velocity models.