Local migration with extrapolated VSP green's functions

A novel VSP imaging method that only requires a local velocity model around the well is presented. This method is denoted as a "local migration", where the model-based forward propagation and backward propagation operators are computed using a local velocity model between the well and the the target body. The velocity model for the complex overburden and salt body are not needed, and the source-side statics are automatically accounted for. All kinematic and dynamic effects, including anisotropy, absorption and other unknown/undefined rock effects outside of this local velocity model are automatically accounted for. Numerical tests on an acoustic 2D Sigsbee VSP data set, an elastic Schlumberger salt model, and a Gulf of Mexico VSP data set empirically validate the effectiveness of this method by accurately imaging the sediments next to the vertical well. No velocity model is needed outside the target area.