Local migration with extrapolated VSP Green’s functions

We have developed a novel vertical seismic profile (VSP) imaging method that requires only a local velocity model around the well. 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 target body. The velocity model for the complex overburden and salt body is not needed, and the source-side statics are automatically accounted for. In addition, kinematic and dynamic effects, including anisotropy, absorption, and other unknown/undefined rock effects outside of this local velocity model, are mostly accounted for. Numerical tests on an acoustic 2D Sigsbee VSP data set, an elastic salt model, and offset 2D VSP data in the Gulf of Mexico partly validate the effectiveness of this method by accurately imaging the sediments next to the vertical well.