Multicomponent Kirchhoff migration

Abstract

Abstract This paper presents a method for elastic and viscoelastic imaging of multicomponent seismic data. The method is based on Claerbout's survey-sinking concept and the (visco)elastic Kirchhoff integral for the displacement field. Assuming a multishot and multireceiver experiment, the migration process is formulated as a wavefield reconstruction problem, using the (visco)elastic Kirchhoff integral twice. First, the receiver coordinates are downward continued. Second, the source coordinates are downward continued. The multicomponent seismic data are treated as a vector wavefield in which the data measurements may be displacement velocity or traction (pressure). The theoretical formulation is based on the viscoelastic Hooke's law and Newton's equation of motion as the physical model for seismic wave propagation. It is valid for linear viscoelastic media with any anisotropic symmetry. When the lowest-order ray approximation is introduced, the migration equation takes a form similar to conventional Kirchhoff migration. To obtain the imaging equations, the downward-continued wavefield is related to the ray-Born approximation. Numerical results are shown from elastic imaging of synthetic and real marine walkaway vertical seismic profiling (VSP) data.