Three-dimensional pre-stack depth migration of receiver functions with the fast marching method: a Kirchhoff approach

We present a novel 3-D pre-stack Kirchhoff depth migration (PKDM) method for teleseismic receiver functions. The proposed algorithm considers the effects of diffraction, scattering and traveltime alteration caused by 3-D volumetric heterogeneities. It is therefore particularly useful for imaging complex 3-D structures such as dipping discontinuities, which is hard to accomplish with traditional methods. The scheme is based on the acoustic wave migration principle, where at each time step of the receiver function, the energy is migrated back to the ensemble of potential conversion points in the image, given a smooth 3-D reference model. Traveltimes for P and S waves are computed with an efficient eikonal solver, the fast marching method. We also consider elastic scattering patterns, where the amplitude of converted S waves depends on the angle between the incident P wave and the scattered S wave. Synthetic experiments demonstrate the validity of the method for a variety of dipping angle discontinuities. Comparison with the widely used common conversion point (CCP) stacking method reveals that our migration shows considerable improvement. For example, the effect of multiple reflections that usually produce apparent discontinuities is avoided. The proposed approach is practical, computationally efficient, and is therefore a potentially powerful alternative to standard CCP methods for imaging large-scale continental structure under dense networks.