Inverse Problem in Seismic Imaging: Seismic Velocity Estimation from Time Migration
Maria Cameron, CIMS

Imaging of earth regions with nonhorisontal subsurface structures and laterally varying sound speed (seismic velocity) is very difficult. Seismic velocity estimation, which is the toughest problem in geophysics, is crucial for accurate imaging of such regions. Moreover, geohysical data naturally come in somewhat unintuitive time coordinates.

I will make an introduction into the seismic imaging. I will present our theoretical results in 2D and 3D connecting the seismic velocities with the velocities we can estimate easily. I will state an inverse problem coming from our theoretical results and introduce numerical approaches in 2D and 3D for solving it. These approaches include Dijkstra-like Hamilton-Jacobi solvers for first arrival Eikonal equations and techniques for data smoothing. We tested these approaches on synthetic examples in 2D and 3D and applied them to a field data example. We demonstrated that our algorithms give a significantly better estimate of seismic velocities than the Dix inversion which is the standard approach.

Joint work with M. Cameron, S. Fomel (UT Austin), J. Sethian (UC Berkeley)