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