Tau tomography

In Chapter , I introduce the concept of tau (vertical travel-time) tomography and derive the operator relating changes in slowness to moveout errors in tau space. I show how tau tomography is less sensitive to the initial guess at reflector position and slowness estimate. Figure 8 shows the model of Figure 4 with the correct and initial reflector positions in depth (left) and tau (right).

 

ref-movement
Figure 8 Reflector movement in depth (left) and tau (right). The solid lines are where the reflectors migrate using the initial v(z) field. The dashed lines are the correct reflector positions in tau and depth. Note that correct and initial positions are much closer in the tau case.

On a synthetic I show how performing tomography in tau rather than depth better constrains the slowness changes. I show that the tau tomography problem converges faster to a more reasonable result than its depth counterpart. The resulting migration is better focused and the reflectors are better positioned by doing tau rather than depth tomography.