Abstract:
The inverse problem of tomography is an iterative procedure. 
It requires the computation of the gradient of the traveltime 
misfit cost function many times. This calculation is 
customarily done by ray tracing, the path length 
of the rays being closely related to the gradient. We propose 
in this work an alternative method to compute the gradient of 
the traveltime cost function without ray tracing. We use 
upwind finite difference schemes to compute the traveltime 
field by solving the eikonal equation. Then by adjoint state 
techniques we derive a closed-form expression of the gradient 
of the traveltime cost function. This approach allows an 
accurate computation of the gradient as well as the freedom 
to change the norm on the model space.