Reflection traveltime tomography and the maximum entropy principle

Abstract

Conventional reflection tomography creates an estimate of subsurface seismic velocity structure by inverting a set of seismic traveltime data. This is achieved by solving a least-squares optimisation problem that finds the velocity and depth model that minimises the difference between raytraced and measured traveltimes. Obtaining the traveltime data can be difficult as manual picking of reflection times is required and all picked reflection events must be associated with the reflector depths defined in the model. Even with good traveltime data the optimisation problem is very non-linear and the surface restriction of the sources and receivers makes the problem generally underdetermined. These issues result in severe ambiguity and local minima problems.

This thesis shows that modifications to the conventional reflection tomography algorithm can make it a more practical and reliable procedure that is less likely to be trapped by local minima. The ray tracing procedure is changed so that reflector depths are not necessary and automatic traveltime interpretation can be successful. Entropy constraints are introduced (after being justified) which prevent unwarranted velocity structure from appearing. This feature adds significant stability and reduces the ambiguity problems. Staged smoothing of the optimisation function helps avoid local minima.

Synthetic data examples show that the algorithm can be very effective on noise free data. Adding noise to synthetic data reduces the algorithms effectiveness, but inversions of real data sets produces updated velocity fields that result in superior pre-stack depth migrations.