Travel-time seismic inversion for a numerically-defined shape

Travel time tomography calculations involving 3D velocity models have become more common place during the past decade or so. Numerous methods have been developed to solve the required forward modeling problem of boundary value ray tracing in 3D. For this problem, source and receiver positions are known and one or more time paths are sought between the fixed end points. Less attention has been given to the approach to model parametrization. Traditionally, the model has been subdivided into constant velocity cells, a process known as voxellation or cellular partitioning. A new approach to model parametrization involving numerically constructing the boundary of a homogeneous subsurface geological feature is proposed here and an efficient method for tracing rays through this model is presented. The ray tracing problem is solved by obtaining the minimum travel time path from a fixed source to a fixed receiver, and its associated travel time, as the solution to a nonlinear optimization problem based on Fermat's principle. The inversion technique will be regulated by using the area, perimeter and the total distance from each vertex to the center of the numerically defined surface as measures of model structure