We use an irregular tetrahedral mesh to represent 3-D velocity models. The mesh is generated by individually inserting data points into the model with refinement of the mesh to include the newly added point. When isolated data points are to be interpolated, a Delauney tessellation is often a good choice since it partitions the model into tetrahedra connecting nearest-neighbor data points by its empty-circumsphere criterion. We use Delauney tessellation to import isolated velocity picks to form a 3-D velocity field and to import isolated surface picks to form a simply connected 3-D surface (Wiggins et. al, 1993). Velocity data comes to the explorationist in small parts: first, velocity picks for a shallow layer; then, a shallow horizon; then a deeper layer velocities and surfaces. A modeling system must represent these parts and combine them lnto a single model.


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