3D Interpolation and Extrapolation of Sparse Well Data Using Rock Physics Principles - Applications to Anisotropic VMB

Mapping sparse well data into 3D volumes is a challenging problem. Specifically, as seismic velocity model buildings (VMB) requires 3D velocity and anisotropy volumes, and as most anisotropy estimates are calibrated to borehole data, generating 3D anisotropic models relies heavily on extrapolating sparse well data. This spatial extrapolation problem is ill posed and many subjective decisions are made during model building. New advancements in basin modeling and analysis enable us to model temperature and compaction history using simple physical principles. These fields can be used as auxiliary fields to solve spatial interpolation problems of sparse well log data using the concept of interpolation in the rock physics domain. The principle suggests that sparse well log measurements in the physical (x,y,z) 3D space may still adequately sample the rock physics space of temperature, porosity, and effective stress to allow proper reconstruction of the anisotropic velocity field in a manner that is consistent with the diagenetic process. We present the basic concepts and give a synthetic example to support this direct link between basin modeling and anisotropic velocity model building.