Mapping sparse well data into 3D volumes is a challenging problem. Because seismic-velocity model building requires 3D velocity and anisotropy volumes and most anisotropy estimates are calibrated to borehole data, the generation of 3D anisotropic models relies heavily on extrapolation of sparse well data. This spatial-extrapolation problem is ill posed, and many subjective decisions are made during model building. New advances in basin modeling and analysis facilitate the modeling of temperature and compaction history using simple physical principles. These fields can be employed 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 of interpolation in the rock-physics domain suggests that sparse well-log measurements in the physical (x, y, z) 3D space might still adequately sample the rock-physics space of temperature, porosity, and effective stress to enable proper reconstruction of the anisotropic velocity field in a manner consistent with diagenetic processes. Synthetic and field examples support this direct link between basin modeling and anisotropic velocity model building.