Rock Property Data Volumes from Well Logs

Geology is sampled densely by wells vertically, but sparsely and irregularly horizontally. A modern seismic survey has sparse samples vertically, but close and uniform sampling horizontally. Seismic data is more useful for regional trends, but does not convey petrophysics, and is difficult to relate to wells. Inverting seismic data to resemble well data is almost impossible. Can we make well data resemble seismic data, not just a single-trace, but a complete volume?