Rock-physics transforms and scale of investigation

Rock-physics velocity-porosity transforms are usually established on sets of laboratory and/or well data with the latter data source being dominant in recent practice. The purpose of establishing such transforms is to (1) conduct forward modeling of the seismic response for various geologically plausible what if scenarios in the subsurface and (2) interpret seismic data for petrophysical properties and conditions, such as porosity, clay content, and pore fluid. Because the scale of investigation in the well is considerably smaller than that in reflection seismology, an important question is whether the rock-physics model established in the well can be used at the seismic scale. We use synthetic examples and well data to show that a rock-physics model established at the well approximately holds at the seismic scale, suggest a reason for this scale independence, and explore where it may be violated. The same question can be addressed as an inverse problem: Assume that we have a rock-physics transform and know that it works at the scale of investigation at which the elastic properties are seismically measured. What are the upscaled (smeared) petrophysical properties and conditions that these elastic properties point to? It appears that they are approximately the arithmetically volume-averaged porosity and clay content (in a simple quartz/clay setting) and are close to the arithmetically volume-averaged bulk modulus of the pore fluid (rather than averaged saturation).