Self-similarity in rock physics

Mavko's (1995) "rock physics bottleneck" dictum refers to a common problem in remote sensing: The measured parameters of the object under examination are fewer than the physical properties they depend upon. Yet, even if we have the luxury of reducing the number of inputs to equal the number of measurements, it may not be practically feasible to resolve the resulting mathematically determined system of equations. For example, it may not be possible to determine the porosity and clay content from the P- and S-wave impedance data because both depend on the same linear combination of porosity and clay content. Such situations are described as "self-similar." A solution to this problem is to procure an additional, depositionally controlled link between the desired outputs, such as a commonly observed relation between the total porosity and clay content.