Scale Independence of Rock Physics Transforms

Rock properties, such as porosity, permeability, and elastic moduli, depend on the scale (volume) of measurement. They may spatially vary within millimeters and, certainly, within inches and feet. This natural variability renders meaningless the concept of a data point, simply because the datum will be different just a few inches away, or if averaged in a larger volume. However, some transforms from one property to another appear scale independent. Obtained at a microscale, they can be potentially applied at a larger scale in the field. This makes us believe that such transforms, stationary with respect to position and scale, should replace single-category properties (e.g., porosity) as the primary attributes of rock.