Characterizing fault roughness—Are faults rougher at long or short wavelengths?

First posted January 29, 2021 For additional information, contact: Contact Information, Menlo Park, Calif. Office—Earthquake Science CenterU.S. Geological Survey345 Middlefield Road, MS 977Menlo CA 94025 Changes in fault roughness with scale, “scaling,” is the topic of this report; changes are considered using a general power law relation between some measure surface height, H, and another length, L, H=kLn, where k constant n an exponent that characterizes scaling. Extensive profile measurements natural surfaces show ratio average height to length decreases scale. Average defined root mean squared Rq. analysis, smoother at long wavelengths (have smaller ratios) than they shorter wavelengths. These other statistical properties hold for more five orders magnitude, huge range from tens micrometers 10 meters. However, different metric, (amplitude) specifically associated wavelength shows opposite sense The amplitude increases wavelength. Thus, same can be deemed rougher wavelength, or smoother, depending on chosen metric. This apparent contradiction curiosity statistics rough have scaling exponents relate Rq 0.5 1, as most faults do. To add context, implied reference synthetic determined. span moderate strong point correlation. potential payoff expanded descriptions improved constraints physical mechanisms generate modify during shear.