Extended Power-Law Scaling of Self-Affine Signals Exhibiting Apparent Multifractality

Many earth and environmental variables appear to scale as multiplicative (multifractal) processes with spatial or temporal increments possessing Gaussian or heavy‐tailed distributions. The behavior, characterized by power‐law scaling, is typically limited to intermediate ranges of separation scales (lags) considered, in the case of fully developed turbulence, to be dominated by inertia. It has been established empirically that, in numerous cases (e.g. turbulence, diffusion‐limited aggregates, natural images, kinetic surface roughening, fluvial turbulence, sand wave dynamics, Martian topography, river morphometry, gravel‐bed mobility, barometric pressure, low‐energy cosmic rays, cosmic microwave background radiation, metal‐insulator transition, irregularities in human heartbeat time series, turbulence in edge magnetized plasma of fusion devices and turbulent boundary layers of the Earth’s magnetosphere), this range of lags can be enlarged significantly, at both ends of the spectrum, via a procedure known as Extended Self‐Similarity (ESS). We demonstrate numerically that a similar procedure extends the power‐law scaling range over which additive (self‐affine) signals exhibit apparent multifractality. We conclude that signals appearing to exhibit either standard or extended (such as those listed) multifractal scaling may potentially represent self‐affine processes.