We apply the wavelet transform modulus maxima method [A. Arnéodo, N. Decoster, and S. G. Roux, Phys. Rev. Lett. 83, 1255 (1999)] to the analysis of simulated surfaces grown by molecular-beam epitaxy. In contrast to the structure function approach commonly used in the literature, this method permits an investigation of the complete singularity spectrum. We focus on a kinetic Monte Carlo model with Arrhenius dynamics, which in particular takes into consideration the process of thermally activated desorption of particles. We find a wide spectrum of Hölder exponents, which reflects the multiaffine surface morphology. Although our choice of parameters yields small desorption rates $\mathrm{}(<3\%),$ we observe a dramatic change in the singularity spectrum, which is shifted toward smaller Hölder exponents. Our results offer a mathematical foundation of anomalous scaling: We identify the global exponent ${\alpha }_g$ with the Hölder exponent that maximizes the singularity spectrum.

• Received 13 January 2000

DOI:https://doi.org/10.1103/PhysRevE.62.1773