  In this paper we study kinetically rough surfaces which display anomalous
scaling in their local properties such as roughness, or height-height
correlation function. By studying the power spectrum of the surface and its
relation to the height-height correlation, we distinguish two independent
causes for anomalous scaling. One is super-roughening (global roughness
exponent larger than or equal to one), even if the spectrum behaves non
anomalously. Another cause is what we term an intrinsically anomalous spectrum,
in whose scaling an independent exponent exists, which induces different
scaling properties for small and large length scales (that is, the surface is
not self-affine). In this case, the surface does not need to be super-rough in
order to display anomalous scaling. In both cases, we show how to extract the
independent exponents and scaling relations from the correlation functions, and
we illustrate our analysis with two exactly solvable examples. One is the
simplest linear equation for molecular beam epitaxy , well known to display
anomalous scaling due to super-roughening. The second example is a random
diffusion equation, which features anomalous scaling independent of the value
of the global roughness exponent below or above one.
