Explicit form of the random field spectral representation and some
  applications
  We present here an explicit form of the random spectral measure element, what
allows us to express a stationary random field as a stochastic integral
explicitly depending on its power spectrum and a spectral tensor if the field
is a vector one. It has been shown here that convergence mechanism of such
integral is significantly different from the one of the Fourier transform and
that the traditional formalism is a partial limiting case of the one presented
here. The fact that there is an explicit expression of a random field makes
calculation of higher order statistics of it much more straightforward (see for
example Chepurnov et al. 2020). For a vector field such expression contains a
projection of an isotropically distributed random vector by a spectral tensor,
what makes geometrical interpretation of harmonics behavior possible,
simplifying its analysis (see Sect. 2). This spectral representation also makes
straightforward numerical generation of a random field, what is extensively
used by Chepurnov et al. 2020. We also present here some practical applications
of this formalism.
