Nonlinear color maps in surf plots

Question

I have the following plot

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    domain = -20:30,
    y domain = 0.01:100,
    ymode=log,
    view = {0}{90},
    xlabel={$x$},
    ylabel={$y$},
    colorbar
    ]

    \addplot3[surf,shader=interp, samples=41]%
    {-1 + (y * sqrt(1+x^2))^2) / (1+y)^2};
  \end{axis}
\end{tikzpicture}
\end{document}

which produces the following

However, I would like the colormap to be equally divided between [0,1] and [1, 1000]. Or possibly two different colormaps for the two ranges. How can I achieve this? I found this but this solution does not change the colormapping, just the colorbar.