The correlation between different interfaces
is an optional argument of the Roughness constructor.
It can be specified through one of
ba.SpatialFrequencyCrosscorrelation(base_crosscorr_depth, base_frequency, power)
ba.CommonDepthCrosscorrelation(cross_corr_depth)
Cross-correlation models determine interaction of the current interface with underlying ones.
If the interface is already using linear growth model, the other cross-correlation settings are not needed.
ba.SpatialFrequencyCrosscorrelation(base_crosscorr_depth, base_frequency, power)
base_crosscorr_depth, $\xi_{\perp base}$, is the vertical distance over
which the correlation of rougness spectrum at base spatial frequency
$\nu_{base}$ between interfaces is damped by a factor $1/e$,base_frequency, $\nu_{base}$, is a spatial frequency, for which the
correlation of rougness spectrum between interfaces is damped by a factor
$1/e$ at vertical distance $\xi_{\perp base}$,power, $p$, is a degree that determines the dependence of cross-correlation
on spatial frequency.Cross-correlation spectrum between interfaces $i$ and $j$ is
$$ S_{ij}(\nu)=\sqrt{S_i(\nu)S_j(\nu)} exp[-\dfrac{t}{\xi_{\perp base}} \Big(\dfrac{\nu}{\nu_{base}}\Big)^p] $$
where $t$ - distance between interfaces, $S_i(\nu),S_j(\nu)$ - autocorrelation spectra.
ba.CommonDepthCrosscorrelation(cross_corr_depth)
cross_corr_depth, $\xi_{\perp}$, is the vertical distance over
which the correlation is damped by a factor $1/e$Subcase of “Spatial frequency” model without dependence on spatial frequency.
Cross-correlation spectrum between interfaces $i$ and $j$ is
$$ S_{ij}(\nu)=\sqrt{S_i(\nu)S_j(\nu)} exp[-\dfrac{t}{\xi_{\perp}}] $$ where $t$ - distance between interfaces, $S_i(\nu),S_j(\nu)$ - autocorrelation spectra.
Example of script using this model.