probably they are more relevant to the corona where the far greater gravitational scale height is no longer the primary feature, leaving complex loop structures to dominate [@VanBraVer08aa]. Chromospheric sunspot fields, dominated be a single monopolar spot, may be expected to be smoother. ]{}

Computational Details
=====================

We employ the Seismic Propagation through Active Regions and Convection (SPARC) $6^{\rm th}$ order linear MHD code of @Han07aa, with uniform $B_0=500$ G or 1 kG magnetic fields of inclination $\theta$ from the vertical threading the Convectively Stabilized solar Model (CSM\_B) atmosphere of @SchCamGiz11aa. The ‘observational height’ for vertical velocities used in seismic calculations is 0.3 Mm, above the $a=c$ equipartition layer for both 500 G and 1 kG (0.24 Mm and 0.08 Mm respectively). A stochastic driving plane is placed at depth $z=-0.156$ Mm. The random sources produce a solar wave power spectrum with maximum power in the range 2 – 5.5 mHz, peaking at about 3.2 mHz. Being a linear code, the overall velocity normalization is arbitrary. The standard ${\leavevmode\kern.1em\raise.5ex\hbox{\the\scriptfont0 2}\kern-.1em/\kern-.15em\lower.25ex\hbox{\the\scriptfont0 3}}$ dealiasing rule is applied to avoid spectral blocking, with $|k_x|$ and $|k_y|$ limited to about 1.9 $\rm Mm^{-1}$.

A $140\,{\rm Mm}\times140\,{\rm Mm}\times26.53\,{\rm Mm}$ box is spanned by a $128\times128\times265$ 