zWeight definition?

[79seismo]

What does zWeight actually define/represent in mgr.invert()? There's no indication of it in documentation or the original paper. Thanks!

[halbmy]

You're right, there is not much description except on https://dev.pygimli.org/user-guide/inversion.html which is missing on www.pygimli.org (dating to v1.5.4), and even there is no detailed description. The first publication is from Coscia et al. (2011), in eq. (2) describing the constraint weight (in case of 1st order smoothness):
$$W_i = 1 + (w_z - 1) n_z$$
where $n_z$ is the vertical component of the normal vector.

Coscia, I., Greenhalgh, S., Linde, N., Doetsch, J. A., Marescot, L., Günther, T., Vogt, T. & Green, A. (2011): 3D crosshole ERT for aquifer characterization and monitoring of infiltrating river water. Geophysics 76(2), G49-G59, doi:10.1190/1.3553003.

[79seismo]

Thanks @halbmy! I guess Wz is equivalent to zWeight and it controls anisotropic smoothing? e.g. when zWeight < 1 the horizontal direction is more strongly smoothed than the vertical direction, and the smoothing is equivalent along horizontal and vertical directions with Wz = 1, correct?

[halbmy]

The (small) $w_z$ IS the zWeight parameter defining the anisotropy of the smoothness operator (for the whole mesh/region), and the individual $W_i$ are computed from it taking the orientation of cell boundaries into account.

[79seismo]

Thanks!