Structural Analysis of the SDSS Cosmic Web I.Nonlinear Density Field
  Reconstructions
  We investigate the ability of three reconstruction techniques to analyze and
investigate weblike features and geometries in a discrete distribution of
objects. The three methods are the linear Delaunay Tessellation Field Estimator
(DTFE), its higher order equivalent Natural Neighbour Field Estimator (NNFE)
and a version of Kriging interpolation adapted to the specific circumstances
encountered in galaxy redshift surveys, the Natural Lognormal Kriging
technique. DTFE and NNFE are based on the local geometry defined by the Voronoi
and Delaunay tessellations of the galaxy distribution. The three reconstruction
methods are analysed and compared using mock magnitude-limited and
volume-limited SDSS redshift surveys, obtained on the basis of the Millennium
simulation. We investigate error trends, biases and the topological structure
of the resulting fields, concentrating on the void population identified by the
Watershed Void Finder. Environmental effects are addressed by evaluating the
density fields on a range of Gaussian filter scales. Comparison with the void
population in the original simulation yields the fraction of false void mergers
and false void splits. In most tests DTFE, NNFE and Kriging have largely
similar density and topology error behaviour. Cosmetically, higher order NNFE
and Kriging methods produce more visually appealing reconstructions.
Quantitatively, however, DTFE performs better, even while computationally far
less demanding. A successful recovery of the void population on small scales
appears to be difficult, while the void recovery rate improves significantly on
scales > 3 h-1Mpc. A study of small scale voids and the void galaxy population
should therefore be restricted to the local Universe, out to at most 100
h-1Mpc.
