  We build an analytical framework to study the observability of anisotropies
and a net chiral polarization of the Stochastic Gravitational Wave Background
(SGWB) with a generic network of ground-based detectors. We apply this
formalism to perform a Fisher forecast of the performance of a network
consisting of the current interferometers (LIGO, Virgo and KAGRA) and planned
third-generation ones, such as the Einstein Telescope and Cosmic Explorer. Our
results yield limits on the observability of anisotropic modes, spanning across
noise- and signal-dominated regimes. We find that if the isotropic component of
the SGWB has an amplitude close to the current limit, third-generation
interferometers with an observation time of $10$ years can measure multipoles
(in a spherical harmonic expansion) up to $\ell = 8$ with ${\cal O }\left(
10^{-3} - 10^{-2} \right)$ accuracy relative to the isotropic component, and an
${\cal O }\left( 10^{-3} \right)$ amount of net polarization. For weaker
signals, the accuracy worsens as roughly the inverse of the SGWB amplitude.

General Relativity and Quantum Cosmology;Instrumentation and Methods for Astrophysics