This paper introduces the data cubes from GHIGLS, deep Green Bank Telescope surveys of the 21-cm line emission of HI in 37 targeted fields at intermediate Galactic latitude. The GHIGLS fields together cover over 1000 square degrees at 9.55 spatial resolution. The HI spectra have an effective velocity resolution about 1.0 km/s and cover at least -450 < v < +250 km/s. GHIGLS highlights that even at intermediate Galactic latitude the interstellar medium is very complex. Spatial structure of the HI is quantified through power spectra of maps of the column density, NHI. For our featured representative field, centered on the North Ecliptic Pole, the scaling exponents in power-law representations of the power spectra of NHI maps for low, intermediate, and high velocity gas components (LVC, IVC, and HVC) are -2.86 +/- 0.04, -2.69 +/- 0.04, and -2.59 +/- 0.07, respectively. After Gaussian decomposition of the line profiles, NHI maps were also made corresponding to the narrow-line and broad-line components in the LVC range; for the narrow-line map the exponent is -1.9 +/- 0.1, reflecting more small scale structure in the cold neutral medium (CNM). There is evidence that filamentary structure in the HI CNM is oriented parallel to the Galactic magnetic field. The power spectrum analysis also offers insight into the various contributions to uncertainty in the data. The effect of 21-cm line opacity on the GHIGLS NHI maps is estimated.
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