We present a detailed X-ray spectral analysis of 1152 AGNs selected in the Chandra Deep Fields (CDFs), in order to identify highly obscured AGNs ($N_{rm H} > 10^{23} rm cm^{-2}$). By fitting spectra with physical models, 436 (38%) sources with $L_{rm X} > 10^{42} rm erg s^{-1}$ are confirmed to be highly obscured, including 102 Compton-thick (CT) candidates. We propose a new hardness-ratio measure of the obscuration level which can be used to select highly obscured AGN candidates. The completeness and accuracy of applying this method to our AGNs are 88% and 80%, respectively. The observed logN-logS relation favors cosmic X-ray background models that predict moderate (i.e., between optimistic and pessimistic) CT number counts. 19% (6/31) of our highly obscured AGNs that have optical classifications are labeled as broad-line AGNs, suggesting that, at least for part of the AGN population, the heavy X-ray obscuration is largely a line-of-sight effect, i.e., some high-column-density clouds on various scales (but not necessarily a dust-enshrouded torus) along our sightline may obscure the compact X-ray emitter. After correcting for several observational biases, we obtain the intrinsic NH distribution and its evolution. The CT-to-highly-obscured fraction is roughly 52% and is consistent with no evident redshift evolution. We also perform long-term (~17 years in the observed frame) variability analyses for 31 sources with the largest number of counts available. Among them, 17 sources show flux variabilities: 31% (5/17) are caused by the change of NH, 53% (9/17) are caused by the intrinsic luminosity variability, 6% (1/17) are driven by both effects, and 2 are not classified due to large spectral fitting errors.
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