– 5 – 2005), providing roughly 23,500 redshifts in the field. In Section 2 we describe the data analysis, and in Section 3 we describe our variability selection criteria. In Section 4, we present the results of this study. The mid-IR structure function analysis is presented in Section 5 followed by a summary in Section 7. Throughout this paper, we use a standard ΛCDM model with (Ω$_{Λ}$ , Ω$_{M}$ , Ω$_{k}$) = (0 . 7 , 0 . 3 , 0 . 0) and h = H$_{0}$/ 100 = 0 . 70. Where needed, we use the galaxy and AGN templates of Assef et al. (2010b) to describe the mid-IR colors of various populations and to make any K -corrections or estimates of absolute luminosities. 2. Data Analysis The SDWFS is described in detail by Ashby et al. (2009). The images were taken with the IRAC instrument (Fazio et al. 2004) on the Spitzer Space Telescope , covering wavelengths of 3.6, 4.5, 5.8, and 8.0 µ m, hereafter referred to as the [3.6], [4.5], [5.8], and [8.0] bands, respectively. A single IRAC frame is 256 × 256 pixels. We work with full-field SDWFS mosaics constructed from the ∼ 20,000 IRAC images/epoch. Each approximately 13600 × 16700 pixel mosaic covers 10.2 deg $^{2}$, centered at (R.A., decl.) = (14:31:27, +34:10:43), with a pixel scale of 0.84 arcsec. Counting the original IRAC Shallow Survey (Eisenhardt et al. 2004) as epoch 1, the SDWFS data span a period of four years between 2004 and 2008, where the intervals between the epochs are approximately 3.5 years, 0.5 years, and 1 month (observations were done on 2004 January 10-14, 2007 August 8-13, 2008 February 2-6, and 2008 March 6-10). For each individual observation of a patch of the sky (256 × 256 pixels), there is only a ∼ 40 s offset between the channel 1/3 and 2/4 observations. For a given SDWFS epoch, each patch of sky was observed ∼ 3 times over a 1–2 day period. Each SDWFS epoch of the entire 10 deg 2 area took ∼ 5 days, and we treat it as a single image with a single Julian Date. This does not affect our final conclusions, as we show later that there is little mid-IR AGN variability on these timescales. To study the variability of objects in the SDWFS field, we used the Difference Image Analysis (DIA) method (Alard & Lupton 1998; Wo´ zniak 2000). While the variability itself is the subject of this paper, the DIA method also proved to be a useful diagnostic tool for constructing artifact-free mosaics (see Ashby et al. 2009). The basic idea behind the DIA method is to match one image, called the template or reference image, both astrometrically and photometrically to another image of the same area of the sky. Once they are astromet- rically aligned, the template image (which is chosen to be of better quality) is convolved with a kernel function to match the point spread function (PSF) of the analyzed image. The two images are then subtracted from each other (Figure 1) to leave only variable objects, noise, and systematic problems (cosmic rays, artifacts, etc.). After some experimentation,