This is an odd one, but I was asked by a customer how to do it, so here's the Spatial Model. I don't think you'd do this as a operation on it's own - it's more of a snippet that you would embed into a larger model to correct the position of data before doing some other processing. Otherwise you'd just use the ImageInfo utility to edit the header of the image.
The idea here is that you have a georeferenced image (in a Projected Coordinate System) but the horizontal position of the image is incorrect and you need to apply a known shift to the header information to correct the inaccuracy. The Offset inputs enable entry of a distance, in Meters, to move the input image East and/or North (with negative values moving the image West and/or South).
The model works by effectively stripping the georeferencing off the raster data and rebuilding a new header where the reference location for the image's upper left corner coordinate has been adjusted by the specified Offsets. Consequently its important to note that this model does not "reproject" the data, it simply shifts it based on the assumption that the original positional information was wrong.
Input Image: Select the input georeferenced image which requires an affine offset correction tot he geolocation information
Output Image: Provide the name of the output file with corrected geolocation information
Easting Offset: Enter the distance in Meters to displace the image in an easterly direction (i.e. to the right). Enter a negative value to shift west (left).
Northing Offset: Enter the distance in Meters to displace the image in a northerly direction (i.e. up). Enter a negative value to shift south (down).