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I am going to merge two DEM raster files with different resolutions (5m and 12.5m). I would like to merge them in a way that they should keep their own resolution.

How can I do this in ArcGIS Pro?

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    You can't combine rasters and retain resolution. You have to choose one or the other. You could downsample to 2.5m and shift to retain content; with compression, the 25x increase in 12.5m's pixel count won't be too oppressive.
    – Vince
    Commented Jun 27 at 12:34

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You would have to either standardize the resolution to merge the two or you could choose to create a mosaic dataset with the two raster files. The merge function would allow you to treat both raster files as a single item for additional edits and calculations whereas creating a mosaic dataset would allow you to keep the varying resolutions and create a combined image with the two raster files. A mosaic dataset can be treated more like an image where the pieces are fit together like a puzzle, while a merged dataset is more like a single new raster layer.

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    Commented Jul 8 at 5:55

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