I have a large elevation raster from the ASTER database made by using raster::mosaic(). Each tile represents a one-degree by one-degree portion of the earth with an estimated raster resolution of 30m^2. I include the code that I used to mosaic them below, but I don't believe that it is the problem.
Mosaic <- do.call(mosaic,c(list of rasters, tolerance = 1, fun=mean)
Once that is run, I get the following elevation tif, which you can DOWNLOAD HERE.
I then measure the topographic ruggedness using raster::terrain(), using theTerrain Ruggedness Index as my method:
TRI <- terrain(Mosaic, opt="TRI")
This yields:
As you can see, there are faint streaks in the map which I cannot explain. Due to the full extent of my study, I need to aggregate this raster to a coarser resolution. Therefore I use the aggregate function in the raster package as well.
TRI_Agg <- aggregate(TRI,fact = 255, fun = mean)
This yields the following raster. 
Here you can see that the streaks are much more pronounced and fairly consistent throughout the whole map. I tried doing this with other study areas and the problem persisted (i.e this would happen with raster tiles all around the world). I can't explain why those streaks are occurring. I have attempted different ways of going about this which include doing a neighborhood analysis (to fill in missing values if any) and processing the tiles before mosaicing them together. None of these have worked.
When I aggregate the raster before, the roughness calculation, the streaks do not appear which makes me believe this issue arises when using aggregate(). However, for my specific research question, I cannot calculate TRI using an aggregated raster.