Thanks Paulo, your suggestion of combining r.neigbors and r.patch worked.

From: Paulo van Breugel <p.vanbreu...@gmail.com>
> Subject: Re: [GRASS-user] 'Growing' a raster on the edges only
> Message-ID: <516ba41a.4060...@gmail.com>
> Content-Type: text/plain; charset=UTF-8; format=flowed
>
> Try r.neighbors function with the mean or medium neighborhood
> operation, or, if you are working with categorical values, use the
> 'mode' neighborhood operation. You can combine the result with the
> original layer using r.patch so only the no-data cells at the borders
> are filled with the newly created values
>
> You may also have a look at r.fillnulls, which fills in no-data cells
> using spline interpolation.
>
> Paulo
>
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