Which preposition to use with besmirch

with Occurrences 4%

And I askt the Maid whether that she did be prepared; and she to be very white and wearied, and all besmirched with the dankness and growths upon the boulders and the hidden pools of the Gorge and the dripping of the waters; but yet did she be sound in her courage, and to show that she had all belief and abiding in me, and her judgement likewise to be with mine, in that her own Reason did approve.

from Occurrences 1%

Rather, they were piling mud, and they were besmirched from head to foot.

Which preposition to use with  besmirch