Graining is a technique for making one kind of wood look like another, more expensive kind. It was a very common practice through the mid-1800s.

Graining made woodwork look more expensive and was easier to maintain that painted surfaces because the varnishes of the time were more durable than the paints.

Graining, among house-painters, is understood to mean the imitation of the several different species of scarce woods used in articles of furniture; such as mahogany, satinwood, rosewood, kingwood, oak, &c. This kind of painting is now very generally practiced, and frequently with great dexterity, some of these woods being so well imitated as scarcely to be distinguished from the originals. Some graining, as the imitations of rare and beautiful woods done in the best manner, is expensive; but graining like oak or wainscot is cheap, costing them little more than flatting, and lasting very much longer. It is admirably adapted for doors, architraves, windows, sash bars, and other parts liable to become dirty; and in many rooms the whole of the woodwork is now grained in imitation of some wood or other.

(From, Thomas Webster, An Encyclopaedia Of Domestic Economy
(New York, 1845).page 76) Quote

The first step in graining is to apply a base coat of paint. The color depends on the wood to be re-created. The base found at Adena is the color traditionally used to undercoat a mahogany grain.

While we know that the doors at Adena were grained to look like mahogany, we do not know the exact pattern in the woodwork. The staff decided to match a door at Monticello, the home of Thomas Jefferson.

The Monticello graining is original, it dates to the period of Adena, and Worthington was a strong support of Jefferson, so the model seemed apt.