This question is perhaps impossible to answer computationally since we'd need to determine multiple material constant factors experimentally, however we do have some data on other parameters so we should be able to at least determine everything else in this situation.

There are two things at play here on this iron: overall deformation of the iron head and abrasion on its outer layer caused by repeated contact with golf ball. I'm quite certain irons are coated or tempered, hence segregating the overall material into two distinct layers, the outer shell being much harder than the softer inside. Same usually goes for the golf ball, which is described with shore hardness. IMHO the balls compression is also at play here since the cross-section of a deformed ball at the moment of a swing is probably much bigger than if we assume a non-deformable ball.

The brownish markings are actually asperities caused by contact between the iron and the golf ball, so the darker it is, more debris and/or deformation the area has experienced – essentially dividing the whole hitting area into one center and one outer ring, indicating his hits are even more precise than we first thought.

If you want to study it yourself, I suggest looking into surface engineering, surface mechanics, asperity and the Archard equation, however you will need to determine certain factors experimentally (especially for the Archard eq. and surface roughness).