First, here is Gabriel’s comment again:
Following with my previous comment, a recent research (*) has shown that using a set of 11 trace elements (Al, Ti, Ni, As, Rb, Y, Mo, Ag, Cd, Ba, and La) and not just a dubtious one like C14, it is possible to identify the region of the world a linen comes from. The authors have achieved to distinguish linens from Poland, Italy and JApan using those 11 trace elements.
I think it would really be helpful to carry out the same analysis on the Shroud and clearly establish whether its linen comes from the Middle East (one point for authenticity) or from let’s say France. In case the linen came from France, we could once and for all rule out the possibility of an authentic relic. In case, it came form the Middle East it wouldn`t mean that the Shroud is authentic 100%, but would represent a very strong point in its favour.
(*)Takako Inoue, Kengo Ishihara and Kyoden Yasumoto.International Journal of Clothing Science and Technology Vol. 22 No. 2/3, 2010 pp. 174-186
[re:] "Comparative analysis of hand properties and compositions of trace elements in linen fabrics produced in different regions" in: International Journal of Clothing Science and Technology, Vol. 22 No. 2/3, 2010
I had a look at this paper thru the university library, and it doesn’t have much relevance to determining the geographical origin of the Shroud.
The samples were all modern, and the researchers were mainly interested in industrial aspects of the "linen fabrics which were used to make suits, jackets, trousers, skirts, blouses, one-piece dresses, etc." In addition to trace elements, they also tested for mechanical properties like thermal conductivities, air permeability, elasticity, drape, etc.
The introduction sounded promising:
"In this paper, the effects of environmental conditions on the growth, development and yield of the following varieties of fiber flax were estimated: Fortuna, Minerwa, Svapo, Waza, and Nike. The environmental parameters were the soil composition, the type and pH of the soil, the climatic conditions, the time of agronomic operations, and the agronomy level."
But then things get very confused. One set of samples was described thus:
"The growing districts for the linen fabrics from company A were Ireland and North France; the yarn was processed in Italy and woven, dyed, and finished in Japan."
To my mind that renders the study fairly useless as far as trace elements related to geographical origin, since some of the elements could have been picked up at various points in the processing.
Even if one had say 18th century linen samples securely provenanced, the cross-breeding of species and borrowing of methods of fertilizing, retting, etc. would cast doubt on a trace element approach, unless one had results of very clear and distinct clusters with no overlap — a very doubtful outcome.
A more promising approach would be stable isotope ratios which should be determined solely by the environment in which the flax was grown. But it is unclear whether this would yield distinctive results that would distinguish specific regions, say the Middle East from North Africa, or Greece from Spain.
It would be good to see a pilot study if pre-modern linen samples could be found.