Dan,
Thanks for responding. The dataset is actually a 2D seismic survey acquired in 1981in onshore Portugal. A number of these old lines have been recently reprocessed and new versions created. The seismic processors are confident that the x/y points they supplied in the data headers are in the ED50/29N projection (EPSG 23029). For reasons difficult to explain, every 10th location is precise - in between they are interpolated locations (ie straight segments with inflection points every 10th). I have determined that the original data are properly located because these inflection points fall on (or VERY near) roads - where the vibroseis trucks would have been positioned. I made this comparison in ArcPRO using the World_Topo_Map in a layer projected with ED50/29N (incidentally, I'm aware that (some) roads may have changed in the last 37 years - accommodating that with my logic). In the same view the reprocessed data are offset from the "correct location" by 150-170 meters (using simple trig) - at locations vibroseis trucks could not have reached.
In an attempt to figure out what may have happened (assuming that somewhere along the line someone miscoded the projection system), I've played around with the data loaded in my seismic interpretation platform (SeisWare) assuming a different original projection system transforming the locations to ED50/29N. Most result in locations so far afield that they are dismissed. The closest I've gotten is calling the data WGS84/29N, but it still doesn't overlay what I think are the correct locations and are actually further offset than the reprocessed locations.
To your knowledge is there any kind of a widget that would allow me to input the correct x,y,crs and errant x,y to calculate what projection system might have been (mis-)used? Sort of a reverse transform that solves for projection system?
Unfortunately the seismic interpretation platform isn't that GIS-robust all around. The data loader allows me to define input and output projections (CRS's), but when I export the locations as a shape file, the CRS doesn't come with it (though I know it to be ED50/29N so imported "unprojected data" into an ED50/29N ArcMap project is OK.
I hope all of these details aren't overly confusing - I recognize that you are (apparently) a helpful GIS-guy, not a geophysicist. I am also aware that I'm working on the "back of an envelope", but am trying to get my arms around location uncertainty for my client, not producing an EXACT solution.
Thanks for trying to help,
Mark