"On a (...) scale" or "at a (...) scale"?

First of all, a core sample is a small piece of rock obtained from the subsurface. The reservoir in this question refers to an oil reservoir.

So here's the question. Is the following statement correct? Or should the word "at" be replaced with "on"?

"You should not try to investigate the effect of that heterogeneity at a core scale. You have to capture the heterogeneity at a reservoir scale."

Solution 1:

The usual expression uses the definite article following at (for a post-modifier); here is an example using better-known analogues, one an attributive use and one a post-modifier, from Oxygen-Enhanced Combustion, Second Edition edited by Charles E. Baukal Jr.

Once lab-scale testing is complete the next step in the typical development pathway is testing the concept at the pilot scale.

Here is an example of one of your descriptors, from Garnier, Patricia; Pot, Valerie; Monga, Oivier; Chenu, Claire; Vieuble-Gonod, Laurent; Vogel, Laure; Nunan, Naoise; Otten, Wilfried; Baveye, Philippe at SAO/NASA ADS Physics Abstract Service:

On the other hand, many experimental results developed at the core scale have showed the importance of soil microbial habitat ...

The expressions 'on a small/large scale' are common and use a different preposition. I'm guessing that 'at' is chosen in 'at the production scale' etc by analogy with 'at the highest level', the level/height metaphor, indicating the level where one chooses to set one's operation.