The discovery of vast petroleum fields in the Barents and Kara Seas has raised fears of catastrophic accidents as ships loaded with oil and, soon, liquefied gas churn through the fisheries off Scandinavia, headed to markets in Europe and North America.

off 是介词，意思等于 away from （离开；远离）； outside （在......外面）

红色部分 off Scandinavia 作 the fisheries 的定语。意为“远离纳维亚半岛的渔场；在纳维亚半岛之外的渔场”。

又如：

They lived in a village off railways. 他们住在一个远离铁路的村庄里。