The phrase "globally pervasive" is correct and usable in written English.
You could use it to describe a phenomenon that is present in many parts of the world, such as the spread of technology. For example: The internet has become a globally pervasive phenomenon, providing access to information and services from almost any corner of the planet.
Globally, pervasive anthropogenic disturbances are reducing species populations, leading to biotic homogenization of communities and changes to the functioning of ecosystems23, 24.
On today's United Nations biodiversity day, we are being asked to focus on small islands and their unique ecology and fragility in times of globally pervasive threats such as climate change.
A preliminary dynamical analysis of landscapes and humans as hierarchical complex systems suggests that strong coupling between the two that spreads to become regionally or globally pervasive should be focused at multi-year to decadal time scales.
The internet proper may be globally pervasive, at the TCP/IP level, but we live in two different online worlds; one of Facebook / Google / Amazon, and one of Tencent / Baidu / Alibaba, with Apple as the only company that seems to bridge both worlds.
Everyone now also knows that American NSA cyberspying is globally pervasive.
"It made me examine the way we perceive Muslim artists, when these customs aren't globally pervasive".
Domestic violence and abuse is recognised globally as a pervasive public health issue, but there is less research in relation to gay and bisexual men.
The uptake of contactless payments [such as Visa payWave and MasterCard PayPass] was one of if not the fastest and most pervasive uptakes globally.
Tapeworms are pervasive and globally distributed parasites that infect millions of humans and livestock every year, and are the causative agents of two of the 17 neglected tropical diseases prioritized by the World Health Organization.
Until 2012, women in Sweden received only one third of government film funding (a pervasive trend globally).
Foster asserts the suggestion that mobile, connectivity and pervasive access to globally shared data has now allowed businesses to look outward in news ways.
