"broad dispersal" is correct and usable in written English.
You can use it to refer to the act of spreading something widely or over a large area. For example, "The company achieved a broad dispersal of their new product in just two months."
As opposed to the broad dispersal of economic development funds, the security assistance cartogram demonstrates the targeted nature of the American national military strategy.
The exotic culture and resistance to assimilation of these wandering people led to widespread discrimination and persecution, contributing to the broad dispersal of the Roma throughout Europe.
Expansion of Pinus strobus might be linked to change in fire occurrence, but the broad dispersal of Pinus pollen makes interpretation difficult.
Most of the colony's men served in Britain, East Africa and the Mediterranean, particularly at first; a more broad dispersal occurred from late 1942.
Some galatheid species have very large egg sizes that apparently give them broad dispersal capabilities [98].
The broad dispersal of marine planktonic microbes contrasts with the limited dispersal ranges of marine and terrestrial plants and animals.
If the colonizers are exceptional dispersers, it becomes more probable that two or more introductions will occur, resulting in broader dispersal within the island and hence contributing to the levels of genetic variation.
The broad geographical dispersal of these newly emerging pathogens in both products and people has raised the need for new surveillance and response capabilities.
Broadly defined as Khoesan, contemporary Khoesan are today largely restricted to the semidesert regions of Namibia and Botswana, whereas archeological, historical, and genetic evidence promotes a once broader southerly dispersal of click-speaking peoples including southward migrating pastoralists and indigenous marine-foragers.
With an idealized coastline structure consisting of an infinite line of equally spaced reserves separated by regions of coastline in which reproduction is nil, the relative settlement as a function of the fraction of coastline and size of reserve is qualitatively very similar over a broad range of dispersal patterns.
