The company offered little 'by way of explanation' for the delays. [=as a way of explaining why there were delays]
Some of the more technical terms need/require 'explanation'. [=they need to be explained]
a likely/probable/possible/plausible 'explanation of' how the accident occurred
(..) You know, uh, it's getting kinda late. - We really need to head to our family. - You don't understand. But we do. There's usually some sort of rational explanation... I have five daughters who are scared to death. I'm so afraid this thing wants to hurt us. You have a daughter. Wouldn't you do (..)2013 The Conjuring
(..) You heard it all through the house because of these pipes leading to the radiator. So this place isn't haunted? No, it rarely is. Yeah, there's usually always some kind of rational explanation. Girls, it's way past your bedtime. Who is that? Who's ever down there, I'm gonna lock you in now! (..)2013 The Conjuring