yuan2 yin1 and yuan2 gu4 different yuan2

From David and Helen in China, Chapter 16, 阅读练习 (yue4du2 lian4xi2, reading practice),
pg. 336 about half way down the essay(titled 历史名城西安).

骊山风景极美，同时温泉闻名，所以自古就是皇帝游玩的地方，这就是为什么这里有很多宫殿式建筑的缘故。

骊山 Li2shan1, name of a mountain outside Xi'an.
温泉 wen1quan2, warm springs，or hot springs [xiaoma lists 温泉 as a place in Xinjiang, but Xi'an is in Shaanxi, so it's a different 温泉, right?]

缘故 yuan2gu4, reason, cause
原因 yuan2yin1, reason

原 of 原因 has xiaoma entry: former; original; primary; raw; level; cause; source
因 has entry: cause; reason; because
缘 has entry: along; predestined affinity; reason; edge
故 has entry: happening; instance; reason; cause; deceased; old

My impression is that 原因 is a more entry level vocabulary word, while 缘故 is a bit more formal. Perhaps 缘故 has more of a flavor of causality, or a story behind the reason. But that could just be impression based on my knowing the word 故事.

Update: Help from my friends at chinese-forums.com here