The phrase meaning to study carefully is pore over. It comes from a little-used sense of the verb pore—namely, to meditate deeply. In modern writing, this sense of pore rarely appears outside this phrase.
Pour over is of course a meaningful phrase in its own right, but it has nothing to do with studying. It’s what you do, for example, with milk to a bowl of cereal.
Major employers are using specialist anti-union lawyers to pore over the legislation. [Libcom.org]
Young men pore over texts crammed with cursive script at the Zia ul Uloom madrassa in search of the values that define the Barelvi school of Islam. [Financial Times]
Yet I eagerly pore over them with the colossal seriousness that someone more educated than I might devote to a Kierkegaard treatise. [SI.com]