A rift or chasm.
the water that lays under the ground is called ground water.
Valley
Such a valley would be called a gorge.
the deep crack in the earth's surface is the rift
An earthquake occurs deep in the earths crust caused by the displacement of two faults in the crust. Directly above the fault on the earths surface is called the epicenter. Which shows the aftermath of the strike slip fault that occured in the earths crust. So the strike slip fault is the effect of the displacement of the crust at that point deep in the earths crust which causes an earthquake to happen whenever there is a displacement of two faults.
a deep, steep-sided, narrow river valley
the water that lays under the ground is called ground water.
continental shelf
igneous
A deep crack in the earth's surface is called a fault.
cracks
A deep valley with steep sides would be called a gorge or canyon.
A fault.
There are more than one term for a deep narrow valley. Glens, canyons, ravines, fjords are terms you could use.
I have heard it called the rim.
Valley
In oceanography, they are usually called "trenches".