What scientist studies the earth crust?

Geologists and seismologists.

I think that, technically speaking, the branch of science is geology (whereas geologists and seismologists are some of the practitioners or specialists of that branch of science). Geology itself has many different fields of study that deal with different aspects of the earth's crust such as volcanology (study of volcanic processes), seismology (study of earthquakes and their detection), geomorphology (study of earth forms e.g., dunes, mountains, rivers, etc.), Paleontology (study of fossils) and so forth.