Which strategy can scientists use to learn about earth's deepest layers?

Scientists use magnetic studies, seismic waves, and gravity to study the layers of the planet earth.

There are three layers namely the crust, mantle, and the core in respective order. The crust is easily accessible due to mining and other processes, therefore, scientists have been able to use practical methods to analyze it.  

The mantle and the core are studied using seismic waves. The propagation of seismic waves changes as they move through different materials providing information which is recorded on a seismometer. The time it takes for the waves to register on a seismometer during the earthquake shed information regarding the material it has travelled through. The waves will change velocity and propagation as it goes through different material such as water or solids.