The strong lower part of the mantle between the asthenosphere and outer core is called the mesosphere.

Here's a breakdown:

* Asthenosphere: The soft, partially molten layer of the upper mantle. This layer allows for the movement of tectonic plates.

* Mesosphere: The solid, rigid lower mantle. It's incredibly strong and behaves more like a solid than the asthenosphere.

* Outer Core: The liquid layer of iron and nickel surrounding the Earth's solid inner core.

The mesosphere is crucial for the Earth's tectonic activity and is also responsible for generating seismic waves that travel through the Earth's interior.