Do we know what the rigid mantle looks like?
Above the asthenosphere is the lithosphere. The main constituent of the lower lithosphere is peridotite, a coarse-grained igneous rock containing the minerals olivine and pyroxene. Samples of peridotite can be found in the surface. Sections of ocean crust can be uplifted onto continental margins, forming ophiolites (perhaps the best-known example being the Troodos Ophiolite). They are also found as fragments in basalts and kimberlites, the vertical intrusions that often contain diamonds. So there are lots of places on the surface where you can go and see what the upper mantle looks like! But in the meantime, a closeup of a peridotite is shown below.