What is this technique of decoupling a building from ground shaking called?

Base isolation is the technique of decoupling a building from ground shaking during an earthquake, achieved by placing flexible rubber-and-steel bearings between the building's foundation and the structure above, allowing the ground to shake more freely underneath while the bearings absorb much of that energy before it can travel upward into the building itself.

Underpinning is a technique for strengthening or extending an existing foundation, typically used when soil conditions change or additional load-bearing capacity is needed, not specifically to absorb earthquake shaking. Sandblasting is a surface-cleaning technique that uses high-pressure sand or abrasive material, unrelated to structural earthquake protection.

Hospitals and other critical buildings often rely on base isolation specifically because it can allow them to remain standing and fully operational immediately after a major earthquake, when continued function can be a matter of life and death for surrounding communities.