Interesting question. Has any research been done on this? Are there any examples of indigenous architecture, in earthquake prone areas, where people built underground? I'm guessing that in areas with sandy soil, liquefied soil could crush underground structures instantly in an earthquake. Building in bedrock may be completely different. There are probably lots of variables to explore.
Seismic stresses tend to decrease with increasing depth; this is quantified with an "rd" reduction factor. The reduction may be on the order of 15-20% at 15 m depths and about 40-60% at 30 m depths, depending on ground conditions. As a consequence, you will see few underground tunnels, deep burial sites for waste, etc. where seismic issues are a real concern.
A few metres will not do to isolate your structure. And in any case, note that the above is only representative of distant effects of the earthquake. The fault undergoing the differential displacement that causes the earthquake will normally be at depths of tens, even hundreds, of kilometres. Thus the above is not representative of near-field effects.
Even if there might be a reduced effect of seismic accelerations underground, I think it might depend on the soil surrounding your structure, which could exercise an important lateral dynamic load on your structure in case of insufficient cohesion.
One should try to model and study the shear and stress distribution. I strongly believe that our structures will resist earthquake forces more compared to the surface one.