What are the geotechnical methods used in seismic prone areas?

If it is a hard strata, isolated footings would be sufficient. However, to withstand the seismic forces, all the isolated footings must be connected with one another using a tie beam. This tie beam can resist the differential movement in strata due to the seismic loads.

If it is a soft strata, then a raft foundation or pile foundation is necessary. But both pile foundation and raft foundation cannot counteract the effect of liquefaction. If the soil is found to be susceptible to liquefaction, then proper ground improvement methods should be followed before the construction of the foundation.

Various ground improvement techniques can be found here.

https://theconstructor.org/geotechnical/ground-improvement-techniques-soil-stabilization/1836/13

If a building foundation sits on soft or filled-in soil, the whole building may fail in an earthquake regardless of the advanced engineering techniques employed. Assuming, however that the soil beneath a structure is firm and solid, engineers can greatly improve how the building foundation system will respond to seismic waves.

Another solution refers to base isolation which involves floating a building above its foundation on a system of bearings, springs or padded cylinders.

From the geotechnical point view, seismic foundation design requires info about plastic deformability, strength, damping and stiffness of soil materials. The last two are needed to study the response characteristics of soil deposit, soil strength is required for foundation stability analyses and plastic deformability for the evaluation of earthquake-induced permanent displacements. Additionally, the duration of seismic excitation influences all four parameters and must be included in the designs.

According to soil bearing capacity but if the overturning moment due to seismic is high, that may require raft foundation or using piles (that happened for building with core walls) and to safe bearing capacity for footing below core wall (even after increasing the allowable bearing capacity due to combination with seismic), that may require raft foundation for whole building or make piled foundation depend on bearing capacity.

Where liquefaction is not a concern, they should be stiff and not prone to differential settlements. Usually, slabs or grillages with large and thick beam elements. Also, resistance to lateral sliding should be checked. For more important buildings, the 6 dynamic impedances should be checked. Where liquefaction is a concern, deep foundations may be used, or some variations of deep foundations, unless soil is engineered (improved), both solutions are costly.