The ALPS II experiment at DESY is searching for new particles beyond the standardmodel of particle physics in a laboratory-based Light-Shining-through-a-Wall experi-ment, using high finesse optical resonators to reach the required sensitivity. The inputand output mirrors on the optical tables have extremely accurate positioning and align-ment requirements, for which the analysis of ground vibration and seismic noise is essen-tial. This thesis, therefore, focuses on this analysis, its evaluation, and the developmentof future seismic isolations for the ALPS II and JURA experiments.This work describes mechanical vibrations, seismic noise sources, seismic isolationprinciples, and also the seismic devices used to perform seismic noise analysis with theirmethods of measuring, calibrating, and analysing the acquired data. It summarises theseismic noise studies carried out in the ALPS II laboratories at HERA West as well asin the hall and tunnels of HERA North at DESY in Hamburg.For a more accurate presentation of the prevailing noise frequencies a new method ofthe modal analysis, the MfwaFFT was developed. Here, a noise-independent procedurefor more precise data analysis is implemented which accounts for the highly sensitiveconditions on-site. Furthermore, a seismic isolation concept based on this analysis inconnection with the ALPS II experiment is developed and presented.