This paper studies the earthquake data which include the building seismic response data as well as the SMART‐1 array data, and use the technique of correlation and spectral analysis to develope some basic result for earthquake engineering and building system identification. In frequency domain analysis, the relative time delays as seismic waves propagate from basement to the roof are estimated as the optimum alignment of records. The ordinary and partial coherent spectrum are also employed to study the correlation of building input/output data. In time domain analysis, the input/output correlation study as well as the input signal management provide data of optimum input for system identification. The SMART‐1 array data was also used to study the spatial‐time correlation of seismic waves. This study can provide information for both building system identification and spatial variation of seismic waves.