Extracting the time-domain building response from random vibrations∗

The extraction of the response from field fluctuations excited by random sources has received considerable attention in a variety of different fields. I show application of this principle to the motion recorded in the Millikan library at the California Institute of Technology in Pasadena, California, after an earthquake. Deconvolution of the recorded motion at different floors unravels the building response from the complicated excitation and from the unknown soil-structure interaction. I give arguments why analyzing the response function in the time domain is more informative than just using the amplitude spectrum of the transfer function. I provide examples that show that it is possible to extract the building response that satisfies the same dynamic equations as does the real building, but that may satisfy different boundary conditions at the base. This means one can obtain from the data the building response with different soil-structure interaction than the real building has.