Prediction of Wave Propagation in Buildings Using Data from a Single Seismometer

Crowd-sourced seismic networks in buildings collect important scientific data, in addition to allowing a diverse audience to visualize the vibrations of buildings. Visualization of a building's deformation requires spatiotemporal interpolation of motions from seismometers that are located wherever the crowd places them. In many cases, a crowd-sourced building network may actually be just a single seismometer. A method to rapidly estimate the total displacement response of a building based on limited observational data, in some cases from only a single seismometer, is presented. In general, the earliest part of the response is simulated by assuming a vertically propagating shear wave. Later motions are simulated using mode shapes derived from a beam model (a shear beam, or more generally a Timoshenko beam), the parameters of which are determined from the ratios of the modal frequencies and the building's exterior dimensions. The method is verified by (1) comparing predicted and actual records from a 54-story building in downtown Los Angeles, California, and (2) comparing finite-element simulations of the 17-story University of California, Los Angeles (UCLA) Factor building. The response of each of these buildings can be simulated with a simple shear beam. The importance of including the traveling wave part of the solution depends on the characteristics of the base ground shaking; the traveling wave becomes more apparent as the excitation becomes more impulsive. The method can be straightforwardly applied to multiple instrumented buildings, resulting in a tool to visualize linear elastic motions of those buildings.