Soil and structure damping from single station measurements

In seismology and seismic engineering soils and structures are modeled as oscillators characterized by modal (resonance) frequencies, shapes and damping. In 1973 Cole proposed the RandomDec technique to estimate both the damping and the fundamental mode of structures from the recorded time series at a single point, with no need for spectral analyses. Here we propose a number of modifications to the original RandomDec approach, that we group under the name DECÓ, which allow to determine the damping as a function of the frequency and therefore the damping of all the vibration modes. However, the motion of structures is so amplified at the resonance frequencies that detecting the characteristic parameters by recording ambient vibrations is relatively easy. More interesting is to apply the DECÓ approach to the soil in the attempt to estimate the mode damping from single station measurements. On soils, the resonance frequencies are normally identified as peaks in the horizontal to vertical spectral ratios of microtremors. However, at these frequencies what is observed is a local minimum in the vertical spectral component, sometimes associated to local maxima in the horizontal components, whose visibility depend on the specific amount of SH and Love waves at the site. The determination of soil damping is therefore a much less trivial task on soils than on structures. By using microtremor and earthquake recordings we estimate the soil damping as a function of shear strain and observe that this is one order of magnitude larger than what is measured in the laboratory on small scale samples, at least at low-intermediate strain levels. This has severe consequences on the numerical seismic site response analyses and on soil dynamic modeling.