Harmonic forms in displacement response spectra and a novel definition of duration in pulse-type strong motion

Neat sine (cosine) shapes have been observed in peaks of high-resolution deformation response spectra corresponding to real earthquake records. Theoretically, these smooth and special spectral forms should appear only when the excitation is a mathematical shock or pulse. Some seismic records, especially near-fault, are considered pulses and more generally, earthquake excitation can be considered as a large action applied over a short time, which is shock excitation; therefore, there is an explanation to the observation or discovery of those harmonic forms. Now, an explanation on why these sinusoidal peaks had not been observed or studied before can lie in that most research has been done on acceleration response spectra, rather than on displacement ones; moreover, previous publications on the latter have been with a very-low resolution. A main objective here is, first, to demonstrate that the shapes in actual response spectra are indeed harmonic, this by means of fitting. Then and additionally, an application to Earthquake Engineering, and Seismology, of these revealed sine forms is presented, which is to the subfield of strong motion duration; in particular, a new procedure is proposed to estimate earthquake duration in the case of pulse-type excitation, which is associated to the near field.