Bogdan Felix Apostol

A set of pointlike inhomogeneities placed on the flat surface of an elastic half-space is put forward as a model for large urban agglomerations, consisting of buildings, constructions, erected on a limited area on Earth’s surface (e.g., cities). Under the action of an incident plane seismic wave a hierarchy of scattered waves arising from these inhomegeneities is identified, and their effect on the pointlike inhomogeneities is analyzed. We show that in the long-wavelength limit the first-order scattered waves are of Coulomb type, i.e. the displacement in these waves goes like the inverse distance from the scattering centres. We estimate the displacement produced by the scattered waves in this case, and find that it is large for large and agglomerated buildings, constructions, placed over large distances, i.e. precisely for what we call "large urban agglomerations". In the short-wavelength limit the Coulomb-like dependence acquires an oscillating factor. In this case we identify a divergent displacement produced by the scattered waves when the incident wave propagates parallel to the surface; leaving aside this special case, a necessary condition for the convergence of the series produced by the hierarchy of the scattered waves is a rare (sparse) distribution of small-size inhomogeneites.

Processed parameters from sensors located on seismically isolated buildings (maximum acceleration, spectral acceleration and oscillation periods) are compared against free-field ground motion to evaluate the improvement in seismic response for these buildings. The study is carried out for three structures in Bucharest, the capital city of Romania. The data used in this research correspond to moderate magnitude earthquakes, 4.2 ≤ M_W ≤ 5.5 generated from the Vrancea-intermediate-depth seismic area, with focal depths greater than ~90 km. The methodology helps to evaluate amplification/reduction in the seismic motion, and confirmed that base-isolation devices reduce the seismic parameters’ amplitudes of the structure directly above the isolating layer. The effectiveness of the base-isolation technique is further assessed by comparing the amplitude of the seismic parameters recorded under and above the earthquake protection devices. The results show a clear decrease in the values right above the isolating system, supporting the efficiency of base-isolation systems. The outcomes provide necessary empirical data for refining seismic design and improving the resilience of critical structures. The work contributes to the mitigation of the seismic risk in the city area, thus targeting a more resilient urban community and sustainable city through implementation of modern base-isolation systems for the retrofitting of vulnerable buildings exposed to a high risk of seismic hazards.

We report on the resolution of the vibration problem for a homogeneous and isotropic elastic half-space (the Lamb problem), with application to the seismic tensorial force. We assume a homogeneous and isotropic half-space with a localized force which produces vibrations. The solution is achieved by introducing vector plane-wave functions. Explicit results are given for an isotropic tensorial force and a half-space with free surface. The contribution of the Rayleigh surface waves to vibrations is analyzed in the special case of a temporal-impulse force, where the solution exhibits unphysical features, as expected: it extends over the entire free surface and time domain, with a (scissor-like) double-wall propagating both in the future and the past.

We use the harmonic-oscillator model to analyze the motion of the sites (ground motion), seimograph recordings, and structures built on the Earth’s surface under the action of the seismic motion. The seismic motion consists of singular waves (spherical-shell P and S primary seismic waves) and discontinuous (step-wise) seismic main shocks. It is shown that these singularities and discontinuities are present in the ground motion, seismographs’ recordings and the motion of the built structures. In addition, the motion of the oscillator exhibits oscillations with its own eigenfrequency, which represent the response of the oscillator to external perturbations. We estimate the peak values of the displacement, the velocity and the acceleration of the ground motion, both for the seismic waves and the main shock, which may be used as input parameters for seismic hazard studies. We discuss the parameters entering these formulae, like the dimension of the earthquake focus, the width of the primary waves and the eigenfrequencies of the site. The width of the seismic waves on the Earth’s surface, which includes the energy loss, can be identified from the Fourier spectrum of the seismic waves. Similarly, the eigenfrequencies of the site can be identified from the spectrum of the site response. The paper provides a methodology for estimating the input parameters used in hazard studies.

The law of energy accumulation in the earthquake focus is presented, together with the temporal, energy and magnitude distributions of regular, background earthquakes. The background seismicity is characterized by two parameters—the seismicity rate and the Gutenberg-Richter parameter, which can be extracted by fitting the empirical earthquake distributions. Time-magnitude and temporal correlations are presented, and the information they can provide is discussed. For foreshocks the time-magnitude correlations can be used to forecast (with limitations) the mainshock. The temporal correlations indicate a decrease of the Gutenberg-Richter parameter for small magnitudes, in agreement with empirical observations for foreshocks. On the other hand, the aftershocks may be viewed as independent earthquakes with changed seismic conditions, so they may exhibit an increase of this parameter, also in accordance with empirical observations. The roll-off effect for small magnitudes and the modified Gutenberg-Richter distribution are discussed for temporal corralations, and the derivation of the Bath’s law is briefly reviewed.

An estimation is given for the free vibration eigenfrequencies (normal modes) of a homogeneous solid sphere with a large radius, with application to Earth's free vibrations. The free vibration eigenfrequencies of a fluid sphere are also derived as a particular case. Various corrections arising from static and dynamic gravitation, rotation, and inhomegeneities are estimated, and a tentative notion of an earthquake temperature is introduced.

The paper highlights the performance of the seismic isolation devices, installed on retrofitted buildings in reducing the seismic response when subjected to earthquakes. Two buildings from the beginning of the XX-th century in Bucharest are chosen from many more, monitored over the city area. We discuss the response of these base-seismic isolated structures, relying on good quality data acquired from the recent strong earthquake (03.11.2022, MW = 5.0). Elastic response spectra computed from recordings at two levels of each structure are used, placed under and right above the isolating layer. At one building the existence of previous recordings and the particularity of the sensors allow a comparison with other two relatively recent medium intensity earthquakes. The assessment is carried out in terms of maximum acceleration amax, measured at certain levels in each structure, spectral acceleration amplitude SAmax and spectral-peak corresponding period. We find that the base-isolation methodology is effective in reducing the response of the building right above the isolating layer, an observation valid for both structures, all components of the recordings, and spectral acceleration values. Moreover, the outcomes from the modal evaluation performed prior to rehabilitation and seismic isolation process are presented, by pointing out a higher newly acquired fundamental period of the isolated structures.

We analyze the usefulness of the foreshocks in forecasting seismic mainshocks. The analysis is based on possible correlations which may exist between foreshocks and mainshocks. Such correlations are expressed by a previously established time-magnitude relationship, which indicates the presence of an abrupt magnitude-decreasing sequence of correlated foreshocks in the proximity of a mainshock. By fitting this formula, we are able to derive the occurrence time of a possible mainshock. Also, we can estimate the magnitude of the mainshock, providing we know the parameters of the background seismicity of the seismic region. We report here on the application of this procedure to three Vrancea (Romania) mainshocks, the l’Aquila (Italy), Yangbi (Yunnan, China) and Izmit (Turkey) earthquakes. The limitations of the procedure are discussed. Also, a discussion is included regarding the so-called temporal variability of the Gutenberg-Richter parameter in the proximity of a mainshock, as resulting from time-magnitude and time-time correlations.

The elastic wave equation with seismic tensorial force is solved in a homogeneous and isotropic medium (the Earth). Spherical-shell waves are obtained, which are associated to the primary P and S seismic waves. It is shown that these waves produce secondary waves with sources on the plane surface of a half-space, which have the form of abrupt walls with a long tail, propagating in the interior and on the surface of the half-space. These secondary waves are associated to the seismic mainshock. The results, previously reported, are re-derived using Fourier transformations and specific regularization procedures. The relevance of this seismic motion for the ground motion, the seismographs’ recordings and the effect of the inhomogeneities in the medium are discussed.