arXiv subjects

Bogdan Felix Apostol

Publications and source records attributed to Bogdan Felix Apostol.

3 recordsLinked to original sources

arXiv2026

Mechanism of production and deviation from the standard Gutenberg-Richter law of the big earthquakes (An analysis of big earthquakes)

We describe two self-replicating mechanisms of energy accumulation in the seismic focus, which modify the Gutenberg-Richter law in the region of the big earthquakes. The first mechanism acts for magnitudes smaller than a narrow region of large critical magnitudes; it slows down the energy accumulation and may produce precursors. The second mechanism acts above that region, and accelerates the energy accumulation; the precursors may be absent. Both mechanisms reduce the Gutenberg-Richter excedence distribution. On the left of the critical region the Gutenberg-Richter magnitude probability density is unchanged, while on the right the probability density is reduced. The procedure described in this paper introduces a critical-magnitude region (range) as an additional fitting parameter. The results may bear relevance upon the recent concepts of "self-arresting" and "dragon-king" earthquakes. The two self-replicating mechanisms may introduce a magnitude gap between the two types of big earthquakes, and two branches in the excedence law, in the vicinity of the critical region.

physics.geo-ph↗

arXiv2020

Bath's law, correlations and magnitude distributions

The empirical Bath's law is derived from the magnitude-difference statistical distribution of earthquake pairs. The pair distribution related to earthquake correlations is presented. The single-event distribution of dynamically correlated earthquakes is derived, by means of the geometric-growth model of energy accumulation in the focal region. The dynamical correlations may account, at least partially, for the roll-off effect in the Gutenberg-Richter distributions. The seismic activity which accompanies a main shock, including both the aftershocks and the foreshocks, can be viewed as fluctuations in magnitude. The extension of the magnitude difference to negative values leads to a vanishing mean value of the fluctuations and to the standard deviation as a measure of these fluctuations. It is suggested that the standard deviation of the magnitude difference is the average difference in magnitude between the main shock and its largest aftershock (foreshock), thus providing an insight into the nature and the origin of the Bath's law. It is shown that moderate-magnitude doublets may be viewed as Bath partners. Deterministic time-magnitude correlations of the accompanying seismic activity are also presented.

physics.geo-ph↗

arXiv2018

The inverse problem in Seismology. Seismic moment and energy of earthquakes. Seismic hyperbola

The inverse problem in Seismology is tackled in this paper under three particular circumstances. First, the inverse problem is defined as the determination of the seismic-moment tensor from the far-field seismic waves (P and S waves). We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. The far-field waves provide three equations for the sixth unknown parameters of the general tensor of the seismic moment. Second, the Kostrov vectorial (dyadic) representation of the seismic moment is used. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved, and the seismic moment is determined, thus solving the inverse problem in the conditions described above. It is shown that a useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). Also, it is shown that the far-field seismic waves allow an estimation of the volume of the focal region, focal strain, duration of the earthquake and earthquake energy; the later quantity is a direct measure of the magnitude of the seismic moment. The special case of an isotropic seismic moment is presented.

physics.geo-ph↗