Vol. 3 No. 1 (2025)

  • Open Access

    Article

    Article ID: 1592

    Background seismicity and seismic correlations

    by Bogdan Felix Apostol

    Journal of AppliedMath, Vol.3, No.1, 2025; 124 Views, 120 PDF Downloads

    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.

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  • Open Access

    Article

    Article ID: 1593

    Site effects in seismic motion

    by Bogdan Felix Apostol

    Journal of AppliedMath, Vol.3, No.1, 2025; 9 Views, 2 PDF Downloads

    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.

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