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Evolution of modulated seismic waves under the external influence of magma up flow

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Abstract

During the occurrence of an earthquake, seismic waves usually carry huge amount of energy through rock materials of the earth crust. By using the method of multiple scale expansion in the semi-discrete approximation, the forced/damped nonlinear Schr\(\ddot{o}\)dinger equation is derived from the modified Burridge–Knopoff model of earthquake fault in which the external influence of magma up flow is considered. Based on the Lagrangian variational approach, we obtained analytical solution of the amplitude equation as modulated seismic waves. It is shown that an increase in the magnitude of the magma thrust force triggered by volcanic eruptions, generally leads to more localized and violent vibrations of earthquake. Results of numerical simulations equally reveal the long-term stability of the modulated seismic waves in a regime of weak damping and magma thrust forces. This study provides a sound theoretical foundation in seismology, as the evolution of modulated seismic waves may serve as a precursor for the occurrence of earthquakes and volcanic eruptions.

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Acknowledgements

The authors are grateful for the financial assistance from the Cameroon Ministry of Higher Education (through the regular research grants to lecturers of state universities) and to the anonymous reviewers whose suggestions have led to improvement of the original manuscript.

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  1. Department of Physics, Higher Teacher Training College Bambili, The University of Bamenda, P.O. Box 39, Bambili, Cameroon

    Nkeh Oma Nfor & Konga Guy Pascal

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  1. Nkeh Oma Nfor
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Correspondence to Nkeh Oma Nfor.

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Nfor, N.O., Pascal, K.G. Evolution of modulated seismic waves under the external influence of magma up flow. Eur. Phys. J. Plus 138, 956 (2023). https://doi.org/10.1140/epjp/s13360-023-04612-y

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