TY - JOUR

T1 - Discrete Mathematical Model of Earthquake Focus

T2 - An Introduction

AU - Arsen’yev, Sergey A.

AU - Eppelbaum, Lev V.

AU - Meirova, Tatiana B.

N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - The process of earthquake appearance in its focus is analyzed on the basis of the oscillation theory. The earthquake focus consisting for simplicity of two blocks (granitic and basaltic) is studied mathematically and physically. The block sizes, density and Young's modulus of the rocks composing these blocks are considered to be known. We assume that the blocks are located on an edge of a regional tectonic fault. The tectonic plate or subplate, moving with a given speed u of shearing, is on the other edge of the fault. The mechanical interaction of the fault edges is due to the friction, which depends on the relative velocity V = u − dx/dt, where x is a coordinate of the concrete block. Physical-mathematical equations of block motion are solved using analytical methods. As a result, we find complete information about seismic vibrations in the focus and their characteristics. The evolutions of kinetic, potential and total energy as well as the function of dissipation in the focus and magnitude of the earthquake are calculated. The computations were carried out at different speeds of movement u. This allowed us to study the dependence of the earthquake magnitude on the velocity u of the main plate. The constructed original model of the earthquake focus unmasks the mechanism of seismic oscillations and their properties.

AB - The process of earthquake appearance in its focus is analyzed on the basis of the oscillation theory. The earthquake focus consisting for simplicity of two blocks (granitic and basaltic) is studied mathematically and physically. The block sizes, density and Young's modulus of the rocks composing these blocks are considered to be known. We assume that the blocks are located on an edge of a regional tectonic fault. The tectonic plate or subplate, moving with a given speed u of shearing, is on the other edge of the fault. The mechanical interaction of the fault edges is due to the friction, which depends on the relative velocity V = u − dx/dt, where x is a coordinate of the concrete block. Physical-mathematical equations of block motion are solved using analytical methods. As a result, we find complete information about seismic vibrations in the focus and their characteristics. The evolutions of kinetic, potential and total energy as well as the function of dissipation in the focus and magnitude of the earthquake are calculated. The computations were carried out at different speeds of movement u. This allowed us to study the dependence of the earthquake magnitude on the velocity u of the main plate. The constructed original model of the earthquake focus unmasks the mechanism of seismic oscillations and their properties.

KW - Earthquake mechanics

KW - earthquake sources

KW - faults

KW - mathematical modelling

KW - seismic oscillations

UR - http://www.scopus.com/inward/record.url?scp=85084149787&partnerID=8YFLogxK

U2 - 10.1007/s00024-020-02485-1

DO - 10.1007/s00024-020-02485-1

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AN - SCOPUS:85084149787

VL - 177

SP - 4097

EP - 4118

JO - Pure and Applied Geophysics

JF - Pure and Applied Geophysics

SN - 0033-4553

IS - 9

ER -