Determination of Effect of the Movement of a Finite, Dip-slip Fault in Viscoelastic Half-space of Fractional Burger Rheology

TL;DR

This paper develops an analytical model to study how fault inclination, creep velocity, and fractional derivative order affect stress, strain, and displacement in a viscoelastic half-space, providing insights into earthquake mechanics.

Contribution

It introduces a mathematical model using fractional Burger rheology and analytical solutions to analyze fault movement effects in seismically active regions.

Findings

Fault inclination and creep velocity significantly affect stress and displacement.

Order of fractional derivative has a moderate impact on deformation components.

Results help understand subsurface deformation and earthquake potential.

Abstract

The seismically active regions often correlate with fault lines, and the movement of these faults plays a crucial role in defining how stress is stored or released in these areas. To investigate the deformation and accumulation/release of stress and strain in seismically active regions during the aseismic period, a mathematical model has been developed by considering a finite, creeping dip-slip fault inclined in the viscoelastic half-space of a fractional Burger rheology. Laplace transformation for fractional derivatives, Modified Green's function technique, correspondence principle and finally, the inverse Laplace transformation have been used to derive analytical solutions for displacement, stress and strain components. The graphical representations were depicted using MATLAB to understand the effect on displacement, stresses and strains due to changes in inclinations and creep velocities of the fault, as well as orders of the fractional derivative. Our investigation indicates that a change in creep velocity and inclination of the fault has a significant effect, while a change in the order of fractional derivative has a moderate effect on displacement, stress, and strain components. Analysis of these results can provide insights into subsurface deformation and its impact on fault movement, which can lead to earthquakes.