Accumulation of Stress and Strain due to an Infinite Strike-Slip Fault in an Elastic Layer Overlying a Viscoelastic Half Space of Standard Linear Solid (SLS)

2020 ◽  
Vol 177 (10) ◽  
pp. 4643-4656
Author(s):  
Debabrata Mondal ◽  
Piu Kundu ◽  
Seema Sarkar (Mondal)
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Strike Slip ◽  
Strike Slip Fault ◽  
Stress And Strain ◽  
Standard Linear Solid ◽  
Standard Linear

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

Stress relaxation in a semi-infinite viscoelastic earth model

1973 ◽  
Vol 63 (6-1) ◽  
pp. 2145-2154
Author(s):  
Martin Rosenman ◽  
Sarva Jit Singh
Keyword(s):  
Free Surface ◽  
Stress Relaxation ◽  
Half Space ◽  
Epicentral Distance ◽  
Strike Slip ◽  
Strike Slip Fault ◽  
Earth Model ◽  
Contour Maps ◽  
Surface Stresses ◽  
Stress Components

Abstract Expressions for quasi-static surface stresses resulting from a finite, rectangular, vertical, strike-slip fault in a Maxwellian viscoelastic half-space are derived. Variation of the stresses with time and epicentral distance is studied. Contour maps are obtained in some representative cases. It is found that all nonvanishing stress components at the free surface die exponentially with time. This is in contrast to the behavior of the displacements and strains which, in general, do not vanish for large times.

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