Time‐domain approach for the transient responses in stratified viscoelastic Earth models

Abstract

We have developed the numerical algorithm for the computation of transient viscoelastic responses in the time domain for a radially stratified Earth model. Stratifications in both the elastic parameters and the viscosity profile have been considered. The particular viscosity profile employed has a viscosity maximum with a contrast of O(10²) in the mid lower mantle. The distribution of relaxation times reveals the presence of a continuous spectrum situated between O(10²) and O(104) years. The principal mode is embedded within this continuous spectrum. From this initial‐value approach we have found that for the low degree harmonics the non‐modal contributions are comparable to the modal contributions. For this viscosity model the differences between the time‐domain and normal‐mode results are found to decrease strongly with increasing angular order. These calculations also show that a time‐dependent effective relaxation time can be defined, which can be bounded by the relaxation times of the principal modes.

Short time-scale heating of the Earth’s mantle by ice-sheet dynamics

“…This model can thus be considered to be the reference case. Since dynamic geoid modeling as well as rotational dynamics require at least an order of magnitude increase of viscosity in the lower mantle (Mitrovica and Forte, 2004), we have increased the lower-mantle viscosity in model M2 by adding a 'lower-mantle viscosity hill' exceeding the value 10 23 Pa s (see also Hanyk et al, 1995), whereas viscosity in the upper mantle remains the same and the thickness of the elastic lithosphere is again 110 km. Finally, the model M3 contains a low-viscosity zone (LVZ) just below the lithosphere, with η = 10 19 Pa s and the thickness of 110 km, which is compensated by an increased viscosity of the magnitude 2×10 22 Pa s in the transition zone in the depth interval 400-670 km.…”

Application of a Numerical Inverse Laplace Integration Method to Surface Loading on a Viscoelastic Compressible Earth Model

“…For incompressible models, both have been developed (e.g., HAGER, 1994, 1995;MARTINEC, 2000;ZHONG et al, 2003;SPADA and BOSCHI, 2006). For compressible models, only time-domain approaches (e.g., HANYK et al, 1995;STEFFEN et al, 2006) have been used. Since the governing equations are solved in the time domain, the effects of all modes including dilatation modes are evaluated without finding the roots.…”

“…It has, however, been shown that the classical normal mode approach suffers from the intrinsic difficulties which arise when compressibility and selfgravitation are considered simultaneously in the governing equations (WU and PELTIER, 1982;WOLF, 1985b;HAN and WAHR, 1995;PLAG and JÜ TTNER, 1995;VERMEERSEN et al, 1996). To circumvent these difficulties, initial value approaches in the time-domain (e.g., HANYK et al, 1995) have been used. In this paper, after a short review of previous studies, we introduce an alternative method to compute surface loading of spherically symmetric, self-gravitating and compressible earth models with continuously varying viscoelastic profiles by applying a numerical inverse Laplace integration method developed for computations of global postseismic deformation (TANAKA et al, 2006(TANAKA et al, , 2007.…”

Spectral-finite element approach to post-seismic relaxation in a spherical compressible Earth: application to gravity changes due to the 2004 Sumatra–Andaman earthquake

“…where represents the strain tensor and λ, μ, K and η are Lamé's constants, the bulk modulus and the dynamic viscosity, respectively (Hanyk et al 1995;Tanaka et al 2011). …”