Abstract
| Original language | English |
|---|---|
| Journal | Geophysical Journal International |
| Volume | 203 |
| Issue number | 3 |
| Pages (from-to) | 2150-2181 |
| ISSN | 0956-540X |
| DOIs | |
| Publication status | Published - 2015 |
Bibliographical note
This article has been accepted for publication in Geophysical Journal International ©: 2015 The authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.Keywords
- Composition of the planets
- Elasticity and anelasticity
- Dynamics
- Gravity and tectonics
- Mechanics, theory and modelling
- Planetary interiors
Cite this
}
An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth. / Pan, E.; Chen, J.Y. ; Bevis, M.; Bordoni, Andrea; Barletta, Valentina Roberta; Tabrizi, A. Molavi .
In: Geophysical Journal International, Vol. 203, No. 3, 2015, p. 2150-2181.Research output: Contribution to journal › Journal article › Research › peer-review
TY - JOUR
T1 - An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth
AU - Pan, E.
AU - Chen, J.Y.
AU - Bevis, M.
AU - Bordoni, Andrea
AU - Barletta, Valentina Roberta
AU - Tabrizi, A. Molavi
N1 - This article has been accepted for publication in Geophysical Journal International ©: 2015 The authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.
PY - 2015
Y1 - 2015
N2 - We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.
AB - We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.
KW - Composition of the planets
KW - Elasticity and anelasticity
KW - Dynamics
KW - Gravity and tectonics
KW - Mechanics, theory and modelling
KW - Planetary interiors
U2 - 10.1093/gji/ggv432
DO - 10.1093/gji/ggv432
M3 - Journal article
VL - 203
SP - 2150
EP - 2181
JO - Geophysical Journal International
JF - Geophysical Journal International
SN - 0956-540X
IS - 3
ER -