An Analytical Solution for the Elastic Response to Surface Loads Imposed on a Layered, Transversely Isotropic and Self-Gravitating Earth

Details

• Personal Author:
  Barletta VR ; Bevis M ; Bordoni A ; Chen JY ; Molavi Tabrizi A ; Pan E
• Description:
  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. [Description provided by NIOSH]
• Subjects:
  Occupational Health Safety
• Keywords:
  Author Keywords: Composition Of The Planets Dynamics: Gravity And Tectonics Elasticity And Anelasticity Elastic Properties Geologic Formations Geologic Models Gravitational Forces Mathematical Models Mechanics Modelling Models Planetary Interiors Theory

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• ISSN:
  0956-540X
• Document Type:
  Text
• Funding:
  Grant
• Genre:
  Journal Article
• Place as Subject:
  Ohio ; OSHA Region 5 ; OSHA Region 6 ; Texas
• CIO:
  National Institute for Occupational Safety and Health (NIOSH)
• Topic:
  Workplace Safety & Health
• Location:
  North America
• Volume:
  203
• Issue:
  3
• NIOSHTIC Number:
  nn:20053113
• Citation:
  Geophys J Int 2015 Dec; 203(3):2150-2181
• Contact Point Address:
  E. Pan, Department of Civil Engineering, University of Akron, Akron, OH 44325-3905, USA
• Email:
  pan2@uakron.edu
• Federal Fiscal Year:
  2016
• Performing Organization:
  University of Texas at Arlington
• Peer Reviewed:
  True
• Start Date:
  20121122
• Source Full Name:
  Geophysical Journal International
• End Date:
  20150831
• Collection(s):
  National Institute for Occupational Safety and Health
• Main Document Checksum:
  urn:sha-512:88e02ba4fca75c4900a51b704138ac3242f23a7e1cd73194244277a7f83c2a5328a053bdc6f89796d9495efb0b12f760b06dcfdaadb3491dc903610c95154d44
• Download URL:
  https://stacks.cdc.gov/view/cdc/215941/cdc_215941_DS1.pdf
• File Type:
  [PDF - 2.03 MB ]