environmental geodesy lecture 10 (march 29, 2011): surface displacements, strain and stress -...
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Environmental Geodesy
Lecture 10 (March 29, 2011): Surface displacements, strain and stress- Displacements, Strain, Stress, Momentum Balance- Spectrum of Surface Displacements- Spatial patterns of temporal signals- Co-Seismic Offsets- Post-Seismic Deformation
Stress in a body is a result of the strain and vice-versa.
(1) Strain is related to displacements: geometry relations
(3) Stress is related to forces: mechanics laws
(2) Stress-Strain relation depends on material: material law, constitutional law
Displacements, Strain, Stress, Momentum Balance
Displacements, Strain, Stress, Momentum Balance
(1) Strain is related to displacements: geometry relations.
Strain tensor:
Linearized relationship between displacements and strain tensor:
(2) Stress-Strain relation depends on material: material law, constitutional law
Displacements, Strain, Stress, Momentum Balance
(2) Stress-Strain relation depends on material: material law, constitutional law
Displacements, Strain, Stress, Momentum Balance
Two classes of forces: Volume forces and Surface forces:
(3) Stress is related to forces: mechanics laws.
Displacements, Strain, Stress, Momentum Balance
(3) Stress is related to forces: mechanics laws.
Fluids, Euler coordinates
Solids, Lagrange coordinates
Displacements, Strain, Stress, Momentum Balance
Spatial Patterns of Surface Displacements
Spatial scales depend on process and time scaleSpatial scales for horizontal displacements are often larger than for vertical motion.
Global Filter Local Filter
Spatial Patterns of Surface Displacements
Spatial scales depend on process and time scaleSpatial scales for horizontal displacements are often larger than for vertical motion.
Global FilterCross-correlation of time series; Up componentLower-right: local trends + seasonal removed
Local Filter
Spatial Patterns of Surface Displacements
Spatial scales depend on process and time scaleSpatial scales for horizontal displacements are often larger than for vertical motion.
Annual (Sa) and Semi-Annual (Ssa) Constituents
Sa global filterMean amplitude: 2 mm
Ssa global filterMean amplitude 3 mm
Sa and Ssa spatiall very homogeneous Ssa larger than Sa and spatially more homogeneous
Displacements during earthquakes
Mexico, 2010/4/4/22:40:39, M=6.9 (7.1),Epicenter: 32.093N, 115.249W (244.75)
Co-Seismic Displacements
Spectrum of Surface Displacements
Displacements during earthquakes
Japan, 2011/ 3/11/ 5/46/21, M=7.8 (9.0),Epicenter: 38.4199990 N, 142.2629964E
Spatial Patterns of Temporal Signals
Static co-seismic offsets
2004/12/26/00/58/53 UTCM=9.1Epicenter: 3.316N, 95.854E
Co-Seismic Displacements
Spatial Patterns of Temporal Signals
Bottom pressure due to tsunami
Vertical displacement due to tsunami
0.5 h 2 h 23 h
Tsunami Loading
Co-Seismic Displacements