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

Spectrum of Surface Displacements

Spectrum of Surface Displacements

Spectrum of Surface Displacements

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

Co-Seismic Displacements

JPL's DGPS network: Positions with delays on the order of ~8 sec.

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

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

Spectrum of Surface Displacements

Displacements during earthquakes

Co-Seismic Displacements

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

Spatial Patterns of Temporal Signals

2005/03/28/16/09/36 UTCM=8.9Epicenter: 2.074°N, 97.013°E

Post-Seismic Displacements