1. 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

2. 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

3. (1) Strain is related to displacements: geometry relations. Strain tensor: Linearized relationship between displacements and strain tensor:

4. (2) Stress-Strain relation depends on material: material law, constitutional law Displacements, Strain, Stress, Momentum Balance

5. (2) Stress-Strain relation depends on material: material law, constitutional law Displacements, Strain, Stress, Momentum Balance

6. Two classes of forces: Volume forces and Surface forces: (3) Stress is related to forces: mechanics laws. Displacements, Strain, Stress, Momentum Balance

7. (3) Stress is related to forces: mechanics laws. Fluids, Euler coordinates Solids, Lagrange coordinates Displacements, Strain, Stress, Momentum Balance

8. Spectrum of Surface Displacements

11. Spatial Patterns of Surface Displacements Spatial scales depend on process and time scale Spatial scales for horizontal displacements are often larger than for vertical motion. Global Filter Local Filter

12. Spatial Patterns of Surface Displacements Spatial scales depend on process and time scale Spatial scales for horizontal displacements are often larger than for vertical motion. Global Filter Cross-correlation of time series; Up component Lower-right: local trends + seasonal removed Local Filter

13. Spatial Patterns of Surface Displacements Spatial scales depend on process and time scale Spatial scales for horizontal displacements are often larger than for vertical motion. Annual (Sa) and Semi-Annual (Ssa) Constituents Sa global filter Mean amplitude: 2 mm Ssa global filter Mean amplitude 3 mm Sa and Ssa spatiall very homogeneous Ssa larger than Sa and spatially more homogeneous

14. Co-Seismic Displacements JPL's DGPS network: Positions with delays on the order of ~8 sec.

15. 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

16. Spectrum of Surface Displacements Displacements during earthquakes Co-Seismic Displacements

17. 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

18. Spectrum of Surface Displacements Displacements during earthquakes Co-Seismic Displacements

19. Spatial Patterns of Temporal Signals Static co-seismic offsets 2004/12/26/00/58/53 UTC M=9.1 Epicenter: 3.316N, 95.854E Co-Seismic Displacements

20. Spatial Patterns of Temporal Signals Bottom pressure due to tsunami Vertical displacement due to tsunami 0.5 h2 h 23 h Tsunami Loading Co-Seismic Displacements

21. Spatial Patterns of Temporal Signals 2005/03/28/16/09/36 UTC M=8.9 Epicenter: 2.074°N, 97.013°E Post-Seismic Displacements