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Earthquake Engineering GE / CEE - 479/679 Topic 13. Wave Propagation 2

Earthquake Engineering GE / CEE - 479/679 Topic 13. Wave Propagation 2. John G. Anderson Professor of Geophysics. Combining in F=ma. In this equation, X i is a body force acting on the point, if any. The Free Surface. SH. S-waves can have two polarizations:

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Earthquake Engineering GE / CEE - 479/679 Topic 13. Wave Propagation 2

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  1. Earthquake EngineeringGE / CEE - 479/679Topic 13. Wave Propagation 2 John G. Anderson Professor of Geophysics John Anderson: GE/CEE 479/679: Lecture 13

  2. Combining in F=ma • In this equation, Xi is a body force acting on the point, if any. John Anderson: GE/CEE 479/679: Lecture 13

  3. John Anderson: GE/CEE 479/679: Lecture 13

  4. John Anderson: GE/CEE 479/679: Lecture 13

  5. The Free Surface SH • S-waves can have two polarizations: • SH - wave motion is parallel to the surface. Causes only horizontal shaking. • SV - wave motion is oriented to cause vertical motion on the surface. • Amplitudes are approximately doubled Motion in and out of the plane of this figure - hard to draw. SV Motion perpendicular to the direction of propagation causes vertical motion of the free surface. John Anderson: GE/CEE 479/679: Lecture 13

  6. Two Media in Contact i1 • This way of drawing is consistent with horizontal layers in the Earth. • Lower velocities near the surface imply wave propagation direction is bent towards the vertical as the waves near the surface. i2 John Anderson: GE/CEE 479/679: Lecture 13

  7. Two Media in Contact Transmitted SV Transmitted P i1 j1 • For an incoming SV wave, the situation gets even more complex. • In this case, both P- and SV-waves are transmitted and reflected from the boundary. • The P- and SV-waves are coupled by the deformation of the boundary. i2 i2 Reflected P j2 Incoming SV Reflected SV Generalized Snell’s Law John Anderson: GE/CEE 479/679: Lecture 13

  8. Realistic Earth Model p is the “ray parameter. It is constant along the ray i1 • Eventually, as the velocity increases with depth, rays are bent back towards the surface. • Waves cannot penetrate into layers where β is too large. i2 β increases John Anderson: GE/CEE 479/679: Lecture 13

  9. Body Waves: Discussion • The travel time curves of body waves can be inverted to find the velocity structure of the path. John Anderson: GE/CEE 479/679: Lecture 13

  10. Seismic Refraction Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ * i1 Refracted wave • Because velocity increases with depth, rays are bent back towards the surface. • Apparent velocity at the array of sensors is the same as the velocity of the refracted ray along the top of the refracting layer. • Records from a profile of sensors radial from an explosion can thus be inverted to find velocity with depth. i2 β increases p is constant along the ray John Anderson: GE/CEE 479/679: Lecture 13

  11. John Anderson: GE/CEE 479/679: Lecture 13

  12. John Anderson: GE/CEE 479/679: Lecture 13

  13. John Anderson: GE/CEE 479/679: Lecture 13

  14. Realistic Earth Model i1 • Due to Snell’s law, energy gets trapped near the surface. • This trapped energy organizes into surface waves. i2 β increases John Anderson: GE/CEE 479/679: Lecture 13

  15. Four types of seismic waves Body Waves P Waves Compressional, Primary S Waves Shear, Secondary Surface Waves Love Waves Rayleigh Waves John Anderson: GE/CEE 479/679: Lecture 13

  16. Surface Waves • Love waves: trapped SH energy. • Rayleigh waves: combination of trapped P- and SV- energy. John Anderson: GE/CEE 479/679: Lecture 13

  17. Surface Waves • For surface waves, geometrical spreading is changed. • For body waves, spreading is ~1/r. • For surface waves, spreading is ~1/r0.5. John Anderson: GE/CEE 479/679: Lecture 13

  18. Surface Waves: Discussion • Body waves are not dispersed. • Surface waves are dispersed, meaning that different frequencies travel at different speeds. • Typically, low frequencies travel faster. These have a longer wavelength, and penetrate deeper into the Earth, where velocities are faster. • Typically, Love waves travel faster than Rayleigh waves. John Anderson: GE/CEE 479/679: Lecture 13

  19. John Anderson: GE/CEE 479/679: Lecture 13

  20. John Anderson: GE/CEE 479/679: Lecture 13

  21. John Anderson: GE/CEE 479/679: Lecture 13

  22. Surface Waves • Surface wave dispersion curves can be inverted to find the velocity structure of the path crossed by the surface waves. John Anderson: GE/CEE 479/679: Lecture 13

  23. Surface Waves: Discussion • Particle motion in S-waves is normal to the direction of propagation. • This is also true of Love waves. • However, Love waves would show changes in phase along the direction of propagation that would not appear in vertically propagating S waves. John Anderson: GE/CEE 479/679: Lecture 13

  24. Surface Waves: Discussion • Motion of Rayleigh waves is “retrograde elliptical”. John Anderson: GE/CEE 479/679: Lecture 13

  25. Site Response • What is site response • What causes it • What are it’s characteristics. John Anderson: GE/CEE 479/679: Lecture 13

  26. Classic example of site effect : Mexico City • Mexico City, Mexico John Anderson: GE/CEE 479/679: Lecture 13

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  30. Figure 2 John Anderson: GE/CEE 479/679: Lecture 13

  31. Physics of Site Response • Layer over half space • Multiple layers over half space • Basins • Topography John Anderson: GE/CEE 479/679: Lecture 13

  32. John Anderson: GE/CEE 479/679: Lecture 13

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  37. John Anderson: GE/CEE 479/679: Lecture 13

  38. Multiple flat layers John Anderson: GE/CEE 479/679: Lecture 13

  39. Basins: major phenomena • Amplification • Energy trapped • Conversion to surface waves at basin edge • Longer duration John Anderson: GE/CEE 479/679: Lecture 13

  40. John Anderson: GE/CEE 479/679: Lecture 13

  41. Basin edge • Kobe, Japan earthquake disaster. John Anderson: GE/CEE 479/679: Lecture 13

  42. Liu and Heaton, ~1980 Study of strong motion from the San Fernando earthquake. Published in Bull. Seism. Soc. Am. Demonstration of a basin effect. John Anderson: GE/CEE 479/679: Lecture 13

  43. John Anderson: GE/CEE 479/679: Lecture 13

  44. Site Characterization • Goal: characterize the average effect of geology on strong motion, and use this to improve predictions. • The shallow geology is an almost miniscule part of the total path from the earthquake to the station. • However, it has a strong effect on the ground motions, because it is the closest to the station. • Geophysical measurements, using wave propagation techniques, are used to measure near-surface site characteristics. • Also need to know basin geometry, depth. John Anderson: GE/CEE 479/679: Lecture 13

  45. Geotechnical Site Classification • Many schemes to classify the site. • Encroaching into the territory that Prof. Siddharthan will discuss later. • But it’s good to introduce the subject from the viewpoint of the seismologist. John Anderson: GE/CEE 479/679: Lecture 13

  46. Seed and Idriss (1982) • 1. Rock sites • 2. Stiff soil sites (< 60 m deep) • 3. Deep cohesionless soil sites (> 75 m deep) • 4. Sites underlain by soft to medium stiff clays Problem with this approach: Does not recognize that the spectral shape also depends on the earthquake magnitude. John Anderson: GE/CEE 479/679: Lecture 13

  47. Geotechnical Classification Schemes • Geology • Material on a geological map • For example, for California one simple approach is the “QTM” approach, using the age of the material. • Q = Quaternary • T = Tertiary • M = Mesozoic • Whether the location is “erosion-dominated” or “sedimentation-dominated” (rock, soil) John Anderson: GE/CEE 479/679: Lecture 13

  48. NEHRP ClassificationShear velocity of near-surface materials John Anderson: GE/CEE 479/679: Lecture 13

  49. Empirical site response and comparison with measured site conditions at ANSS sites in the Reno area Pancha, Anderson, Biasi, Anooshepor, Louie John Anderson: GE/CEE 479/679: Lecture 13

  50. Results from Pancha’s ReMi studies in the Central Truckee Meadows John Anderson: GE/CEE 479/679: Lecture 13

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