Earthquake Engineering GE / CEE - 479/679 Topic 13. Wave Propagation 2 John G. Anderson Professor of Geophysics March 4, 2008 1 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Combining in F=ma In this equation, Xi is a body force acting on the point, if any. March 4, 2008 2 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 3 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 4 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 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. March 4, 2008 5 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 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 March 4, 2008 6 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Two Media in Contact Transmitted SV 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. i1 Transmitted P j1 i2 i2 Reflected P j2 Incoming SV Reflected SV Generalized Snell’s Law March 4, 2008 7 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Realistic Earth Model i1 p is the “ray parameter. It is constant along the ray i2 β increases Eventually, as the velocity increases with depth, rays are bent back towards the surface. Waves cannot penetrate into layers where β is too large. March 4, 2008 8 John Anderson: GE/CEE 479/679: Lecture 13

Body Waves: Discussion The travel time curves of body waves can be inverted to find the velocity structure of the path. March 4, 2008 9 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Seismic Refraction * Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ i1 Refracted wave i2 β increases 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. p is constant along the ray March 4, 2008 10 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 11 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 12 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 13 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Realistic Earth Model i1 i2 β increases Due to Snell’s law, energy gets trapped near the surface. This trapped energy organizes into surface waves. March 4, 2008 14 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Four types of seismic waves Body Waves P Waves Compressional, Primary S Waves Shear, Secondary Surface Waves Love Waves Rayleigh Waves March 4, 2008 15 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Surface Waves Love waves: trapped SH energy. Rayleigh waves: combination of trapped P- and SV- energy. March 4, 2008 16 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Surface Waves For surface waves, geometrical spreading is changed. For body waves, spreading is ~1/r. For surface waves, spreading is ~1/r0.5. March 4, 2008 17 John Anderson: GE/CEE 479/679: Lecture 13

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. March 4, 2008 18 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 19 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 20 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 21 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Surface Waves Surface wave dispersion curves can be inverted to find the velocity structure of the path crossed by the surface waves. March 4, 2008 22 John Anderson: GE/CEE 479/679: Lecture 13

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. March 4, 2008 23 John Anderson: GE/CEE 479/679: Lecture 13

Surface Waves: Discussion Motion of Rayleigh waves is “retrograde elliptical”. March 4, 2008 24 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Site Response What is site response What causes it What are it’s characteristics. March 4, 2008 25 John Anderson: GE/CEE 479/679: Lecture 13

Classic example of site effect : Mexico City Mexico City, Mexico March 4, 2008 26 John Anderson: GE/CEE 479/679: Lecture 13

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John Anderson: GE/CEE 479/679: Lecture 13 Figure 2 March 4, 2008 30 John Anderson: GE/CEE 479/679: Lecture 13

Physics of Site Response Layer over half space Multiple layers over half space Basins Topography March 4, 2008 31 John Anderson: GE/CEE 479/679: Lecture 13

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John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 33 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 34 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 35 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 36 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 37 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Multiple flat layers March 4, 2008 38 John Anderson: GE/CEE 479/679: Lecture 13

Basins: major phenomena Amplification Energy trapped Conversion to surface waves at basin edge Longer duration March 4, 2008 39 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 40 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Basin edge Kobe, Japan earthquake disaster. March 4, 2008 41 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Liu and Heaton, ~1980 Study of strong motion from the San Fernando earthquake. Published in Bull. Seism. Soc. Am. Demonstration of a basin effect. March 4, 2008 42 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 43 John Anderson: GE/CEE 479/679: Lecture 13

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. March 4, 2008 44 John Anderson: GE/CEE 479/679: Lecture 13

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. March 4, 2008 45 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 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. March 4, 2008 46 John Anderson: GE/CEE 479/679: Lecture 13

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) March 4, 2008 47 John Anderson: GE/CEE 479/679: Lecture 13

NEHRP Classification Shear velocity of near-surface materials NEHRP Category Description Shear velocity (m/s) A Hard rock >1500 B Firm to hard rock 760-1500 C Dense soil, soft rock 360-760 D Stiff soil 180-360 E Soft soil <180 F Special studies soils March 4, 2008 48 John Anderson: GE/CEE 479/679: Lecture 13

Pancha, Anderson, Biasi, Anooshepor, Louie Empirical site response and comparison with measured site conditions at ANSS sites in the Reno area Pancha, Anderson, Biasi, Anooshepor, Louie March 4, 2008 49 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Results from Pancha’s ReMi studies in the Central Truckee Meadows March 4, 2008 50 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Figure 1a This map is horizontally exaggerated- the distance scale may be accurate for the horizontal or vertical direction, but it cannot be accurate for both. Any map should be plotted so the scale works in any direction. March 4, 2008 51 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Figure 3 March 4, 2008 52 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 53 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Figure 1b This map is horizontally exaggerated- the distance scale may be accurate for the horizontal or vertical direction, but it cannot be accurate for both. Any map should be plotted so the scale works in any direction. March 4, 2008 54 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Figure 5 March 4, 2008 55 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Alternate Figure 9 March 4, 2008 56 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 March 4, 2008 57 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Figure 3 March 4, 2008 58 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Figure 2 March 4, 2008 59 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 Figure 6 March 4, 2008 60 John Anderson: GE/CEE 479/679: Lecture 13

John Anderson: GE/CEE 479/679: Lecture 13 OLD Figure 7 March 4, 2008 61 John Anderson: GE/CEE 479/679: Lecture 13