Engineering Earthquake GE / CEE - 479/679
Topic 16. Seismic Waves 2 and Site Response
John G. Anderson Professor of Geophysics
Schedule
Midterm April 4. Raj Siddharthan will lecture after the midterm May 9. Oral presentation of seismic hazard analyses (term projects) by each of the teams.
1
Four types of seismic waves Body Waves P Waves Compressional, Primary S Waves Shear, Secondary
Surface Waves Love Waves
Rayleigh Waves
The Free Surface
SH
Motion in and out of the plane of this figure - hard to draw.
Amplitudes doubled. 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.
SV
Motion perpendicular to the direction of propagation causes vertical motion of the free surface.
2
Two Media in Contact
i1
1 , 1 , 1 2 , 2 , 2
i2
sin i1 sin i 2 = 1 2
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.
Two Media in Contact
i1
1 , 1 , 1 2 , 2 , 2
i2
Lower velocities near the surface also imply that waves are bent towards the horizontal at depth.
sin i1 sin i 2 = 1 2
3
Realistic Earth Model
i1
1 , 1 , 1 2 , 2 , 2
i2
increases
sin i1 sin i 2 = 1 2
Due to Snell's law, energy gets trapped near the surface. This trapped energy organizes into surface waves.
Four types of seismic waves Body Waves P Waves Compressional, Primary S Waves Shear, Secondary
Surface Waves Love Waves
Rayleigh Waves
4
Two Media in Contact
i1
1 , 1 , 1 2 , 2 , 2
i2 i2
Incoming SH
In addition to the "refraction" of energy into the second medium, some energy is reflected back. The angle of reflection is equal to the angle of incidence. This brings up the issue: how is the energy partitioned at the interface?
Two Media in Contact
The energy partitioning is determined by "reflection" , , and "transmission" , , i2 i2 coefficients. The coefficients are A Incoming SH R determined by matching T Transmission coefficient boundary conditions A For incoming SH waves, the R form is relatively simple. Reflection coefficient
i1
1 1 2 1 2 2
T
A
5
Two Media in Contact
T
i1
1 , 1 , 1 2 , 2 , 2
i2 i2
A
Incoming SH
T 2 2 2 = A 2 2 + 1 1 R 2 2 - 1 1 = A 2 2 + 1 1
R
These coefficients are not a function of frequency. At most, the transmitted wave has an amplitude of 2 x the amplitude of the incoming wave. Going from a stiffer to a softer material, the transmission coefficient is never less than 1.0.
Two Media in Contact
T
i1
1 , 1 , 1 2 , 2 , 2
i2 i2
A
Incoming SH
T 2 2 2 = A 2 2 + 1 1 R 2 2 - 1 1 = A 2 2 + 1 1
R
Going from a softer to a stiffer material, the transmission coefficient is never more than 1.0. If there is a large impedence contrast from softer to stiffer, the transmission coefficient approaches zero.
6
Two Media in Contact
T
i1
1 , 1 , 1 2 , 2 , 2
i2 i2
A
Incoming SH
T 2 2 2 = A 2 2 + 1 1 R 2 2 - 1 1 = A 2 2 + 1 1
R
The reflection coefficient is always less than 1.0. In the limit of the two media being identical, the transmission coefficient is 1.0 and the reflection coefficient is 0.0. In the limit of a reflection from a much stiffer or much softer medium, the reflection coefficient approaches 1.0.
Two Media in Contact
T
i1
1 , 1 , 1 2 , 2 , 2
i2 i2
A
Incoming SH
T 2 2 2 = A 2 2 + 1 1 R 2 2 - 1 1 = A 2 2 + 1 1
R
An important case is when waves in a soft medium contact a stiff boundary. In this case, the reflection coefficient is almost 1.0 (actually -1.0), meaning that the energy is trapped in the softer material. This applies to energy in a sedimentary basin.
7
Two Media in Contact
Transmitted SV
For an incoming SV wave, the situation gets , , , even more complex. , , , i2 i2 Reflected P In this case, both P- and j2 SV-waves are Incoming SV transmitted and reflected Reflected SV from the boundary. Generalized Snell's Law The P- and SV-waves are sin i1 sin i 2 sin j1 sin j 2 coupled by the = = = deformation of the 1 2 1 2 boundary.
i1 Transmitted P j1
1 1 2 1 1 2 2 1
Two Media in Contact
Transmitted SV
For an incoming P wave, the situation is similar to , , , incoming SV. , , , i2 j2 Reflected P In this case also, both Pj2 and SV-waves are Incoming P transmitted and reflected Reflected SV from the boundary. Generalized Snell's Law The P- and SV-waves are sin i1 sin i 2 sin j1 sin j 2 again coupled by the = = = deformation of the 1 2 1 2 boundary.
i1 Transmitted P j1
1 1 2 1 1 2 2 2
8
Site Response
What is site response What causes it What are it's characteristics.
Recognition of site effect : Mexico City
Mexico City, Mexico
9
10
11
Recognition of site effect
Los Angeles basin
Site effects are quantified with the Fourier spectral ratio of sediment to rock sites.
12
Nuclear explosion, NTS
San Fernando M6.4
Note time scales differ
Ratio Scales 0-12 Generally sites in the central Los Angeles basin. Nuclear (solid) Earthquake (dashed) Why might they differ?
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.
14
Site Effects on Rock
Humphrey and Anderson ~1992 Guerrero, Mexico Site effect is defined relative to a smoothed spectral shape.
15
Solid: from Humphrey and Anderson. Dashed: from Castro et al. Two different methods give similar results. Main point for class: site response is not the same at all the rock sites. Some have sharp peaks, others are flat.
More examples, from the same paper. Castro approach was to find site effect relative to the average spectral shape of all the recordings.
16
Physics of Site Response
Layer over half space Multiple layers over half space Basins Topography
Cartoon showing some differing of causes site response.
17
Topography
Ridge - amplifies motions Valley - deamplifies motions
Layer over a half space
18
Two Media in Contact
T
i1
1 , 1 , 1 2 , 2 , 2
i2 i2
A
Incoming SH
T 2 2 2 = A 2 2 + 1 1 R 2 2 - 1 1 = A 2 2 + 1 1
R
These coefficients are not a function of frequency. At most, the transmitted wave has an amplitude of 2 x the amplitude of the incoming wave. Going from a stiffer to a softer material, the transmission coefficient is never less than 1.0.
Two Media in Contact
T
i1
1 , 1 , 1 2 , 2 , 2
i2 i2
A
Incoming SH
T 2 2 2 = A 2 2 + 1 1 R 2 2 - 1 1 = A 2 2 + 1 1
R
Going from a softer to a stiffer material, the transmission coefficient is never more than 1.0. If there is a large impedence contrast from softer to stiffer, the transmission coefficient approaches zero.
19
Two Media in Contact
T
i1
1 , 1 , 1 2 , 2 , 2
i2 i2
A
Incoming SH
T 2 2 2 = A 2 2 + 1 1 R 2 2 - 1 1 = A 2 2 + 1 1
R
The reflection coefficient is always less than 1.0. In the limit of the two media being identical, the transmission coefficient is 1.0 and the reflection coefficient is 0.0. In the limit of a reflection from a much stiffer or much softer medium, the reflection coefficient approaches 1.0.
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21
For La Llave, there is an obvious site resonance at f=2 Hz. The resonant frequency is f=/4H. If =300 m/s, then H=38 m, or about 120 feet. By total coincidence, about equal to the thickness now being used to characterize sites. Vs30 is the average velocity in the upper 30 meters. Newest ground motion prediction equations use Vs30 to characterize the site.
Multiple flat layers
22
23
Basins: major phenomena
Amplification Energy trapped Conversion to surface waves at basin edge Longer duration
24
Basin edge Kobe, Japan earthquake disaster.
25
Pause for a video
26
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.
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.
27
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 amplification also depends on the earthquake magnitude.
Site Classification of Taiwan Free-field Strong-Motion Stations by Chyi-Tyi Lee, Chin-Tung Cheng, Chi-Wen Liao and Yi-Ben Tsai
28
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)
NEHRP Classification Shear velocity of near-surface materials
NEHRP Category A B C D E F Description Hard rock Firm to hard rock Dense soil, soft rock Stiff soil Soft soil Special studies soils Shear velocity (m/s) >1500 760-1500 360...