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# Elastic Waves

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### Elastic Waves

1. 1. Introduction to Seismology-KFUPM Introduction to Seismology Chapter 3 Body Elastic Waves http://faculty.kfupm.edu.sa/ES/oncel/geop204chap3.htm Chapter 4, Bullen and Bolt Ali Oncel oncel@kfupm.edu.sa Department of Earth Sciences KFUPM Introduction to Seismology-KFUPM http://faculty.kfupm.edu.sa/ES/oncel/geop204presenta.htm http://faculty.kfupm.edu.sa/ES/oncel/oncellinks.htm Some Links http://faculty.kfupm.edu.sa/ES/oncel/geop204link.htm Introduction to Seismology-KFUPM Recall: Wave crests (high points) equilibrium (middle) troughs (low points) wave speed = wavelength/period = wavelength x frequency. We often express this as v=fλ 1
2. 2. Introduction to Seismology-KFUPM Wave Equation α and β are termed for the P-wave and S-wave velocities. Often, the symbols Vp and Vs are used instead of α and β. Θ is the scalar displacement potential. Where µ,λ are the Lamé coefficients where λ is bulk modulus (incompressibility), µ shear modulus (rigidity) and r density. Introduction to Seismology-KFUPM Seismic velocities P wave velocity α and S wave velocity β depend on physical properties of medium through which they travel: k + ( 4/3)µ λ + 2µ V = α = = ρ p ρ µ Question: How α and β depend Vs = β = ρ on density ρ? Where µ,λ are the Lamé coefficients and λ is λ = k - 2µ = νE 3 ( 1 + ν ) ( 1 - 2ν ) Introduction to Seismology-KFUPM Elastic Coefficients and Seismic Velocities Rock Type Density Young's Modulus Poisson's Ratio Vp Vs Vp/Vs Vs as %Vp r E m (m/s) (m/s) Shale (AZ) 2.00 0.120 0.040 2454 1698 1.44 69.22% Siltstone (CO) 2.00 0.120 0.040 2454 1698 1.44 69.22% Limestone (PA) 2.00 1.100 0.156 7640 4877 1.57 63.84% Limestone (AZ) 2.00 1.100 0.180 7728 4828 1.60 62.47% Quartzite (MT) 3.00 0.636 0.115 4675 3083 1.52 65.96% Sandstone (WY) 3.00 0.140 0.060 2169 1484 1.46 68.42% Slate (MA) 3.00 0.487 0.115 4091 2698 1.52 65.96% Schist (MA) 3.00 0.544 0.181 4440 2771 1.60 62.41% Schist (CO) 2.70 0.680 0.200 5290 3239 1.63 61.24% Gneiss (MA) 2.64 0.255 0.146 3189 2053 1.55 64.38% Marble (MD) 2.87 0.717 0.270 5587 3136 1.78 56.13% Marble (VT) 2.71 0.343 0.141 3643 2355 1.55 64.65% Granite (MA) 2.66 0.416 0.055 3967 2722 1.46 68.62% Granite (MA) 2.65 0.354 0.096 3693 2469 1.50 66.85% Gabbro (PA) 3.05 0.727 0.162 5043 3203 1.57 63.51% Diabase (ME) 2.96 1.020 0.271 6569 3682 1.78 56.05% Basalt (OR) 2.74 0.630 0.220 5124 3070 1.67 59.91% Andesite (ID) 2.57 0.540 0.180 4776 2984 1.60 62.47% Tuff (OR) 1.45 0.014 0.110 996 659 1.51 66.20% 2
3. 3. Introduction to Seismology-KFUPM Velocity and Density “Birch’s law” Crust and mantle rock observations A linear relationship between density and seismic velocity where a and b are constants (Birch, 1961). V = a ρ + b Three pressures 6km 18km 30km Introduction to Seismology-KFUPM Nafe-Drake Curve An important empirical relation, used in joint interpretation of wide angle reflection and refraction data and gravity data, exists between P wave velocity and density. Cross-plotting velocity and density values of crustal rocks gives the Nafe-Drake curve after its discoverers. Only a few rocks such as salt (unusually low density) and sulphide ores (unusually high densities) lie off the curve. Introduction to Seismology-KFUPM Nafe-Drake Curve Sediments and sedimentary rock Igneous and metamorphic rock Figure 3.10 of Lillie, 1999, modified from Birch, 1960 Reference L=limestone; Q=quartz; Sh=shale; Ss=sandstone. 3
4. 4. Introduction to Seismology-KFUPM Factors affecting P-wave velocity Increases with mafic mineral content (Nafe-Drake curve) pressure (modulus change > density change) Decreases with temperature (modulus change > density change) Introduction to Seismology-KFUPM Factors affecting S-wave velocity Increases with mafic mineral content (Nafe-Drake curve) with pressure (modulus change > density change) Decreases due to presence of fluid, e.g. porous sand or partial melt No S waves in fluids, e.g. water of molten rock. Velocity zero Introduction to Seismology-KFUPM Velocity-Geology Grifts and King, 1981 4
5. 5. Introduction to Seismology-KFUPM Amplitude Changes of Particle Motion Reference Maximum amplitude of particle motion occurs along the 90 degree phase wave front. Other wave fronts correspond to positions where the wave goes from positive to negative amplitude (180 degree) and at the minimum amplitude (270). Introduction to Seismology-KFUPM Wave Fronts and Raypaths Initial wavefronts for compressional (P),shear (S), and Rayleigh ( R ) waves. Changes in velocity cause segments of wave fronts to speed up or slow down, distorting the wave fronts from perfect spheres. Reference Ray paths thus bend (refract) as velocity changes. Seismic energy travels along trajectories perpendicular to wave fronts. Introduction to Seismology-KFUPM Seismic Trace Reference Seismic waves radiating from a source to one receiver. Seismic trace recording ground motion by the receiver, as a function of the travel time from the source to the receiver. For controlled source studies (seismic refraction and reflection), the travel time is commonly plotted positive downward. 5
6. 6. Introduction to Seismology-KFUPM Introduction to Seismology Chapter 3 Body Elastic Waves http://faculty.kfupm.edu.sa/ES/oncel/geop204chap3.htm Chapter 4, Bullen and Bolt Ali Oncel oncel@kfupm.edu.sa Department of Earth Sciences KFUPM Introduction to Seismology-KFUPM Previous Lecture Wave equation Elastic Coefficients and Seismic Waves Birch's Law Nafe-Drake Curve Factors affecting P-wave and S-wave velocity Seismic velocities for Geological Materials Amplitude Changes of Particle Motions Animation: Particle Motion in Seismic Waves Wavefronts and RayPaths Seismic Trace Introduction to Seismology-KFUPM Recall: Wavefronts and raypaths nt fro ular v e erpendic t3 P a le ang W t2 Ray p ath t1 t0 Com pressional Source (P) m otion Shear (S) m otion From: http://web.ics.purdue.edu/~braile/edumod/slinky/slinky.htm 6
7. 7. Introduction to Seismology-KFUPM http://www.geol.binghamton.edu/faculty/jones/SeismicWavesSetup.exe Seismic Waves A program for the visualization of wave propagation contributor: Alan Jones Year: 2006 Introduction to Seismology-KFUPM From: http://www.citiesoflight.net/AlaskaQuake.html Introduction to Seismology-KFUPM Solution for Homework 2 Write up phases of from 1 to 6? 1 2 3 6 5 4 7
8. 8. Introduction to Seismology-KFUPM Body Wave Propagation P- and S- Waves (propagation along raypath) Earth’s surface Seismograph X Y Source * SH SV P-wave particle motion -- parallel to direction of S-wave particle propagation motion -- perpendicular to direction of propagation (usually approximately in SV and SH Z (down) directions) Modified from http://web.ics.purdue.edu/~braile/edumod/slinky/slinky.htm Introduction to Seismology-KFUPM Introduction to Seismology-KFUPM Identify the waves of Body and Surface? 8
9. 9. Introduction to Seismology-KFUPM Introduction to Seismology-KFUPM Introduction to Seismology-KFUPM coast of Chile earthquake recorded at NNA Three-component seismograms for the M6.5 west 9
10. 10. Introduction to Seismology-KFUPM Recall: Seismic Wave Types “body waves” travel in Earth’s interior P-waves (“P” for primary) Expansion/compression: push/pull motion S-waves (“S” for secondary) Shear: side-to-side motion “surface waves” travel on Earth’s surface Surface Waves - Body Waves Introduction to Seismology-KFUPM Reference Introduction to Seismology-KFUPM Seismic Body Waves Wave Type Particle Motion Other Characteristics (and names) P, Alternating compressions P motion travels fastest in Compressional (“pushes”) and dilations materials, so the P-wave is the Primary, (“pulls”) which are directed in first-arriving energy on a Longitudinal the same direction as the seismogram. Generally smaller and wave is propagating (along the higher frequency than the S and raypath); and therefore, Surface-waves. P waves in a liquid perpendicular to the or gas are pressure waves, wavefront. including sound waves. S, Alternating transverse S-waves do not travel through Shear, motions (perpendicular to the fluids, so do not exist in Earth’s Secondary, direction of propagation, and outer core (inferred to be Transverse the raypath); commonly primarily liquid iron) or in air or approximately polarized such water or molten rock magma). S that particle motion is in waves travel slower than P waves in vertical or horizontal planes. a solid and, therefore, arrive after the P wave. From: www.eas.purdue.edu/~braile/edumod/waves/WaveDemo.htm 10
11. 11. Seismic Surface Waves Introduction to Seismology-KFUPM Wave Particle Motion Other Characteristics Type (and names) L, Transverse horizontal Love waves exist because of the Earth’s motion, perpendicular surface. They are largest at the surface Love, to the direction of and decrease in amplitude with Surface propagation and depth. Love waves are dispersive, that is, waves, Long generally parallel to the the wave velocity is dependent on waves Earth’s surface. frequency, generally with low frequencies propagating at higher velocity. Depth of penetration of the Love waves is also dependent on frequency, with lower frequencies penetrating to greater depth. R, Motion is both in the Rayleigh waves are also dispersive and the Rayleigh, direction of propagation amplitudes generally decrease with depth in Surface and perpendicular (in a the Earth. Appearance and particle motion waves, Long vertical plane), are similar to water waves. Depth of waves, and “phased” so that penetration of the Rayleigh waves is also Ground roll the motion is generally dependent on frequency, with lower elliptical – either frequencies penetrating to greater depth. prograde or Generally, Rayleigh waves travel slightly retrograde. slower than Love waves. From: www.eas.purdue.edu/~braile/edumod/waves/WaveDemo.htm Downloading the AmaSeis software Introduction to Seismology-KFUPM The Using AmaSeis Tutorial: http://web.ics.purdue.edu/~braile/edumod/as1lessons/UsingAmaSeis/UsingAmaSeis.htm http://www.geol.binghamton.edu/faculty/jones/AmaSeis.html Homework due to March, 19: Plot Seismic Trace for one of available recent earthquakes given by program and try to explain your observations for Seismic Waves such as Picking Body Waves, time for S-P and values of maximum amplitude? 11
12. 12. Introduction to Seismology-KFUPM Seismic Waves of Argentina EQ Introduction to Seismology-KFUPM Next Class: Class Presentation Introduction to Seismology-KFUPM Introduction to Seismology Chapter 3 Body Elastic Waves http://faculty.kfupm.edu.sa/ES/oncel/geop204chap3.htm Chapter 4, Bullen and Bolt Ali Oncel oncel@kfupm.edu.sa Department of Earth Sciences KFUPM 12
13. 13. Introduction to Seismology-KFUPM Previous Lecture Seismic Wave Types Revisit: Wavefronts and raypaths Seismic Waves A program for the visualization of wave propagation contributor: Alan Jones Body Wave Propagation Example: M6.5, 1998 West Coast of Chile Earthquake Example: Ms7.8, 1999 Izmit Earthquake, Turkey Revisit: Seismic Wave Types Downloading the AmaSeis Software Homework: Seismic Trace Exercise by AmaSeis, Due to March, 19 Introduction to Seismology-KFUPM Term Paper: Refraction Seismology Due to March 21 For more detail, visit to Project Page of Geop204 http://faculty.kfupm.edu.sa/ES/oncel/geop204termproject.htm Introduction to Seismology-KFUPM Travel-Time Graph Initial wave fronts for P, S and R waves, propagating across several receivers at increasing distance from the source. •Travel time graph. The seismic traces are plotted according to the distance (X) from the source to each receiver. The elapsed time after the source is fired is the travel time (T). T=X/V X distance from source to the receiver, T total time from the source to the Reference receiver V seismic velocity of the P, S, or R arrival. 13
14. 14. Introduction to Seismology-KFUPM Estimates of Seismic Velocity A) The slope of line for each arrival is the first derivative (dT/dX). Reference B) The slope of the travel time for each of the P,S, and R arrivals (see earlier figure) is the inverse of velocity. Model Calculation Introduction to Seismology-KFUPM Simple, Horizontal Two Layers © John F. Hermance September 05, 2002 Introduction to Seismology-KFUPM Ray paths © John F. Hermance September 05, 2002 14
15. 15. Introduction to Seismology-KFUPM © John F. Hermance September 05, 2002 Ray paths for direct, reflected, and critically refracted waves, arriving at receiver a distance (X) from the source. The interface separating velocity (V1) from velocity (V2) material is a distance (h) below the surface. Introduction to Seismology-KFUPM From: www.aug.geophys.ethz.ch/teach/seismik1/03_geometry.pdf Introduction to Seismology-KFUPM Huygen’s Principle pp. 20 of Burger’s book. See pp.75 and 152 of Bullen&Bolt 15
16. 16. Introduction to Seismology-KFUPM Fermat’s Principle pp. 20 of Burger’s book. Fermat's principle leads to Snell's law; Introduction to Seismology-KFUPM Snell’s Law © John F. Hermance September 05, 2002 For a wave traveling from material of velocity V1 into velocity V2 material, ray paths are refracted according to Snell’s law. Introduction to Seismology-KFUPM Reflection/Refraction The angle of incidence equals the angle of reflection θ i =θ r , where both angles are measured from the normal: θi θr Note also, that all rays lie in the “plane of incidence”. How is the angle of refraction related to the angle of incidence? Unlike reflection, θ 1 cannot equal θ 2 θ1 !! n1 • Why?? Remember v = fλ n2 v1 ≠ v2 θ2 Therefore, θ 2 must be different from θ 1 !! 16
17. 17. Introduction to Seismology-KFUPM Reflected/Refracted Waves A) A compressional wave, incident upon an interface at an oblique angle, is split into four phases: P and S waves reflected back into the original medium; P and S waves refracted into other medium. See pp.140-152 of Bullen&Bolt Introduction to Seismology-KFUPM Seismic Refraction •Wave fronts are distorted from perfect spheres as energy transmitted into material of different velocity. Ray paths thus bend (“refract”) across an θ1 interface where velocity θ2 changes. The angles for incident and refracted are measured from a line drawn perpendicular to the interface between the two layers. Introduction to Seismology-KFUPM Behavior of Refracted Ray on Velocity Changes 17
18. 18. Behavior of Seismic Waves Introduction to Seismology-KFUPM Penetrating the Earth At the mantle-outer core (fluid) boundary the decrease in velocity causes those rays refracted into the core to bend towards the normal In the mantle and inner core, the velocities increase with depth, so the ray bend away from the normal Introduction to Seismology-KFUPM Recall Modules of Bulk (k) and Shear (µ) Bulk Modulus where Θ = dilatation = ∆V/V and P = pressure k= (∆P/Θ) Ratio of increase in pressure to associated volume change shear stress = (∆F /A) shear strain = (∆l /L) shear modulus shear stress µ = shear strain Force per unit area to change the shape of the material Introduction to Seismology-KFUPM Recall Poisson’s Ratio/Young Module Poisson’s Ratio ∆L εxx = σ= ( εyy / εxx ) L ∆W Young Module εyy = W (∆F /A) Ε = (∆L/L) Ratio Vp and Vs depends on Poisson ratio: where Poisson’s ratio varies from 0 to ½. The elastic constants E, σ, µ are Poisson’s ratio has the value ½ for mostly used in works of engineering fluids seismology because they are easily measured by simple experiments. See pp.32 of Bullen&Bolt 18
19. 19. Introduction to Seismology-KFUPM Recall Seismic Velocities (P-wave) See pp.318 and 471 of Bullen&Bolt Introduction to Seismology-KFUPM Rock Velocities (m/sec) pp. 18-19 of Berger See pp.319 of Bullen&Bolt Introduction to Seismology-KFUPM Recall Influences on Rock Velocities • In situ versus lab measurements • Frequency differences • Confining pressure • Microcracks • Porosity • Lithology • Fluids – dry, wet • Degree of compaction •…………… 19
20. 20. Introduction to Seismology-KFUPM Introduction to Seismology Refraction and Reflection Ali Oncel oncel@kfupm.edu.sa Department of Earth Sciences KFUPM Introduction to Seismology-KFUPM Previous Lecture Travel-time Graph Estimates of Seismic Velocity Huygens's Principle Fermat's Principle Calculation of Travel Times Snell's law-Critically Refracted Arrival Reflection/Refraction Reflected/Refracted waves Seismic Refraction Behavior of refracted ray on velocity changes Behavior of seismic waves refracted ray penetrating the Earth Representative P-wave Velocities for various Rocks Influences on Rock Velocities Introduction to Seismology-KFUPM Refracted Ray and Angle The angle of refraction increases as the angle of incidence increases. 20
21. 21. Introduction to Seismology-KFUPM Energy Return and Critical Angle θc θc θc θc θc θc Lillie, Whole Earth Geophysics, Fig 3.25 A critically refracted wave, traveling at the top of the lower layer with velocity V2, leaks energy back into the upper layer at the critical angle (θ2) Introduction to Seismology-KFUPM Modified Table Table 2.3 after Berger, pp.29. Angle of For Incident P wave For Incident S wave Incidence Reflected Refracted Reflected Refracted P-wave S-wave P-wave S-wave S-wave P-wave S-wave P-wave 10 10.0 6.0 27.6 16.1 10.0 16.8 27.6 50.5 11 11.0 6.6 30.6 17.8 11.0 18.5 30.6 58.0 12 12.0 7.2 33.7 19.4 12.0 20.3 33.7 67.5 13 13.0 7.8 36.9 21.1 13.0 22.0 36.9 88.8 14 14.0 8.3 40.2 22.8 14.0 23.8 40.2 #NUM! 15 15.0 8.9 43.6 24.5 15.0 25.6 43.6 #NUM! 16 16.0 9.5 47.3 26.2 16.0 27.3 47.3 #NUM! 17 17.0 10.1 51.2 27.9 17.0 29.2 51.2 #NUM! 18 18.0 10.7 55.5 29.6 18.0 31.0 55.5 #NUM! 19 19.0 11.3 60.2 31.4 19.0 32.9 60.2 #NUM! 20 20.0 11.8 65.8 33.2 20.0 34.8 65.8 #NUM! 21 21.0 12.4 72.9 35.0 21.0 36.7 72.9 #NUM! 22 22.0 13.0 87.4 36.8 22.0 38.6 87.4 #NUM! 23 23.0 13.6 #NUM! 38.7 23.0 40.6 #NUM! #NUM! 24 24.0 14.1 #NUM! 40.6 24.0 42.7 #NUM! #NUM! 25 25.0 14.7 #NUM! 42.5 25.0 44.8 #NUM! #NUM! 26 26.0 15.2 #NUM! 44.5 26.0 46.9 #NUM! #NUM! 27 27.0 15.8 #NUM! 46.6 27.0 49.2 #NUM! #NUM! 28 28.0 16.4 #NUM! 48.7 28.0 51.5 #NUM! #NUM! 29 V1-P (m/s) 29.0 1500 16.9 #NUM! 50.9 29.0 53.9 #NUM! #NUM! V1-S (m/s) 900 30 V2-P (m/s) 30.0 4000 17.5 #NUM! 53.1 30.0 56.4 #NUM! #NUM! V2-S (m/s) 2400 Introduction to Seismology-KFUPM Total Time of Refraction ⎛ 1 ⎞ 2 h1 ⎜ ⎟ t refraction = ⎜ ⎟ X + V 22 − V12 ⎝ V2 ⎠ V1V2 Ttotal= T1+T2+T3 21
22. 22. Introduction to Seismology-KFUPM Travel time for Direct/Refracte d Waves Xc=critical distance Xcr=crossover distance V1 +V 2 T1= Intercept time xcr = 2h1 V2 −V 1 Introduction to Seismology-KFUPM Seismic =Z1 Reflection =Z2 Lillie, Whole Earth Geophysics, Fig 3.28 Reflection occurs when Z1 differs from Z2, where Z Acoustic impedance which is product of density and velocity V-shaped ray paths for a compressional wave from a source to 6 receivers, reflected from a horizontal interface. Introduction to Seismology-KFUPM Reflection equation for a reflection hyperbolae: (X 2 + 4h 2 )1 / 2 tr = V 1 22
23. 23. Introduction to Seismology-KFUPM ? ed ? ct fle ave Re ad W Time do r He acte Refr ti ? Crossover distance ? ct re Di Distance Introduction to Seismology-KFUPM Introduction to Seismology-KFUPM IRIS Deployment in Venezuela, 2001 "line" of fifteen Reftek 125 "Texan" recorders The source of energy: Betsy M3 Seisgun From: http://www.passcal.nmt.edu/%7ebob/passcal/venezuela 23
24. 24. Introduction to Seismology-KFUPM That is what named as “Model 130-01” which was ordered for ESD in 2006. From: http://www.reftek.com/productshome.html#Seismic%20Recorders Introduction to Seismology-KFUPM 21 “Texans” from Refraction Technology, Inc. From: http://www.seismo.unr.edu/geothermal/ Introduction to Seismology-KFUPM 200 “Texans” From: http://www.seismo.unr.edu/geothermal/ 24
25. 25. Introduction to Seismology-KFUPM The N. Walker Lane Experiment, 2002 From: http://www.seismo.unr.edu/geothermal/ Introduction to Seismology-KFUPM How Thick is the Crust? ? Horizontal Rays Refraction ? “Tunneling” 7.2 km/s Moho Journal Publication: Louie, J. N., W. Thelen, S. B. Smith, J. B. Scott, M. Clark, and S. Pullammanappallil, 2004, The northern Walker Lane refraction experiment: Pn arrivals and the northern Sierra Nevada root: Tectonophysics, 388, 253-269. Introduction to Seismology-KFUPM The length of profile, which is 180 meter in this case, provided a depth of resolution to 60 meter but note that velocity in shallow is not detailed due to increased spacing of receivers (=15 meter)? KFUPM BEACH-2005 Elevation (m) 180 meter 25
26. 26. Introduction to Seismology-KFUPM In this case, the receiver distance is about 0.4 meter but provided detail information in depth of very shallow even we could not have info about the detail. KFUPM-2006 Elevation, m 10 meter Introduction to Seismology-KFUPM Class Feedback What is the most important thing you learned this week? What is one thing you still do not understand? Respond to me anonymously over a piece of small paper within 1 or 2 minutes. 26