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Seismology: Wave Propagation

Seismology: Wave Propagation. Art McGarr Based on lectures by James Mori and Dave Boore . Contents. ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes

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Seismology: Wave Propagation

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  1. Seismology: Wave Propagation Art McGarr Based on lectures by James Mori and Dave Boore

  2. Contents ・ Rays Snell’s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes Free oscillations of the Earth

  3. Wave Propagation • As seismic waves travel through Earth, they interact with the internal structure of the planet and: • Refract – bend / change direction • Reflect – bounce off of a boundary (echo) • Disperse – spread out in time (seismogram gets longer) • Attenuate – decay of wave amplitude • Diffract – non-geometric “leaking” of wave energy • Scatter – multiple bouncing around

  4. What is a Wave ? • A wave is a disturbance that transfers energy. • Waves are common in nature: • Light is a wave • Sound is a wave • Waves are periodic in both space and time (they have wavelengths and periods)

  5. Sound Wave Analogy • Seismic waves represent acoustic (sound) energy and so are analogous to speech: Speech Earthquakes • Vocal cords vibrate • (2) Sound waves propagate • thru atmosphere • (3) Ears record these • vibrations • (4) Brain processes the • recordings • A locked fault segment fails (ruptures) • (2) Sound waves propagate thru the Earth • (3) Seismometers record these vibrations • (4) Seismologists process these recordings (seismograms)

  6. Homogeneous Earth If the Earth had constant velocity the wave paths would be very simple.

  7. Structure in the Earth results in complicated paths Lowrie, 1997, fig 3.69 Bolt, 2004, fig 6.3

  8. q1 Air Water q2 sin q1 / sin q2 = n21 Snell’s Law Fermat’s Principle Rays

  9. a1 q1 q2 a２ a1 > a2 Ray Paths in a Layered Medium a = velocity of seismic energy in the layer Faster a1 q1 Slower Slower q2 Faster a２ a1 < a2

  10. Time 1/a3 1/a2 1/a1 Distance Ray Paths in a Layered Medium a1 a2 a3

  11. The Moho Andrija Mohorovicic (1857-1936) Found seismic discontinuity at 30 km depth in the Kupa Valley (Croatia). Mohorovicic discontinuity or ‘Moho’ Boundary between crust and mantle The Moho The Moho Copywrite Tasa Graphic Arts

  12. Forward Branch شاخه در حال پيشروی Receding Branch شاخه در حال عقب نشينی

  13. Forward Branch شاخه در حال پيشروی Shadow Zone زون سايه Forward Branch (PKPbc) شاخه در حال پيشروی Receding Branch (PKPab) شاخه در حال عقب نشينی

  14. PcP Shadow Zone ・ 1912 Gutenberg observed shadow zone 105o to 143o ・ 1939 Jeffreys fixed depth of core at 2898 km (using PcP) Backward Branch Forward Branch PKP Forward Branch PcP Shadow Zone P Forward Branch Forward Branch Backward Branch

  15. PcP Core Reflections انعکاسات هسته

  16. IASP91, Kennett and Engdahl, 1991

  17. Seismic Waves ・ Different types of waves (Body, Surface) ・ Wave Equation ・ Static Displacements ・ Frequency content

  18. Seismic Wave Types Seismic waves can be labeled by the paths they take in the Earth. • Body Waves: • P waves • S waves • Surface Waves: • (1) Love Waves • (2) Rayleigh Waves

  19. Body Waves

  20. Surface Waves امواج سطحی

  21. January 26, 2001 Gujarat, India Earthquake (Mw7.7) زلزله گجرات هند، 26 جنوری سال 2001 شدت 7.7 عمودی vertical Rayleigh Waves امواج ری لی P PP S SS radial دايروی transverse متقاطع Love Waves امواج لف Recorded in Japan at a distance of 57o (6300 km) در فاصله 57 درجه (6300 کيلومتر) در جاپان ثبت گرديده است.

  22. 1-D Wave Equation معادله موج يک بعدی Solution: c = propagation speed c = سرعت پخش This is the equation that explains the waves on a spring: constant velocity wave propagation, no mass transfer, different from circulation eq.

  23. Wave Period and Wavelengthپيريود يا دوران موج و طول موج Velocity = Wavelength / Period سرعت =طول موج تقيسم بر پيريود يا دوره Space فضاء x Velocity 6 km/s سرعت 6 کيلومتر فی ثانيه Wavelength طول موج period 50 s Wavelength 300 km Time زمان t period 50 s frequency = 1/period= 0.02 hz Period پيريود يا دوره

  24. پيريود Period طول موج Wavelength

  25. Multiple-Frequency Signals • Most signals are composites of waves with many different frequency components. • The range of frequency is sometimes called the “band” and we speak of bandwidth.

  26. 3-D Wave Equation with Source معادله سه بعدی با منبع آن Source منبع spatial 2nd derivative مشتق دوم فضايي Near-field Terms (Static Displacements) مراحل نزديک به ساحه (بيجايي ستاتيک) Solution حل Far-field Terms (P, S Waves) مراحل ساحه دور امواج پی و اس

  27. r/a r/b r/a r/b Near-field terms مراحل نزديک به ساحه • ・ Static displacements • بيجايی ستاتيک • ・ Only significant close to the fault • فقط زمانيکه به منبع نزديک باشد مهم است • ・ Source of tsunamis • منبع سونامی ها t　→

  28. Static Displacements بيجايی ستاتيک (ساکن) Bei-Fung Bridge near Fung-Yan city, 1999 Chi-Chi, Taiwan earthquake پل بی فنگ نزديک شهرفنگ يان، زلزله منطقه چی چی تايوان سال 1999

  29. Static displacements بيجايی ستاتيک يا ساکن Co-seismic deformation of 2003 Tokachi-oki Earthquake (M8.0) تغيير شکل حاصله از زلزله تکاچی اوکی سال 2003 مقياس 8.0

  30. Generation of Tsunami from Near-field Term توليد سونامی از مرحله نزديک به ساحه زلزله! ترينچ ساحه ذخيره سترين يا فشار سونامی EA برگشت الاستيکی PAC

  31. Far-field Terms مرحله دور از ساحه • ・ Propagating Waves • پخش امواج • ・ No net displacement • in an elastic medium • هيچ نوع بيجايی در جسم • الاستيکی صورت نمی گيرد • ・ P waves • امواج P • ・ S waves • S امواج

  32. Normal Modes Liberty Bell (USA) Useful for studies of ・ Interior of the Earth ・ Largest earthquakes l=1 m=3 l=1 m=1 l=1 m=2 Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html

  33. Toroidal and Spheroidal Modes حالات تورويدل و کروی Toroidal تورويدل Spheroidal کروی Dahlen and Tromp Fig. 8.5, 8.17

  34. Natural Vibrations of the Earth اهتزازات طبيعی زمين Indexes describe spherical harmonics اندکس های حالات مختلف کروی را تشريح می کند بعضی از دوره های حالت نورمال مشاهده شده حالتهای کروی حالتهای تورويدل Shearer Ch.8.6 Lay and Wallace, Ch. 4.6

  35. Summary خلاصه Rays شعاعها Velocity structure includes gradients, discontinuities and LVZ’s, causing complicated ray paths through the Earth (P, PKP, PcP) ساختمان سرعت گريدينتها، انقطاعها و زونهای سرعت پايين را در بر دارد که مسير شعاعها را در زمين مغلق ميسازد. Wave theory explains تيوری امواج چيز های ذيلرا تشريح می نمايد: ・ P and S waves امواج پی و اس ・ Static displacements بيجايی ستاتيک ・ Surface waves امواج سطحی Normal Modes حالاتهای نورمال The Earth rings like a bell at long periods زمين مانند زنگ برای مدتهای طويل به صدا می آيد

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