Seismic waves and global seismology

1. Seismic waves and global seismology

2. Waves move energy (not matter!) in space-time Spherical wave W(r,t) = f(r-v*t) Plane wave W(x,t) = f(x-v*t)

3. Spherical wave propagating outward at velocity V (Sinusoidal source)note the amplitude decay of the waves as it moves away from the source

4. Transverse (shear) wave propagating in 2-dimensions Spherical shear wave propagating in radial-direction Shear wave propagating in x-direction Y (0,0) X

5. Waves: wavelength, velocity, and amplitude Note that both waves are propagating the disturbance in the medium (spring,rope) to the right at a velocity (wave-speed). Also, the force that excites the spring-wave is perpendicular to the force that excites the rope-wave. SPRING: Note the compressed and dilatated regions of the spring which is where elastic energy is present. The wavelength is define as the length of one cycle of the waves compressed and dilitated regions. ROPE: Note the wiggle in the rope has peaks and trough that define the wavelength. At a latter time the wave ‘wiggles’ (kinetic/potential energy) has move forward in the direction of the wave’s propagation.

6. 1-dimensional P and S wave propagation in a slinky

7. Wave parameters: velocity, frequency, period, wavelength, amplitude Waves may be graphed as a function of time or distance. A single frequency wave will appear as a sine wave in either case. From the distance graph the wavelength may be determined. From the time graph, the period and frequency can be obtained. From both together, the wave speed can be determined.

8. Longitudinal compressional P-wave The deformation (a temporary elastic disturbance) propagates.  Particle motion consists of alternating compression and dilation (extension).  Particle motion is parallel to the direction of propagation (longitudinal).  Material returns to its original shape after the wave passes.

9. The deformation (a temporary elastic disturbance) propagates.  Particle motion consists of alternating transverse motion.  Particle motion is perpendicular to the direction of propagation (transverse).  The transverse particle motion shown here is vertical but can be in any direction; however the Earth’s approximately horizontal layers tend to cause mostly SV (in the vertical plane) or horizontal (SH) shear motions.  Material returns to its original shape after the wave passes.

10. The deformation propagates.  Particle motion consists of alternating transverse motions.  Particle motion is horizontal and perpendicular to the direction of propagation (transverse).  To best view the horizontal particle motion, focus on the Y axis (red line) as the wave propagates through it.  Amplitude decreases with depth.  Material returns to its original shape after the wave passes.

11. The deformation (a temporary elastic disturbance) propagates.  Particle motion consists of elliptical motions (generally retrograde elliptical as shown in the figure) in the vertical plane and parallel to the direction of propagation.  Amplitude decreases with depth.  Material returns to its original shape after the wave passes.

12. Review: Exciting a wave, longitudinal and transverse waves Pushing at the spring’s end with a force over a distance (work) cause the A-B coils to add elastic (compressional) energy. This energy then propagates to the right. The end of the spring is pulled back with a force over a distance (work) to add elastic (dilitational) energy. Note relation between propagation direction and wave vibration direction. Longitudinal P-wave Transverse S-wave

13. Concept: a wave pulse versus a sinusoidal wave • Two ‘kinds’ of waves: • A harmonic sinusoidal wave • F(x,t) = A*sin( x– t) that oscillates up and down across all space and time (everywhere!). • A space-time localized wave pulse that is a superposition of many different frequency components moving in unison (phase).

14. Relation between wave raypaths and wavefronts An explosion makes a force that creates a wave pulse that propagates outwards in time. The increasing diameter circles are the wave-fronts at successively increasing times. Draw the rays? Rays are a very useful concept that shows the path that one parcel of the wavefront travels along. Each ray is always perpendicular to the wavefront. The ray has an arrow to indicate the direction of energy transport.

15. Measuring very small motions at the Earth’s surface in 3-dimensions The ground motion (displacement, velocity, acceleration) at the surface is measured by seismometers. Because space is three-dimensional, we will need to record the ground motion in three perpendicular directions (up-down, north-south, east-west). A seismometer works by hanging a mass that is from a frame attached firmly to the earth so that the frame moves with the ground motion. The trick to on inertial seismometer is that the inertia of the mass suspended by the spring causes the mass to ‘lag behind’ the motion of the frame. This cause the mass to be displaced with respect to the frame, and this displacement can be measured by the ‘ruler’ and amplified a million times.

16. A modern seismometer: an inertial magnet inside a coil As before, a mass (inertia) is hanging from a spring attached the frame (case) of the seismometer. As the inertial mass ‘lags’ behind the motion of the case, there is differential motion between the mass and the electrical coil that can be measured via electrical induction. The trick is that the mass is magnetized vertically (note poles). So as the magnet (mass) moves with respect to the coil, a current is induced in the coil circuit that can be measured at the two (+/-) wires. The voltage associated with the current will be proportional to the velocity of the ground motion!

17. Spherical symmetry of the Earth In a spherical geometry, the distance between two points on the earth’s surface is denoted by the angle subtended from the center of the earth. This is called the epicentral angle (∆). Therefore in (a), all the chords (A1 – B1, A2 - B2, etc ) have the SAMEepicentral angle. And, if the travel-times along each of these chords (seismic raypaths) is the same, then that means that the earth velocity structure only varies with radius (spherically symmetric) and does not vary with azimuth. (b) same as (a) except for larger epicentral angle.

18. Spherical symmetry: velocity only changes with radius! V(r) V(r) V(r) V(r) V(r) V(r) V(r) V(r) The properties (e.g., seismic velocity) along the radial lines that start at the center of the sphere are all are the same! This is spherical symmetry also called radial spherical symmetry.

19. Distance versus time travel-times for uniform and Velocity(r) earth Around 1920, enough travel-time measurements from earthquakes at different epicentral angles (distances) was accomplished. This is the observed time curve below. This showed that at greater distances (epicentral angles) the travel-times came in earlier than for a uniform velocity earth. Ah hah! This means that the earth’s velocity increases with depth and is NOT uniform!

20. Plotting millions of P and S-wave travel-times reveals seismic phases

21. Incident P-wave: P-Reflection, P-transmitted, S-reflection, S-transmitted When a P-wave hits a velocity boundary, it makes three P-waves: a refracted, a transmitted, and a reflected wave. But, it also forms a reflected and transmitted S-wave too! Snell’s law still works, except when the outgoing ray is a S-wave, the S-wave velocity must be used in the Law.

22. Refraction of a (P or S) ray due to velocity change: Snell’s Law reflected When a ray traverses a velocity contrast (change), the ray MUST refract. Why? Because otherwise the wave would ‘tear’ apart which the physics does not permit. Also, in most all cases a reflected wave is made. All waves - seismic, light, EM, water - waves refract! incident transmitted The refraction law: Snell’s Law. Note that all angles between the ray and interface are reckoned with respect to the surface normal. For a wave reflected from a flat interface, the angle of incidence EQUALS the angle or reflection.

23. Snell’s Law derivation An explosion makes a wavefield at (S). The waves travel outwards as represented by the wavefront at different times. Where the wave hits the velocity interface, the waves refracts (and reflects). What determine the angle of the refraction into the rock-2 layer ?

24. T0 λ1 T1 Ѳ1 Ѳ1 v1 Ѳ1 B A Ѳ2 v2 Ѳ2 Ѳ2 λ2 The ratios of the velocities and wavelengths and sin(angles) are all equal! Otherwise, the wavefield would ‘tear’ apart. T0 T1

25. Tracing rays using Snell’s Law in multiple layer medium Tracing a raypath through multiple layers is simple. It is just the process of using Snell’s Law at each successive interface. Note that the angle (i1) at the top and the bottom (i1’) of a layer is the same! If the lower layer’s velocity increases ( v2 > v1 ), the ray refracts AWAY from the interface normal. In the converse, the ray refracts TOWARDS the normal. If the deeper layer have a monotonic increase in velocity, the ray will continue to flatten out with depth. Eventually, the ray will reach its turning depth where it goes exactly horizontal and will start to go up!

26. Using Snell’s Law for a spherical geometry (not Cartesian) Note that the angle at the top and the bottom of a spherical shell are NOT the same! This is because the ‘layers’ are curved. But, if one is just calculating the angles on either side of an interface, then the two radius values (r1 and r2 ) are the same and the Cartesian form of Snell’s Law is operative (i.e., the radius scaling cancels out in the spherical Snell’s Law.

27. Radial Earth velocity models, Ray paths, and travel-time curves s1 s2 Representing the earth’s velocity structure as many shells of constant velocity. Tracing ray-paths through the constant velocity shells. Each ray has a different ‘take-off’ angle. Travel-time curve. The changes is the slope (slowness units s/m) of the curve are directly related to the changes in velocity with depth. The farther the distance a ray travels, the deeper the ray dives before turning around to come back to the surface.

28. The compressional (bulk) and shear (rigidity) modulus: P and S wave velocity

29. Average radial velocity structure of Earth The Vp and Vs velocity profile of the Earth. The crust, mantle lithosphere, upper mantle, transition zone, lower mantle, outer core, inner core are the primary divisions of the planet’s velocity profile. This was not know until the 1950’s at best. Why is the shear velocity of the outer core zero? What is velocity at core-mantle boundary.

30. Radius and volume of earth main chemical/phase subdivisions: inner and outer core, mantle, crust

31. Phase names: P, PP, PS, PPP, PKP(P’), PcP, PcS and Shadow zones The different raypaths with both P and S-wave ‘legs’ have been named. A ‘P’ denotes a P-wave leg and an ‘S’ denotes a S-wave leg. PcP denotes a reflection off the core-mantle boundary. PP and PPP are free-surface multiple reflections. ‘K’ is used for a core traversing wave such as PKP. Because there is a very large velocity decrease across the core-mantle boundary, Snell’s Law predict the waves will refract ‘towards the normal’. This refraction creates a ‘shadow zone’ for both the P- and S-waves at epicentral distances >97°.

32. More seismic phases and raypaths

33. Travel times of P-waves for ∆ = 0-180⁰ Note that the rays that take off at the source from dive progressively deeper into the mantle before reaching their turning depths after which the ray comes back up. For the core-traversing P-wave, there are 2-3 P-wave arrivals between (L) and (I) due to the strong refraction effects of the low velocity outer core and the high velocity inner core.

35. North-ridge, California earthquake recording by global seismic network stations

36. The 4 effects that make a seismomgram: eq source, propagation, site, instrument.

38. Earthquake in Nevada (Feb. 2008) recorded by vertical component of many seismometers. Can you identify the P-wave, the Love and Rayleigh waves and measure their velocities ?

39. Low velocity zone: a region just under the lithosphere often thought to be the weak asthenosphere where plate shear accululates Lithosphere A combination of increasing temperature and pressure affect the rock modulus to make a LVZ. The LVZ generally extends to deeper than about 200 km depth.

40. Shear velocity North America from surface wave measurement inversion

41. Tomography: make whole earth 3-d images of velocity structure from millions of P and S-wave travel-time measurements! Note high velocity (blue) slab image under north Turkey going into lower mantle

42. Blue is seismically fast and red is seismiclly slow material. Note the slab image in lower mantle under SE coast of North America in both the P and S-wave images.

43. Mean vertical average crustal shear velocity Shear velocity (m/s) Note oceans at 3.3 km/s and oceans at 3.4-3.9 km sec. Passive margin/delta sediments at 3.0 km/s

44. Mean Moho depth from surface wave measurement ‘inversions’ Note 8-12 km beneath oceans and 28-80 km beneath continents. What causes this crustal thickness difference between oceans and continents?

45. Crustal thickness from surface wave seismic measurement inversionnote oceans at 10 km and continents at >35 km