General Seismology or Basic Concepts of Seismology. Göran Ekström

Transcription

1 General Seismology or Basic Concepts of Seismology Göran Ekström

2 Basics Concepts of Seismology Travel Time

3 Ground displacement at Petropavlovsk following the M8.4 Sea of Okhotsk earthquake

4 Ground displacement at Petropavlovsk following the M8.4 Sea of Okhotsk earthquake

5 PET 2891 km

6 sscs ScSScS sscsscs ScSScSScS sscsscsscs ScS

7 2891 km

8 930 sec sscs ScSScS sscsscs ScSScSScS sscsscsscs ScS

9 Travel time and distance gives us speed: v=x/t Average speed of the seismic wave through the mantle and crust: 2x2891 / 930 = 6.21 km/sec

10 Basics Concepts of Seismology Elasticity and P and S waves

11 Deformation of a solid (a) c a q Seismology deals with small strains: Hooke s law applies L crl Strain (e) modified from Lowrie, 2007

12 Young s modulus: Elastic moduli E = 1 1 with 2 = 3 = 0. Poisson s Ratio: = 2 1 = 3 1 For much of the mantle, 0.25 (a Poisson solid ). Incompressibility (Bulk modulus): K = V P V If 1 = 2 = 3 = P, K = with 1 = 2 = 3 = 1 3 V/V.

13 Rigidity (Shear modulus): µ = S S = S = 1 = 2, 3 = 0; S = 2 1 = 2 2, 3 = 0 [ r - - l l"' Modulus of simple longitudinal strain (Axial modulus): = 1 1 where 2 = 3 = 0. = K µ

14 Equation of motion: F = ma Application to elastic deformation in shear: 2 2 = µ v = r the wave equation - propagating wave speed Fig. 3. I 2 (a) Shear distortion caused by the passage of a onedimensional S-wave. (b) Displacements and lorces in the z-direction at the positions x and -x*dx bounding a small sheared element.

15 In an isotropic solid only two elastic moduli are independent, and there are two types of waves, P and S = v S = µ = v P = + 4µ 3 modified from Stein and Wysession, 2009

16 Basics Concepts of Seismology Seismic rays ; refraction, reflection, conversion

17 Huygen s principle, wavefronts, rays wavefront ray ) ^ r r ' B {v' { 7 Fig Application of Huygens'principle to explain the advance of a plane wavefront. The wavefront at CD is the envelope of wavelets set up by particle vibrations when the wavefront was at the previous position AB. Similarly, the envelope of wavelets set up by vibrating particles in the wavefront CD forms the wavefront EF.

18 ray

19 Refraction and Snell s law Thus and sini, = BC / AB - 7t.,Lt / AB s i n i, = A D /, a n = 7 ) 2 A t / A B so that s i n l, _ a, sin i, u2 Tl'ris is Snell's law of refraction. Medium 1 ( velocity o1) Medium 2 (velocity rr2) f 9 + A l Figure Iluygens' s constructiou for refraction of a wave at a plane boundary. Positions of a wavcfront at times f,, and (1,, + z1l) are shown bv broken and solid lines arrd arrows on thc rays show the direction of propagation. Each point on the wavefront at f,, acts as a source of wavelets ( sl' rown as short arcs), the envelope of r,r'hich is thc wavefront at (t + /t). slower faster

20 Geometry of refraction, reflection, and conversion at an interface (abrupt change) lncident SV Medium 1 ' M e d i u m 2 slower faster Refracted I I I I Refracted 5V

21 Rays paths in a layered flat earth +zr tan e I I I i0- l z slower faster Figure 5.9. Geometry of seismic rays in a plane layered Earth model, having P wave speed, a, progressively increasir-rg with depth. Waves that travel for much of their paths in deeper and faster layers, as illustrated, arc known as head waves.

22 Ray refraction, smooth variationsno interfaces, no reflections, no conversions slower faster

23 Basics Concepts of Seismology Travel-time curve

24 Travel time curve for horizontal rays Time slope=1/speed Distance

25 T ATq ats ATz Travel times in a layered, flat Earth Figure Travel-time curve for first arriving pulscs from ;r layerecl structttre, as in Fig. 5.tt. Numbcrs on segments indicate the deepest layer penetrated by each "farnily" of rays. Ray parameter (flat Earth) +zr tan e I I I i0- l z slower (constant along the ray): p = sin i v faster Figure 5.9. Geometry of seismic rays in a plane layered Earth model, having P wave speed, a, progressively increasir-rg with depth. Waves that travel for much of their paths in deeper and faster layers, as illustrated, arc known as head waves.

26 Refracted rays and a velocity model

27 modified from Stein and Wysession (2009)

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29 Basics Concepts of Seismology Triplications, shadow zones

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31 Why does velocity typically increase with depth? = v S = µ

32 Why does velocity typically increase with depth? = v S = µ 1. Weaker rock types at shallow depth (crust) 2. Pressure effects on elastic moduli dominate over pressure effects on density 2. Pressure effects dominate over temperature effects 3. Phase changes make rocks stiffer (generally) (but temperature, melt, and water can lead to a velocity decrease)

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35 Triplications in the upper mantle Rapid velocity increases at 400 km and 650 km due to mineralogical phase changes

36 For example, low velocities in the asthenosphere (high temperature, partial melting?)

37 Basics Concepts of Seismology Gross Earth structure

38 Phases identified in seismogram Associated with paths through the Earth

39 Travel-time curve for the Earth - ('. F ( a ) 20. +u ,20. Delta deg

40 PREM (Dziewonski & Anderson, 1981)

41 Density is part of PREM This gives pressure at all depths Depth surface center

42 Elastic moduli in the Earth Incompressibility, K fi L B Transition Zone - Lower Mantle Rigidity, p Pressure, P (10rtPa) Figure Variations of the elastic moduli, K and,r.r, with pressure, P, for the I,REM earth model.

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44 Relaxed (low pressure, low temperature) density O = o) Y oo R r 6 -_ ac o 4 A Figure 5.19(a). Profile of clensity, p, through the earth moclel PREM with corresponding zero prcssure, low temperature density, estimated by finite strain theory.

45 Basics Concepts of Seismology Surface waves, dispersion

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47 Surface waves 1. travel along the Earth s surface 2. exist as Love waves and Rayleigh waves, each with a distinct particle motion 3. have speeds that depend mainly on the rigidity (shear modulus) of the rock 4. are dispersive

48 Seismic surface waves - analogy with water waves is apt

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51 Rayleigh wave

52 Love wave

53 Travel time curve for horizontal rays Time slope=1/speed Distance

54 Kermadec to Pasadena, Δ = 85 o Raw data sec sec sec

55 Raw data Kermadec to Pasadena, Δ = 85 o dispersion sec sec sec

56 Waves of different periods travel at different speeds Time T=175s T=100s T=45s Distance slope=1/speed

57 Sensitivity of surface wave velocities to elastic stucture at depth 200 seconds 300 km 20 seconds 30 km

58 Dispersion curve for an elastic Earth profile Speed Period

59 Measured disperion curve (example) Mitra et al., 2006

60 s Sensitivity kernels Rayleigh Love 35 s 200 depth (km) V SV 350 s sensitivity 350 s 0 1 V SH sensitivity Figure 2.1: Sensitivity functions for fundamental-mode Rayleigh and Love waves at the frequencies measured for this work, calculated for the spherically symmetric Earth model PREM (Dziewonski and Anderson, 1981). The bulk of the dataset consists of measurements at s, made using the method of Ekström et al. (1997); kernels for these periods are shown in blue and red. A smaller set of phase-velocity measurements at longer periods ( s) made by Nettles et al. (2000) is also included; kernels for these periods are shown in grey. Nettles, 2005

61 Basics Concepts of Seismology Standing waves, normal modes

62 Great Circle Wave Propagation R1 R2 R3 R4 R5 ~3 hours

63 Figure 2.7-3: Multiple surface waves circle the earth.

64 Standing wave as result of traveling-wave interference Animation courtesy of Dr. Dan Russell, Grad. Prog. Acoustics, Penn State

65 r Back to the wave 2 2 = 2 2 X This r equation X has standing-wave mode solutions: U n (x) cos(! n t) Any motion can be represented as a sum modes: u(x, t) = NX a n U n (x) cos(! n t) n=1

66 Frequency spectrum of a beer bottle

67 Animation courtesy of Dr. Dan Russell, Grad. Prog. Acoustics, Penn State

68 1882.] On the Vibrations of an Elastic Sphere. 189 On the Vibrations of an Elastic Sphere. By HORACE LAMB, M. A. [Read May llta, 1882.] The following paper contains an examination into the nature of the fundamental modes of vibration of an elastic sphere by the method employed in a previous communication, " On the Oscillations of a Viscous Spheroid."* The problem here considered is one of considerable theoretic interest, being as yet the only case in which the vibrations of an elastic solid whose dimensions are all finite have been discussed with any attempt at completeness. I have therefore thought it worth while to go into considerable detail in the interpretation of the results, and have endeavoured, by numerical calculations and the construction of diagrams, to present these in as definite and intelligible a form as possible. I find that some of my results (the most important being the general classification of the fundamental modes given in 5 below) have been already obtained by Paul Jaerisch, of Breslan,, in Orelle, t. lxxxviii. (1879) ; but the methods employed, as well as the form in which the results in question are expressed, are entirely different in the two investigations. Sir Horace Lamb

69 0S2 - the football mode

70 Lamb s estimate of 0S2 13. As an application of the preceding results we may calculate tho frequency of vibration of a steel ball one centimetre in radius, for tho slowest of those fundamental modes in which the surface oscillates in the form of a harmonic spheroid of tho second order. In 12 we obtained for this case ka/w = '842. Now, kajir = T 0 /r, where r is the period, and T Q 2a/ y/fnp' 1 ). Making then a=l, and adopting p 2 from Everett* the values n = 819 X10", p = 7*85, in C. G. S. measure, I find that the frequency r" 1 = , about. For a steel globe of any other dimensions, this result must be divided by the radius in centimetres. For a globe of the size of the earth [o = 6*87 X10"], I find that the period r = 1 hr. 18 m.f x period=2 x R0/vs for steel Earth, 78 minutes

71 3233 sec frequency