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Transcript of Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W...
![Page 1: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/1.jpg)
Geology 5640/6640Introduction to Seismology
20 Apr 2015
© A.R. Lowry 2015Read for Wed 22 Apr: S&W 185-198 (§3.7)
Last time: Anisotropy(Cont’d)• Anisotropy refers to directional dependence of velocity
• The fourth-order elasticity tensor, cijkl, can be expressed more succinctly as a 6x6 “Voight matrix” Cmn.
• Transverse anisotropy describes e.g. SPO in horizontally layered media, and is characterized by one P-velocity for x1 & x2 propagation, a different P-velocity for x3 propagation, and differing SV- & SH-velocities:
• Azimuthal anisotropy describes the more complicated case of azimuthally-varying P-velocity, generalizing to:€
VP12 =A
ρ; VP 3 =
C
ρ; VSH =
N
ρ; VSV =
L
ρ
€
vP θ( ) = A1 + A2 cos2θ + A3 sin2θ + A4 cos 4θ + A5 sin 4θ
![Page 2: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/2.jpg)
Reminder: The Final Exam is posted on the course website… Due 8:30 am Fri May 1.
6640 Semester Project due-dates: • Presentations on your research results are to be given 11:30 am to 1:20 pm on Mon Apr 27; will be max 30 minutes each• Research reports are due Fri May 1 at 5 pm. No fixed length, but these should include ‡ Intro/Context (presumably including relevance to your thesis topic) ‡ Description of Math/Physics of the problem ‡ Methods Used (if any) ‡ Details of Analysis ‡ Results, Discussion, Future Work (if any)
![Page 3: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/3.jpg)
Fluid-filled cracks in an isotropic medium will havean elasticity tensor of the form:
In this example we’ve assumed that the normals totwo-dimensional cracks parallel the x1 axis. Note how theshear modulus is reduced by the cracks. If the fluid isincompressible, P-wave velocity is unaffected, butS-wave velocity is.
Here, ε = Na3/V, with N being the number of cracks pervolume V, and a is the half-width of the cracks.
€
Cmn =
λ +2μ λ λ 0 0 0
λ λ +2μ λ 0 0 0
λ λ λ +2μ 0 0 0
0 0 0 μ 0 0
0 0 0 0 μ 1−ε( ) 0
0 0 0 0 0 μ 1−ε( )
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
![Page 4: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/4.jpg)
Lin & Schmandt, Geophys. Res. Lett. 2014
Example of uppercrustal (10-16 s)Rayleigh velocityanisotropy
![Page 5: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/5.jpg)
… Interpreted as compressional stress direction closed fractures
Lin & Schmandt, Geophys. Res. Lett. 2014
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Here, observations were made usingmarine seismic observations of refraction travel-times near Hawaii.
Azimuth is measured relative to trendof magnetic isochrons in the region,so velocity peaks at 90° and 270°indicate that the fast direction is inthe direction of spreading at the timethe lithosphere was formed.
So is that more likely to representfluid-filled fractures or flow of mantleolivine?
![Page 7: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/7.jpg)
The depth and agedependence ofanisotropy in theoceans also lendsinsight into physicalprocesses…
Important to note, forinterpreting this signal,that the direction andmagnitude ofanisotropy reflects anintegral of the strainhistory of the rocks!
€
ξ =N
L=
VSH
VSV
⎛
⎝ ⎜
⎞
⎠ ⎟
2
![Page 8: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/8.jpg)
Too
mey
et a
l. N
atur
e 20
07
More recent data from the EastPacific Rise tell a morecomplicated (and moreinteresting) story…
With significant implications foractive- vs passive-componentsof the flow dynamics in oceanicspreading centers (not tomention segmentation ofridges, and the bathymetryand melt chemistry variationsalong a mid-ocean ridge…)
![Page 9: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/9.jpg)
Shear Wave Splitting is commonly-used to identifyazimuthal anisotropy. Given initial signal s(t) on the radialcomponent only of the SKS arrival & angle f between radial &fast directions,
Radial:
Transverse:€
s1 t( ) = s t( )cosφ s2 t( ) = s t −δt( )sinφ
€
R t( ) = s t( )cos2 φ + s t −δt( )sin2 φ
€
T t( ) = s t( )+s t −δt( )
2
⎡
⎣ ⎢
⎤
⎦ ⎥sin2φ
Note that normallyone wouldn’t get atransversecomponent SKSarrival; only radial!but anisotropy “splits”the arriving energy incomponents & || toanisotropy axes.
![Page 10: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/10.jpg)
In practice, try lots of rotations and t’s to find which maximizesthe radial component of amplitude.
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Note gives youthe fastdirection;t describesthicknesstimes v!
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Miller & Savage, Science, 2001
Time-varyinganisotropyhas beenobservede.g. beforeand afteran eruptionof MountRuapehuin NewZealand…
1994, <30 km 1998, <30 km
1994, >50 km 1998, >50 km
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Attenuation and AnelasticityWave amplitudes depend on:
• Source energy
• Transmission/Reflection at interfaces (i.e., Zoeppritz’ Equations)
• Geometric Spreading: As a wavefront propagates from a finite source and encompasses a larger volume, conservation of energy requires amplitude to diminish.
• Multipathing: Focusing and defocusing of waves (analogous to mirages in the case of light).
• Scattering: Like multipathing, but this occurs when velocity heterogeneities have wavelengths of the order of the propagating wave.
• Anelasticity: Elastic energy is converted to heat during unrecoverable deformation.
![Page 14: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/14.jpg)
Geometrical Spreading:Recall from our derivation of the wave equation in spherical coordinates that amplitudes of a spherical (body) wavefront decay as 1/r; we also noted that a (cylindrical) head wave amplitude decays as 1/ .
A surface wave on a spherefollows a ring whose circumferenceequals asin. The energy per unitwavefront decreases as
Amplitude is proportional to thesquare-root of energy, so
which is a minimum at = 90° andmaximum at = 0° & 180°!
€
r
€
1
r=
1
a sin Δ
€
A∝1
a sin Δ
![Page 15: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/15.jpg)
Multipathing:
Seismicwavesalso canbe focusedanddefocusedby velocityvariationsin themedium.
![Page 16: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/16.jpg)
Reverse shot from a seismic refraction profile collected on afarm near Gosport, IN.
(Note: You’ll be looking at something similar to this for yourFinal Exam…)
![Page 17: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/17.jpg)
4 m4 m
Gosport Best Fit RMS = 1.39 ms
![Page 18: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/18.jpg)
Note that the amplitudes for these first arrivals do not follow asimple 1/r or 1/√r decay… !
![Page 19: Geology 5640/6640 Introduction to Seismology 20 Apr 2015 © A.R. Lowry 2015 Read for Wed 22 Apr: S&W 185-198 (§3.7) Last time: Anisotropy(Cont’d) Anisotropy.](https://reader036.fdocuments.in/reader036/viewer/2022062517/56649e795503460f94b7994b/html5/thumbnails/19.jpg)
These amplitudes decay rapidly even after correcting forgeometrical spreading (due to anelastic attenuation with lowQ: We’ll come back to that shortly). But geometric plusanelastic decay modeling poorly fits arrivals where two waves
come in at aboutthe same time..,
This is also anexample ofmultipathing!
1 2 3
V = 1250 m/sf = 250 Hz
Q = 5.1(10.2)
V = 3680 m/sf = 125 Hz
Q = 3.2(6.3)X
X
5301006.6
(13.3)