Damagingandhealingofearthmaterialsasamulti-scalephenomenon

RoelSnieder

1

(Brenguier etal.,Science,321,1478-1481,2008) 2

(NakataandSnieder,JGR,117,B01308,2012)3

S-wavesinNiigataandearthquakes

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S-velocitychangeswithseasons

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Rainfall/vs forsoft-rocksites

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VelocitychangesinChili1492 M. Gassenmeier et al.

Figure 2. (a) Similarity matrix (R) of station PATCX between 10–15 s and 4–6 Hz. Negative correlation coefficients appear white. The blue dots in thesimilarity matrix symbolize the daily velocity variations δv. The rare blue dots at velocity decreases larger than 1.5 per cent before 2014 April result from cycleskipping. The MW 7.7 Tocopilla and the MW 8.1 Iquique earthquake are marked with T and Iq, respectively. A–K mark selected earthquakes corresponding toTable 1 and Fig. 1. The absolute ground acceleration integrated over one day at station PATCX is plotted with black bars in (b).

Richter et al. (2014). We therefore calculate high-frequency dailyautocorrelations for the vertical components in the frequency rangesof 1–3 Hz, 4–6 Hz and 7–10 Hz. We follow the processing schemeof Richter et al. (2014) with the aim to have a consistent databasefor analysing velocity changes with PII. In the pre-processing, thewaveforms are downsampled to 50 Hz, detrended and filtered. Torecover the Green’s function as faithfully as possible, we would liketo suppress the unwanted effect of earthquakes, which occur veryfrequently in this seismically active area. Therefore, time windowswith an envelope larger than 10 times the root mean square of theenvelope in quiet periods are detected and set to zero. We makesure that the deleted time windows are at least two minutes longand we taper the edges in order to avoid artefacts in the autocor-relation function (ACF) at small lapse times. Additionally, 1-bitnormalization is applied before calculating daily ACFs.

Relative velocity changes ("v/v = δv) were measuredwith the stretching method (Sens-Schonfelder & Wegler 2006;Hadziioannou et al. 2009, 2011), which compares individual ACFs(φ(ti, τ )) calculated from noise signal that was recorded at time tito stretched or compressed versions of a long-term averaged refer-ence ACF ξ (τ ). Here τ indicates the lapse time of the ACF, that is,the traveltime of waves. For each time window and each velocitychange δϵj, the comparison between φ and ξ is performed in termsof the correlation coefficient

R(ti , ϵ j ) =∫ τ2

τ1

φ(ti , τ )ξ(τ ∗ (1 + ϵ j )

)dτ (1)

of a set of stretching values ϵj in a lapse time window (τ 1, τ 2).The set of correlation coefficients R for all times ti and stretching

values ϵj is hereafter referred to as similarity matrix. The stretchingvalue ϵm that results in the maximum correlation R(ti, ϵm) yieldsthe relative velocity change δv(ti) = ϵm at time ti. The stretchingwas implemented in the range of ±3.3 per cent and the temporalresolution of the velocity change estimation is one day. To gain thehighest sensitivity for velocity changes, we use the frequency rangeof 4–6 Hz and the lag time window between 10 and 15 s (Richteret al. 2014). Lower frequencies were found to be less sensitive forshaking-induced velocity variations and higher frequencies led tovelocity variations with a lower signal-to-noise ratio (see Supple-mentary Material Fig. S1). The velocity changes were also estimatedin lag time windows between 5–10 and 15–20 s showing identicalfeatures, but with a lower signal-to-noise ratio (see SupplementaryMaterial Fig. S2). For the calculation of the reference trace, we usean iterative process (Richter et al. 2014) in which a preliminaryreference trace is calculated as the mean over all autocorrelationtraces, leading to a preliminary estimate of the velocity changes. Ina second step, the ACFs are corrected for the preliminary estimatedvelocity changes and a final reference trace is calculated as the meanover the corrected autocorrelation traces. For high frequencies andlate lag times, this two-step approach minimizes the problems ofcycle skipping although it cannot eliminate it completely. Such in-stances are easily identified by consideration of neighboring days(Fig. 2). In order to validate the reliability of the measurement,we repeated the velocity change estimation with autocorrelationsfor the horizontal components for a time between 2012 and 2014.The results show comparable velocity variations—confirming theresults estimated with the vertical component (see SupplementaryMaterial Fig. S1).

at Colorado School of M

ines on April 6, 2016

http://gji.oxfordjournals.org/D

ownloaded from

(Gassenmeier etal.,Geophys.J.Int.,204,1490-1502,2016) 7

Seismicsensorsarrayonadam

Crest

Bottom

SensorsArray

CourtesyofIchiroKuroda8

Directioncomponentsinadam

Vst

Vax

9

DayssinceTohoku-oki earthquake

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DayssinceTohoku-oki earthquake10-2 10-1 100 101 102

11

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Mineralizedfractures

13(Credit:NASA/JPL-Caltech/MSSS)

Intrusionbyadike

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Color-enhanced Scanning Electron Microscope (SEM) image of human tooth dentine (fracturesurface) showing a crack in the surface. 70% of dentin consists of the mineral hydroxyapatite,20% is organic material, and 10% is water. Magnification: x1200 when printed 10 cm wide.

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Human Tooth Dentine, SEM

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Color-enhanced Scanning Electron Microscope (SEM) image of human tooth dentine (fracturesurface) showing a crack in the surface. 70% of dentin consists of the mineral hydroxyapatite,20% is organic material, and 10% is water. Magnification: x1200 when printed 10 cm wide.

Filename: K14SEM--tooth062.jpgCopyright Not Applicable

© Sciencephotography.com | CONTACT Powered by PhotoShelter

Human Tooth Dentine, SEM

Like 0

17

18

Micro-structureofarockfracture

19(BrownandScholz,J.Geophys.Res.,91,4939-4948,1986)

Powerspectrumofrocksurface

20

(BrownandScholz,J.Geophys.Res.,90,12575-12582,1985)

1m 10micron

Healingofafracture

21(BrownandScholz,J.Geophys.Res.,91,4939-4948,1986)

Healingofafracture

22(BrownandScholz,J.Geophys.Res.,91,4939-4948,1986)

Pressuresolution

23

24

Pressuresolutionofoolitic limestone

Analoguemodelforcracks

25(Renard etal.,Geofluids,9,365-372,2009)

Ahealingcrackinagel

26(Renard etal.,Geofluids,9,365-372,2009)

Ahealingcrackinaquartz

27(Renard etal.,Geofluids,9,365-372,2009)

Log(time)behaviorinresonanceVOLUME 85, NUMBER 5 P H Y S I C A L R E V I E W L E T T E R S 31 JULY 2000

log10 (t/t0)

δf /

f 0

0.40

0.78

1.17

1.92

2.64 |ε|

m

0 1 2 3x10–6

2

1

0

x10–5

0.5 1 1.5 2 2.5 3 3.5 4

2

0

–2

–4

–6

–8

–10

–12

–14

x10–5

x10–6

FIG. 5. Dependence of recovery slope on conditioning magni-tude. Maximal conditioning strain indicated for individual re-coveries !df"t# 2 df"t0#$%f0 ! m ln"t%t0#, and the relation ofslope to maximal instantaneous conditioning strain, m & 11.1 3"j´j 2 4.7 3 1027#, is shown inset.

creep restores contact area, reducing the number of low-barrier events available. If the number of higher-barrierevents diminishes in kind, r0"Echar # will decrease overtime, correlated with 1%Q. Such a correlation, togetherwith the observation that Q increases with temperature,would explain how decreasing r0 compensates the T -linearslope of Eq. (5) to produce Fig. 3. Why this is more visibleat 36 h than at 12 h we do not know.

The prediction that modulus reduction results from aninduced internal strain field of arbitrary origin can be testedby comparing the magnitudes of acoustically and ther-mal-shock driven shifts. Figure 5 shows modulus recoveryas a function of time at five different acoustic condition-ing strains. The relation of the logarithm coefficient tomaximal conditioning strain, m & 11.1 3 "j´j 2 4.7 31027#, is shown (inset).

The acoustic scaling relation can be extrapolated andcompared to the thermal recoveries. Under 5 ±C tem-perature change, the internal strain of a randomly ori-ented matrix of quartz crystals may be estimated from thedifference of grain parallel- and perpendicular-axis coef-ficients of expansion, da & 0.65 3 1025 ±C21 [18], asj´j ' 3.25 3 1025. The slope then predicted by the Fig. 5dependence is m ! 3.6 3 1024, close to the fit valuem & 2.8 3 1024 from Fig. 4.

Logarithmic scaling persists in Fig. 4 to '3 3 104 s,where the acoustic scaling regime ended at '103 s. In spinglass aging [19], the transition time between logarithmicand power-law scaling is known to depend on the time

between quench and removal of the external induction. Ifa similar dependence characterizes the dc susceptibility ingranular magnetic media [4], it would be interesting to seeif they experience a symmetry-breaking susceptibility shiftunder ac drive, analogous to ours.

This work was supported by the Department of Energy,Office of Basic Energy Sciences, Contract No. W-7405-ENG-36.

[1] N. Carter, Rev. Geophys. Space Phys. 14, 301 (1976).[2] C. Zener, Elasticity and Anelasticity of Metals (The Uni-

versity of Chicago Press, Chicago, 1948).[3] K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge

University Press, Cambridge, 1991), p. 8.[4] L. J. Swartzenruder, L. H. Bennett, F. Vajda, and E. Della

Torre, Physica (Amsterdam) 233B, 324 (1997).[5] D. L. Sparks, Soil Physical Chemistry (CRC Press, Boca

Raton, FL, 1986).[6] L. D. Landau and E. M. Lifschitz, Theory of Elasticity

(Pergamon, New York, 1986), 3rd (revised) English ed.[7] K. R. McCall and R. A. Guyer, J. Geophys. Res. 99, 23887

(1994); R. A. Guyer, K. R. McCall, and G. N. Boitnott,Phys. Rev. Lett. 74, 3491 (1995).

[8] E. Smith and J. A. TenCate, Geophys. Res. Lett. (to bepublished).

[9] F. Heslot, T. Baumberger, B. Perrin, B. Caroli, andC. Caroli, Phys. Rev. E 49, 4973 (1994).

[10] J. A. TenCate and T. J. Shankland, Geophys. Res. Lett. 23,3019 (1996).

[11] J. A. TenCate, E. Smith, and R. A. Guyer (to be published).[12] T. Bourbie, O. Coussy, and B. Zinszner, Acoustics of

Porous Media (Editions Technip, Paris, 1986), pp. 17, 37,45, and 185; P. A. Scholle, American Association of Petro-leum Geologists Memior 28 (Rogers Litho, Tulsa, 1979),pp. 11, 17, 44, and 113 [ISBN No. 0-89181-304-7].

[13] A. P. Radlinski, E. Z. Radlinska, M. Agamalian, G. D. Wig-nall, P. Lindner, and O. G. Randl, Phys. Rev. Lett. 82, 3078(1999).

[14] G. D. Guthrie and J. W. Carey, Cem. Concr. Res. 27, 1407(1997).

[15] X. Jia, C. Caroli, and B. Velicky, Phys. Rev. Lett. 82, 1863(1999).

[16] L. Bocquet, E. Charlaix, S. Ciliberto, and J. Crassous,Nature (London) 396, 735 (1998).

[17] J. P. Hirth and J. Lothe, Theory of Dislocations (Wiley, NewYork, 1982), 2nd ed., p. 80.

[18] P. Hidnert and H. S. Kridner, in AIP Handbook (McGrawHill, York, PA, 1957), pp. 4–61.

[19] Ref. [3], pp. 276, 284–292.

1023

(TenCateetal.,Phys.Rev.Lett.,85,1020-1023,2000) 28

Log(time)behaviorinresonance

(TenCateetal.,PureAppl.Geophys,168,2211-2219,2011)Figure 4Resonance frequency versus log(time) recovery curves for four different geomaterials, all 25.4 mm diameter and approximately 0.3 m long. Asimilar length concrete sample was not available; this sample is 0.12 m long. Each sample was conditioned for 1,000 s with a strain of 10–6,

the conditioning drive turned off, and the resonance frequency peak tracked with time. The log(time) behavior of all these samples is

remarkable and typical of many rocks. Note that the Lavoux limestone shows signs of departing from log(time) behavior at around 800 s.Errors in determining the resonance frequencies for these samples are around 0.1 Hz

Figure 5Comparison of resonance frequencies versus log(time) for the same Berea sandstone sample of Fig. 3. Conditioning resonance frequencies are

shown on the left plot, recovery resonance frequencies are shown on the right plot (similar to those shown in Fig. 4). Both conditioning andrecovery in slow dynamics appear to go as log(time). This figure should be compared with Fig. 1c of (PANDIT and SAVAGE, 1973) where those

authors studied creep with time during and after excitation of a flexural mode in a sandstone sample

2216 J. A. TenCate Pure Appl. Geophys.

29

Perturbingsamples

Chapter 6. Laboratory tests of shaking induced velocity variations

(a) (b)

Figure 6.1: Experimental setup: a) A pair of ultrasound transducers is attached to two cylindricalsand-gypsum samples. A sound transducer is mounted on the top of sample A. It generates ashaking every 30min on sample A, which is coupled to sample B with lower amplitude. b) Thesamples are placed in a climate chamber at a temperature of 30�C.

The signals were band-pass filtered between 10 and 50 kHz, and after autocorre-lation of the transmitter and receiver signal possible velocity changes were analyzedwith the stretching method (chapter 2.5.1) in a time window of 2-4ms.

6.2 Results

The observed velocity variations corresponding to cross-correlation values largerthan 0.7 are shown in Fig. 6.2. This threshold affects only the data of sample Aduring shaking. On average, correlation values are very large with mean values of0.991 for sample A and 0.999 for sample B. Additionally, the data was corrected fora small positive linear trend estimated over the first 15 minutes.

The velocity shows sharp decreases at both samples at the times of the shocksfollowed by a subsequent recovery (Fig. 6.2 a). The amplitudes of the decreases atsample A are larger than at sample B, which is expected from the field observationsat station PATCX, as the amplitude of the shaking at sample A is also larger thana sample B. At both samples it can be observed that the amplitude decrease is thelargest for the first shock. After the first shock the amplitude of velocity changefor later shocks shock deceases slightly. As the sample was at rest for more thanfour days before the experiment, this behavior can be attributed to aging effects, asdescribed in chapter 3.4.1.

82

(Gassenmeier,2015,PhDthesis,Universität Leipzig)30

Healingofrocksamples

(Gassenmeier,2015,PhDthesis,Universität Leipzig) 31

Sorockhealingclearlygoesaslog-time

32

Logarithmmeansthereisnotime-scale

ln(t/⌧) = ln(t)� ln(⌧)

anytime-scalecorrespondstoanoffset

33

Relaxationprocessforonerelaxationtime

R(t) = e�t/⌧

34(Snieder,R.,C.Sens-Schoenfelder,and R.Wu,Geophys.J.Int.,208,1-9,2017)

Relaxationprocessforonerelaxationtime

R(t) = e�t/⌧

Superpositionofrelaxationprocesses

R(t) =

Z ⌧max

⌧min

1

⌧e�t/⌧d⌧

followsfromArrhenius’law1

⌧35

Howtogetlog-timebehavior?

R(t) =

Z ⌧max

⌧min

1

⌧e�t/⌧d⌧

36

Howtogetlog-timebehavior?

R(t) =

Z ⌧max

⌧min

1

⌧e�t/⌧d⌧

u = t/⌧

R(t) =

Z t/⌧min

t/⌧max

1

ue�udu

37

Howtogetlog-timebehavior?

R(t) =

Z ⌧max

⌧min

1

⌧e�t/⌧d⌧

u = t/⌧

R(t) =

Z t/⌧min

t/⌧max

1

ue�udu

dR(t)

dt=

1

t

⇣e�t/⌧

min � e�t/⌧max

⌘

38

Howtogetlog-timebehavior?

dR(t)

dt=

1

t

⇣e�t/⌧

min � e�t/⌧max

⌘

39

Howtogetlog-timebehavior?

dR(t)

dt=

1

t

⇣e�t/⌧

min � e�t/⌧max

⌘

⌧min

⌧ t ⌧ ⌧max

when

dR(t)

dt=

1

t(0� 1) = �1

t

40

Howtogetlog-timebehavior?

dR(t)

dt=

1

t

⇣e�t/⌧

min � e�t/⌧max

⌘

⌧min

⌧ t ⌧ ⌧max

when

R(t) = B � ln(t)

dR(t)

dt=

1

t(0� 1) = �1

t

41

Relaxationfunction

t(s)100 101 102 103 104

R(t

)

0

1

2

3

4

5

6

7

8 τ

max = 104 s

τmax

= 103 s

τmax

= 102 s

42

Relaxationfunction

t(s)100 101 102 103 104

R(t

)

0

1

2

3

4

5

6

7

8 τ

min = 1 s

τmin

= 10 s τ

min = 100 s

43

44

Onceasemester,Iwillengageinaprofessionalorpersonalactivitythat

frightensmealittlebutwhichmakesmefeelalive.

45