Adv Advanced anced Worksho shop p on n Ea Earthquake Fa Fault - - PowerPoint PPT Presentation

Adv Advanced anced Worksho shop p on n Ea Earthquake Fa Fault Mechanics: The Theory, , Simulation

• n and Observation
• ns

ICTP, Trieste, Sept 2-14 2019 Lecture 6: macroscopic source properties Jean Paul Ampuero (IRD/UCA Geoazur)

Overview

Macroscopic source properties constrained by seismology:

• seismic moment
• source time function
• corner frequency
• radiated energy

à stress drop, rupture speed, rupture size

Outputs of dynamic rupture models: Detailed space-time distribution of slip

• n the fault

120 140 = 4.67 x 1021 Nm = 67.7 s, Td = 109.5 s 1018 1019 1020

Moment (N−m)

10−3 10−2 10−1 100

Frequency (Hz)

Er = 5.16e+16 Er/M0 = 1.10e−05 fc = 5.2 mHz n0 = 1.46 n1 = 1.74, r1 = 0.17 n2 = 1.58, r2 = 0.23 σp = 0.11 MPa

= 310.0 , = 18.0 , = 63.0 4.9 17.2

Depth (km)

=60.3 , =58.3 GT.DBIC. P φ=77.1°, ∆=71.8 II.ASCN.00 P φ=89.4°, ∆=58.4 IU.TSUM.00 P φ=108.8°, ∆=85.9 II.SUR.00 P φ=122.3°, ∆=85.1 II.HOPE.00 P φ=151.5°, ∆=47.6 IU.PMSA.00 P φ=174.6°, ∆=48.9 IU.SPA.00 P φ=180.0°, ∆=73.8 IU.CASY.00 P φ=181.7°, ∆=97.7 IU.SBA.00 P φ=190.7°, ∆=80.1 G.DRV.00 P φ=192.7°, ∆=93.6 IU.SNZO.00 P φ=224.5°, ∆=94.8 IU.PTCN.00 P φ=250.6°, ∆=53.2 G.PPT. P φ=256.3°, ∆=72.2 IU.KIP.00 P φ=292.1°, ∆=90.8 CI.BAR. P

Detailed source parameters

= 5.12 MPa = 3.05 MPa

676 G.ECH. SH φ=41.4°, ∆=96.0° 1143 IU.PAB.00 SH φ=46.4°, ∆=85.1° 763 IU.LSZ.00 SH φ=108.1°, ∆=96.7° 1527 II.SUR.00 SH φ=122.3°, ∆=85.1° 794 IU.CASY.00 SH φ=181.7°, ∆=97.7°

+ seismograms & ground displacements

From ground motion recordings …

Seismograms = ground velocity

From ground motion recordings to the rupture process

How much did the fault slip? How did it slip? Fast/slow? Smooth/tortuous? Loud/silent?

Outputs of dynamic rupture models: Detailed space-time distribution of slip

• n the fault

+ seismograms & ground displacements Macroscopic source parameters:

• Seismic moment
• Seismic moment rate (source time function)
• Rupture size
• Rupture duration
• Average rupture speed

120 140 = 4.67 x 1021 Nm = 67.7 s, Td = 109.5 s 1018 1019 1020

Moment (N−m)

10−3 10−2 10−1 100

Frequency (Hz)

Er = 5.16e+16 Er/M0 = 1.10e−05 fc = 5.2 mHz n0 = 1.46 n1 = 1.74, r1 = 0.17 n2 = 1.58, r2 = 0.23 σp = 0.11 MPa

= 310.0 , = 18.0 , = 63.0 4.9 17.2

Depth (km)

=60.3 , =58.3 GT.DBIC. P φ=77.1°, ∆=71.8 II.ASCN.00 P φ=89.4°, ∆=58.4 IU.TSUM.00 P φ=108.8°, ∆=85.9 II.SUR.00 P φ=122.3°, ∆=85.1 II.HOPE.00 P φ=151.5°, ∆=47.6 IU.PMSA.00 P φ=174.6°, ∆=48.9 IU.SPA.00 P φ=180.0°, ∆=73.8 IU.CASY.00 P φ=181.7°, ∆=97.7 IU.SBA.00 P φ=190.7°, ∆=80.1 G.DRV.00 P φ=192.7°, ∆=93.6 IU.SNZO.00 P φ=224.5°, ∆=94.8 IU.PTCN.00 P φ=250.6°, ∆=53.2 G.PPT. P φ=256.3°, ∆=72.2 IU.KIP.00 P φ=292.1°, ∆=90.8 CI.BAR. P

=58.3° 636 =71.8° 835 II.ASCN.00 P =58.4° 481 IU.TSUM.00 P =85.9° 527 =85.1° 717 II.HOPE.00 P =47.6° 384 IU.PMSA.00 P =48.9° 292 =73.8° 113 IU.CASY.00 P =97.7° 331 =80.1° 166 =93.6° 130 IU.SNZO.00 P =94.8° 543 IU.PTCN.00 P =53.2° 373 =72.2° 121 φ=356.2°, ∆=56.7°

30 60

Time (s)

= 2.40 km/s, Var. = 0.1772 = 29.6 km, Hc = 18.1 km

6.8 10.2 13.6 17.0

Coseismic Slip(m)

φ=331.2 IU.RSSD.00 P φ=336.7 IU.CCM.00 P φ=343.5 IU.DWPF.00 P φ=350.3 IU.SSPA.00 P φ=356.2 CN.SCHQ. SH = 4.1 ,

Fine vs. coarse source parameters

=58.3° 636 =71.8° 835 II.ASCN.00 P =58.4° 481 IU.TSUM.00 P =85.9° 527 =85.1° 717 II.HOPE.00 P =47.6° 384 IU.PMSA.00 P =48.9° 292 =73.8° 113 IU.CASY.00 P =97.7° 331 =80.1° 166 =93.6° 130 IU.SNZO.00 P =94.8° 543 IU.PTCN.00 P =53.2° 373 =72.2° 121 φ=356.2°, ∆=56.7°

30 60

Time (s)

120 140 = 4.67 x 1021 Nm = 67.7 s, Td = 109.5 s 1018 1019 1020

Moment (N−m)

10−3 10−2 10−1 100

Frequency (Hz)

Er = 5.16e+16 Er/M0 = 1.10e−05 fc = 5.2 mHz n0 = 1.46 n1 = 1.74, r1 = 0.17 n2 = 1.58, r2 = 0.23 σp = 0.11 MPa

= 310.0 , = 18.0 , = 63.0 4.9 17.2

Depth (km)

=60.3 , =58.3 GT.DBIC. P φ=77.1°, ∆=71.8 II.ASCN.00 P φ=89.4°, ∆=58.4 IU.TSUM.00 P φ=108.8°, ∆=85.9 II.SUR.00 P φ=122.3°, ∆=85.1 II.HOPE.00 P φ=151.5°, ∆=47.6 IU.PMSA.00 P φ=174.6°, ∆=48.9 IU.SPA.00 P φ=180.0°, ∆=73.8 IU.CASY.00 P φ=181.7°, ∆=97.7 IU.SBA.00 P φ=190.7°, ∆=80.1 G.DRV.00 P φ=192.7°, ∆=93.6 IU.SNZO.00 P φ=224.5°, ∆=94.8 IU.PTCN.00 P φ=250.6°, ∆=53.2 G.PPT. P φ=256.3°, ∆=72.2 IU.KIP.00 P φ=292.1°, ∆=90.8 CI.BAR. P

= 2.40 km/s, Var. = 0.1772 = 29.6 km, Hc = 18.1 km

6.8 10.2 13.6 17.0

Coseismic Slip(m)

φ=331.2 IU.RSSD.00 P φ=336.7 IU.CCM.00 P φ=343.5 IU.DWPF.00 P φ=350.3 IU.SSPA.00 P φ=356.2 CN.SCHQ. SH = 4.1 ,

−40

Distance along dip (km)

17.2 29.6

Depth (km)

∆σ0.15 = 5.12 MPa ∆σE = 3.05 MPa

676 G.ECH. SH φ=41.4°, ∆=96.0° 1143 IU.PAB.00 SH φ=46.4°, ∆=85.1° 763 IU.LSZ.00 SH φ=108.1°, ∆=96.7° 1527 II.SUR.00 SH φ=122.3°, ∆=85.1° 794 IU.CASY.00 SH φ=181.7°, ∆=97.7°

Time Moment rate

High definition More detail High fidelity Less uncertainty

Trade-offs in earthquake source studies

Source time functions

Global source studies

Ye et al (JGR 2016)

. finite source inversions with teleseismic data, 0.005-0.9 Hz . Uniform method and careful manual analysis . Robust source time functions (STF, moment rate) . 116 M7+ shallow subduction zone thrust earthquakes

Global source studies

Ye et al (JGR 2016)

. finite source inversions with teleseismic data, 0.005-0.9 Hz . Uniform method and careful manual analysis . Robust source time functions (STF, moment rate) . 116 M7+ shallow subduction zone thrust earthquakes

STF from deconvolution

seismogram = (Green’s function)*(Source Time Function) !"($) = '"($) ∗ ̇ *+($) * means convolution G can be synthetic or empirical Deconvolution: infer ̇ *+($) from !"($) SCARDEC (by Martin Vallée, IPGP): real-time STF from teleseismic data large catalog of past events new events posted rapidly on Twitter by @geoscope_ipgp

https://www.iris.edu/hq/inclass/fact-sheet/

Teleseismic waves

Questions to address:

• What are the common features of earthquakes?
• Do small and large earthquakes start equal?
• Are earthquakes self-similar at all magnitudes?
• How are earthquakes different from each other?
• Is there such a thing as a freak event?
• What do those similarities and differences tell us

about earthquake dynamics?

Enabled by global earthquake source products by Lingling Ye (Caltech), Martin Vallée (IPGP) and Gavin Hayes 5USGS)

General patterns of Source Time Functions

. In each bin, at each point in time, compute median STF . Bin STFs by magnitude, 20 nearest neighbours

Median STFs have linear onset, same for all magnitudes Mw>7.2

General patterns of Source Time Functions

. Normalize ze ea each ST STF by by it its dura rati tion . Scale them such that they integrate to 1 . Compute median of normalized STF

On average, all STFs can be scaled to a very simple, quasi-triangular shape General patterns of STFs

On average (median), all STFs can be scaled to a very simple, quasi-triangular shape

Meier, Ampuero and Heaton (2017)

Implications for moment / duration scaling

Linear growth suggests M0 ~ T2 scaling In contrast to the widely reported M0 ~ T3 scaling à scaling break !

Why is linear moment rate growth surprising?

Self-similar model for small earthquakes: Circular rupture with constant stress drop and constant rupture speed Ruptures become elongated after they break the whole seismogenic width: moment grows s sl slower than quadratic

! ̇ 0 ∝ %2

∆! !

But the linear trend (!"~$) is

• bserved after ~5 s,

before rupture sa saturates s the se seism smogenic width

Seismogenic width Slip rate (m/s)

Implications for Rupture Growth Scaling

. Observed STF growth is linear . … and average slip grows as . If rupturing area grows as . Since we observe linear growth

!(!) ∝ !! !(!) ∝ !! !!(!) ∝ !(!)!(!) ∝ !!!! ! = ! + ! − 1 !!"#~ 1 → ! + ! ~ ! !"# ∝ &1

à How can we lower the moment rate growth? . Seismic moment . Moment rate exponent . Self-similar pulse or crack

!!! = 2 + 1 = 3

. Pulse-like rupture with areas of systematic slip deficits? . Lower alpha, lower beta, or combination of both?

Nucleation Propagation Arrest

Intermediate-size event unzipping part of the lower edge of the coupled zone (Junle Jiang, Caltech)

Pre-stress Final stress

Avouac et al (Nat Geo, 2015)

2015 Mw 7.8 Gorkha, Nepal earthquake All M>7 subduction earthquakes

?

All M>7 subduction earthquakes

?

Thingbaijam et al (2017)

Rupture length Rupture width

S l

• p

e = 1

L x 2.8 W x 2

STF residuals in magnitude bins normalized by fitting function

Fit a function to STFs:

STF residuals

Multiplicative noise

Fluctuations around the median STF

Empirical cumulative distribution

• f STF residuals

STF fluctuations are multiplicative and Gaussian

STF fluctuations are multiplicative, Gaussian and Brownian

1 / f n

• i

s e

Summary of observed STF characteristics, Mw>7

• All STFs can be scaled to a common,

quasi-triangular shape

• Onsets are linear and the same for all
• Fluctuations are multiplicative,

Gaussian and Brownian

CONCLUSIONS

A few things are certain … . Earthquakes have large variability, but on average they follow a simple pattern More questions than answers … . What causes break of self-similarity at ~1s? . Transition to el elong ngated ed ru ruptu tures at the bottom of seismogenic zone? . What dynamical models can explain the linear STF growth? Today we have enough data to unc uncover er general patterns of

• f earthquake rupture

. The pattern deviates from standard models after few seconds . Large earthquakes are small earthquakes that did not stop (all earthquakes start the same) . Rupture evolution is weakly predictable . Physical origin of the pattern? Focusing on temporal evolution facilitates testing conceptual rupture models

What to do next?

• Analysis of strike-slip ruptures
• Source studies with uncertainty quantification
• Develop methods for systematic analysis across the magnitude range
• f scaling transition from M6 to M8+

à break of self-similarity, scaling of rupture aspect ratio

• Develop dynamic rupture models consistent with these observations

Corner frequency

Earthquake spectra

seismogram = (Green’s function)*(Source Time Function) !(#) = &(#) ∗ ̇ )*(#) In the far-field, & # ∝ ,(# − ./0) ! # ∝ ̇ )*(# − ./0) à Far-field displacements are proportional to Source Time Function à Far-field spectrum ! 1 proportional to moment rate spectrum ̇ )*(1)

Earthquake spectra

seismogram = (Green’s function)*(Source Time Function) !(#) = &(#) ∗ ̇ )*(#) In the far-field, & # ∝ ,(# − ./0) ! # ∝ ̇ )*(# − ./0) à Far-field displacements are proportional to Source Time Function à Far-field spectrum ! 1 proportional to moment rate spectrum ̇ )*(1) Lay et al (2011)

!" model of earthquake spectrum

One corner frequency, #

$, that separates

flat spectrum at low-f and 1/!" at high-f: ̇ () # ≈ () 1 + # #

$ "

At low frequencies (# ≪ #

$):

̇ () # ≈ () At high frequencies (# ≫ #

$):

̇ () # ≈ ()#

$"/#"

.//0 1 # ∝ ̇ () # à 3(#) ∝ #" ̇ () # ≈ ()#

$"

Attenuation vs corner frequency

Bostock et al (2017) With attenuation W i t h

• u

t a t t e n u a t i

• n

Attenuation (low Q) multiplies the spectrum by exp(−&'(/*+) It reduces the apparent corner frequency

Attenuation quality factor Q

Trade-off between attenuation and corner frequency

Lior and Ziv (2018) !

" = 1

%& ∼ 1 ( !

)

Self-similar source model

Corner frequency !

" ∼ 1/(source duration)

à !

" ∼ $% &'/)

Allmann and Shearer (2009)

Circular rupture model

Circular rupture, constant rupture speed, final radius R. Only one characteristic time-scale: source duration ! ≈ 2$/&'

• corner frequency

(

) = +&'

$ ≈ 1/! where + is a factor of order 1 that depends mildly on rupture speed (+ = 0.44 for &' = 0.912).

• relation between stress drop and slip from elasticity theory:

Δ4 = 76 16 8 9 $

• definition of seismic moment :; = 896<=

à Corner frequency scaling (

) = +&' >? @ AB CD >/E

à estimate of stress drop: Δ4 =

@ >? F

G

HIJ E

:;

Rectangular rupture model

Rupture length L ≫ width W.

• Rupture duration controlled by the longest rupture dimension: "

# ∼ 1/' with ' = )/*+ .

• Elastic stiffness controlled by the shortest rupture dimension: Δ- ∼

. / 0

• Seismic moment: 12 = 304) ∼ Δ-45)

à corner frequency scaling "

# ∼ Δ-45*+×12 78

à estimate of stress drop Δ- ∼ 12"

#/45*+

A dependence of rupture aspect ratio on magnitude can break self-similarity and affect estimates of stress drop.

Spectra with two corner frequencies

Two time scales: à two corner frequencies: Total rupture duration !

"#$ = &/("

)

* = 1/! "#$

Local slip duration, rise time !

",-

)

. = 1/! ",-

)

*

)

.

Haskell’s model, unilateral pulse-like rupture

Radiated energy

Radiated energy

Bostock et al (2017)

Energy radiated to the far-field: ! ∝ ∫ ̇ %('))*' ! ∝ ∫ ̇ %(+))*+ … integrated over a far-field sphere Observational challenges:

• attenuation
• incomplete coverage of take-off angles
• interference between depth phases

Radiated energy

Energy radiated to the far-field: ! ∝ ∫ ̇ %&'( ∝ ̇ %& ) Self-similar model: Δ+ and ,- do not depend on earthquake size . /0 ∝ .1 ) ∝ . Far-field displacement and veocity: % ∝ ̇ /0 ∼ /0/) ∝ .&∝ /0

&/1

̇ % ∝ ̈ /0 ∼ /0/)& ∝ . ∝ /0

5/1

à Energy radiated to the far-field: ! ∝ ̇ %& ) ∝ /0 log50 ! = log50 /0 + ; Δ<, ,- + ⋯

Earthquake energy balance

!" ≠ !$

• vershoot/undershoot

Potential energy change = fracture energy + heat + radiated energy Δ& = ()* + , + -. Per unit of fault surface: 1 2 !1 + !" 2 = () + !$2 + -./* () = 1 2 !1 − !" 2 − -. * + !" − !$ 2 !$ !1 !5 () Heat ,/* D Potential energy Δ&/*

Seismological constraints

Gc inferred from radiated energy, seismic moment and corner frequency,

• r from finite source inversion

Viesca and Garagash (2015)

Fracture energy Slip

Seismological constraints

Gc inferred from radiated energy, seismic moment and corner frequency, or from finite source inversion Consistent with thermal pressurization weakening

Viesca and Garagash (2015)

Fracture energy Slip Hydrothermal diffusion Undrained- adiabatic ! = #(% − ')

Ve Velocity-an and-sl slip-de depende dent friction law: 4(6, 8) ∼ 4;< 6 6

=

4>? 8 8= 4<@ 8 8A Flash heating: 4;< B = 4A + 4E − 4A 1 + B Undrained-adiabatic thermal pressurization: 4>? B = exp −B Diffusion-dominated thermal pressurization: 4<@ B = 1/(1 + BP/Q)

Overview

Macroscopic source properties constrained by seismology:

• seismic moment
• source time function
• corner frequency
• radiated energy

à stress drop, rupture speed, rupture size