beroza_iris-faulting from first principles

Faulting from First Principles

Gregory C. BerozaStanford University

2012 IRIS Workshop - Boise, Idaho - June 13-15

Earthquakes as slip on planar faults

(Beroza and Spudich, 1988)

Back-Projection for Off-Sumatra Earthquake:Complex Geometry, Deep Centroid

Back-‐Projec+on Indicates 4 Faults Involved

(Ishii et al , 2005; Hutko, 2009)

(Meng et al, 2012)

Intermediate-Depth Earthquakes

Sub-‐Horizontal Faul+ng; Mul+ply-‐Connected Rupture; Dehydra+on EmbriGlement?

(Kiser et al, 2011)

Depth-Dependent Faulting

Lay et al. (2012)

Observed systema+cs of low-‐frequency vs. high-‐frequency radia+on

Depth-Dependent Faulting

Lay et al. (2012)

Inferred spa+al varia+on of fric+onal proper+es.

Dynamic Effects of Geometry

Kozdon and Dunham (2012)

Geometry has a strong influence on dynamics – hanging-‐wall effect

Effect of Plasticity

(Ma, 2012)

off-fault plastic strain

slip

velocity seismogram

fault friction

[Candela et al., 2009]

Self-similar surfaces, rough at all scales(0.1-1 km roughness wavelengths

1-10 Hz ground motion)

[Dunham et al., 2010]

Fault Geometry and High-Frequency Ground Motion

PGVPGA

NGA 2008 GMPEs

• Relates ground mo/on to magnitude and distance• Up to 19 predic/ve/descrip/ve parameters: site/soil condi/ons, depth to top of rupture, mechanism, geometry, hanging wall effect…• “Stress drop” assumed to decrease with earthquake size.

Stress Drop Variability

Baltay (2011)

Earthquake Scaling

Allman and Shearer (2009)

PGA Point Source Model

€

a(t) 2 dt−∞

∞

∫ =1

2π˜ a (ω) 2 dω

−∞

∞

∫

€

˜ a (ω) =Ωo(2πfc )2 and fc << fmax

Parseval’s Theorem

Following Hanks, [1979]

€

Δσ =106ρRΩo fc3Brune stress drop

€

aRMS =2Rθφ2(2π )2

106ΔσρR

fmaxfc

€

PGA = aRMS 2ln 2 fmaxfc

⎛

⎝ ⎜

⎞

⎠ ⎟

€

PGA =2Rθφ2(2π )2

106ΔσρR

fmaxfc

⎛

⎝ ⎜

⎞

⎠ ⎟ 2ln

2 fmaxfc

⎛

⎝ ⎜

⎞

⎠ ⎟

Random vibration theory[Vanmarcke and Lai, 1977]

Brune [1970] ω-2 spectrum

€

PGA =2.86Rθφ

2(2π )2

106Δσ 5 / 6

ρR βMo

1/ 6 fmax⎛

⎝ ⎜

⎞

⎠ ⎟ 2ln

2 fmax 8.47Mo( )1/ 3

Δσ1/ 3β

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

PGA Point Source Model

€

a(t) 2 dt−∞

∞

∫ =1

2π˜ a (ω) 2 dω

−∞

∞

∫

€

˜ a (ω) =Ωo(2πfc )2 and fc << fmax

Parseval’s Theorem

Following Hanks, [1979]

€

Δσ =106ρRΩo fc3Brune stress drop

€

aRMS =2Rθφ2(2π )2

106ΔσρR

fmaxfc

€

PGA = aRMS 2ln 2 fmaxfc

⎛

⎝ ⎜

⎞

⎠ ⎟

€

PGA =2Rθφ2(2π )2

106ΔσρR

fmaxfc

⎛

⎝ ⎜

⎞

⎠ ⎟ 2ln

2 fmaxfc

⎛

⎝ ⎜

⎞

⎠ ⎟

Random vibration theory[Vanmarcke and Lai, 1977]

Brune [1970] ω-2 spectrum

€

PGA ~ Mo1/ 5Δσ

Only nearest ~30 km of fault contributes to PGA

30 km/ 3 km/s = 10 s = 0.1 Hz

€

fc =Δσ8.5MO

⎛

⎝ ⎜

⎞

⎠ ⎟

13

β0.1 Hz = use Δσ=2.4 MPa à Mw 6.7

• SaturaLon effect at M 6.7, consistent with NGA• Simple source models match GMPEs well

PGA Model

Olsen et al. (2006)

Ground Motion Simulations Instead of Data

Olsen et al. (2006)

Ground Motion Simulations Instead of DataHow to Validate Simulations?

Olsen et al. (2006)

Deploy seismic stations

Wait for earthquake to test predictions

Ground Motion Simulations Instead of DataHow to Validate Simulations?

Olsen et al. (2006)

Ground Motion Simulations Instead of DataHow to Validate Simulations?Alternative: Validate Using Ambient-Field

Extract impulse response

Model extended-‐source response using the representaLon theorem

Weak coherent ambient seismic field recorded at

staLons

Convert surface impulse responseto buried double-‐couple response

Alternative: Ground Motion Simulation Validation with Ambient-Field

Ambient Noise Impulse Responses vs. Earthquake

Depth and Mechanism Correc>ons Improve the Fit

The Dark Ages: Richter “Reading” a Seismogram

Gerber variable scale (adjustable ruler) used to measure >me precisely.

Earthquake Seismogram

Seismographic Network to Detect and Locate Earthquakes

Measuring arrival >mes at mul>ple sta>ons to locate earthquakes.

Mul+ple Earthquakes

A`ershocks in New Zealand

STA/LTA Detector -‐ takes raLo of short-‐term average and long-‐term average signal -‐ maximized at/near the Lme of the first arrival.

Earle and Shearer (1994)

Earthquake Swarm

STA/LTA algorithms get overwhelmed when things get really acLve/interesLng.

The Cocktail Party Problem

The “cocktail party problem” refers to the quesLon of how people hear the person they are talking with, while ignoring simultaneous background conversaLons and noise.

“The Cocktail Party” by Alex Katz

Cholame Tremor

LFE Template

Shelly (2010)

Detec>on Algorithm is Powerful (few Type II errors)

LFEs embedded in data at snr of 0.1

34/36 are detected

Template detec+on allows us to “follow the conversa+on”

Shelly et al. (2007)

Cholame Tremor ~540,000 LFEs over 8.5 years in this small area.

~216,000 events in NCSN catalog during that +me.

Shelly (2009, 2010)5 years ago, few CA earthquakes were known deeper than 18 km.Now we have over half a million that are deeper in one locaJon!

Good luck Charlie!

Templates: Scale of the Problem

40 samples per second6 seconds per correlaLon4.8 x 102 floaLng point ops per correlaLon

Good luck Charlie!


Good luck Charlie!

Templates: Scale of the Problem40 samples per second6 seconds per correlaLon4.8 x 102 floaLng point ops per correlaLon

10 lags per second86,400 seconds/day365 days/year10 years digital dataN = 10*86,400*365*10 = 3.1 x 1010 correlaLons

Good luck Charlie!

Templates: Scale of the Problem40 samples per second6 seconds per correlaLon4.8 x 102 floaLng point ops per correlaLon


60 channel seismic network

Good luck Charlie!


~1015 opera>ons per template

40 samples per second6 seconds per correlaLon4.8 x 102 floaLng point ops per correlaLon


60 channel seismic network

What if we don’t have a template?

Example of “Blind Source Separa>on” (knowledge of source is limited)

Can s>ll use no>on of looking for similar events across the network.

Compare everything with everything else.

3 Hours of LFEs during tremor in the

Nankai Trough

Brown et al. (2009)

40 samples per second10 second correlaLon window8 x 102 floaLng point ops per correlaLon

10 lags per second86,400 seconds/day365 days/year10 years digital dataN = 10*86,400*365*10 = 3.1 x 1010 Lme windowsN(N-‐1)/2 = 5 x 1020 unique correlaLons

5 x 102 channel seismic network

Scale of the Problem





1026 opera>ons




Good luck Charlie!


1026 opera>ons

Being clever allows us to reduce by effort by orders of magnitude, but it’s s>ll computa>onally imposing.

We need to learn how to make lots of measurements(capacity) to exploit fully the wealth of data that new sensor technology will soon deliver.

Huge opportuni>es: earthquakes real-‐>me network seismology volcanoes geothermal shale gas other?

Scale/Poten+al of the Problem

Capability compu>ng. Use of most powerful supercomputers to solve the largest and most demanding problems. Main figure of merit is Lme to soluLon. A system is ohen dedicated to running one problem.

Capacity compu>ng. Use of smaller and less expensive high-‐performance systems to run parallel problems with more modest computaLonal requirements. Main figure of merit is the cost/performance raLo.

(Graham et al., 2005)

Earthquakes and 21st Century Low/No Carbon Energy Options

Earthquakes and Enhanced Geothermal

Earthquakes and Nuclear Power PlantsKashiwazaki Kariwa

Fukushima Daichi

Earthquakes and Hydro-Electric Power

Koyna Dam

1967 M 6.3 Koyna Earthquake

200 fatali+es

Gupta (2002)

Earthquakes and Shale Gas

The disposal of flowback water (not fracking) implicated in earthquake triggering. (Zoback, 2012)

Earthquakes and CO2 Sequestration

(Zoback and Gorelick, 2012)

Earthquakes Impact 21st Century Energy Options

Hydro-‐Electric Enhanced Geothermal Nuclear Shale Gas Carbon Dioxide SequestraLon

Conclusions

• Seismology is cri>cal to the future of civiliza>on.

• We have a lot of data, we will soon have a lot more. We need to think hard about how to use it. Doing so will allow us to see earthquakes, and Earth structure, much more clearly. HPC will be an important part of this.

• It is the best of >mes… to be a seismologist.

Greens func>ons between sta>ons opera>ng asynchronously can be recovered.

Red: recording at all LmesBlue: on at t1, off at t2Black: on at t2, off at t1

Poster #12 explores relevance of this for the 1 in 4 ini>a>ve.(Ma and Beroza, 2012)

Correla>on of Coda of Noise Correla>ons (C3)

(Stehly et al., 2008)

5 – 10 s

10 – 20 s

Stability of Virtual Coda for Periods 5 – 10 s

Black: GFs using data in January – June, 2007Blue: GFs using data in July – December, 2007 (Ma and Beroza, 2012)

Retrieving Green’s FuncLons from Asynchronous Data

R1 R2

(Ma and Beroza, 2012)


Fiducial network that spans t1 and t2

R1 R2



R3-‐R1

R3


R1 R2



R3-‐R1R3-‐R2

R3


R1 R2



R1-‐R2

R3-‐R1R3-‐R2

R3


R1 R2


52 fiducial staLons


Comparison of Synchronous and Asynchronous Green’s Func+onsR1: ADOR2:

Black: 1-‐yr noise GF Red: coda GF (Ma and Beroza, 2012)

Comparison of Synchronous and Asynchronous Green’s Func+ons

Mean correlaLoncoeff. 0.77




R1: ADOR2:

Black: 1-‐yr noise GF Red: coda GF (Ma and Beroza, 2012)

beroza_iris-faulting from first principles

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