Faulting from First Principles
Gregory C. BerozaStanford University
2012 IRIS Workshop - Boise, Idaho - June 13-15
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
Dynamic Effects of Geometry
Kozdon and Dunham (2012)
Geometry has a strong influence on dynamics – hanging-‐wall effect
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.
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
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
The Dark Ages: Richter “Reading” a Seismogram
Gerber variable scale (adjustable ruler) used to measure >me precisely.
Seismographic Network to Detect and Locate Earthquakes
Measuring arrival >mes at mul>ple sta>ons to locate earthquakes.
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)
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
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!
40 samples per second6 seconds per correlaLon4.8 x 102 floaLng point ops per correlaLon
Good luck Charlie!
Templates: Scale of the Problem
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
10 lags per second86,400 seconds/day365 days/year10 years digital dataN = 10*86,400*365*10 = 3.1 x 1010 correlaLons
60 channel seismic network
Good luck Charlie!
Templates: Scale of the Problem
~1015 opera>ons per template
40 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
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.
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
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
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
Good luck Charlie!
Scale of the Problem
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 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 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)
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
Fiducial network that spans t1 and t2
R1 R2
(Ma and Beroza, 2012)
Retrieving Green’s FuncLons from Asynchronous Data
R3-‐R1
R3
Fiducial network that spans t1 and t2
R1 R2
(Ma and Beroza, 2012)
Retrieving Green’s FuncLons from Asynchronous Data
R3-‐R1R3-‐R2
R3
Fiducial network that spans t1 and t2
R1 R2
(Ma and Beroza, 2012)
Retrieving Green’s FuncLons from Asynchronous Data
R1-‐R2
R3-‐R1R3-‐R2
R3
Fiducial network that spans t1 and t2
R1 R2
(Ma and Beroza, 2012)
Comparison of Synchronous and Asynchronous Green’s Func+onsR1: ADOR2:
Black: 1-‐yr noise GF Red: coda GF (Ma and Beroza, 2012)