Probabilistic earthquake early warning in complex earth models using prior sampling Andrew Valentine, Paul Käufl &

Jeannot Trampert

EGU 2016 – 21st April

www.geo.uu.nl/~andrew

a.p.valentine@uu.nl

A case study: The Whittier and Chino faults

An ideal EEW source determination system…

Ø  Treats all physical effects properly, particularly: Ø  Complex wave propagation phenomena Ø  Strongly heterogeneous crustal structures

Ø  Operates in a probabilistic framework – includes full treatment of uncertainties

Ø  Has low computational costs during operation

Achieving any two of these is reasonably straightforward – but can we have all three?

Treating physical effects properly…

User Manual

COMPUTATIONAL INFRASTRUCTURE FOR GEODYNAMICS (CIG)

Version 3.0

PRINCETON UNIVERSITY (USA)CNRS and UNIVERSITY OF MARSEILLE (FRANCE) ETH ZÜRICH (SWITZERLAND)

SPECFEM 3DCartesian

g→

Ø  Full numerical regional wavefield simulations: SPECFEM 3D (e.g. Peter et al., GJI, 2011).

Ø  3D structural model for Southern California,

CVMH11.9 (Tape, Liu, Maggi & Tromp, Science, 2009).

Ø  Simulation cost: ~100 CPU hours/source

model that do not have a measurable travel-timedifference in the initial model (e.g., Fig. 1B).Thus, to facilitate a direct comparison between thetwo models, we compute a simple waveform dif-ference using the time windows that were se-lected for the final model for the 143 earthquakesused in the tomographic inversion (Fig. 3A).

We also consider a separate set of 91 earth-quakes that was not used in the tomographicinversion. An earthquake not used in the tomo-graphic inversion—or any future earthquake, forthat matter—may be used to independently as-sess the misfit reduction from m00 to m16. Thereduction in waveform difference misfit for theextra earthquakes is almost the same as it is forthe earthquakes used in the inversion (Fig. 3).This result provides validation for the tomographicmodel and suggests that future earthquakes willsee the same misfit reduction. We also computewaveform differences for the entire seismogram(Fig. 3, B and D), including information outsideour measurement windows. We observe a reduc-tion of misfit that is essentially the same for thetwo sets of earthquakes, and less than that ob-served for the individual windows.

The travel-time differences in the final modelhave a standard deviation of less than 1 s for theentire data set (fig. S4). In other words, given anadequate location, origin time, and focal mech-anism for any earthquake in southern Californiawith moment magnitude (Mw) between 3.5 and5.5, we expect most travel-time differences com-puted using our crustalmodel to be≤1 s for seismicrecords at periods of 2 to 30 s.

Our model shows reductions in wave speeddue to both compositional and thermal features.Consider the earthquake in Fig. 1A. Above thesource is the southern San Joaquin sedimentarybasin (22), and east of the Camp Rock fault (andnorth of 34.3°N) there is higher heat flow (25),likely related to Quaternary volcanism. West ofthe Camp Rock fault, slow wave speeds andhigh heat flow are not observed at the surface,

nor is volcanic activity. Horizontal cross sec-tions (Fig. 4) reveal lateral variations in the newcrustal model. At 2 km depth, large-scale slow(3.5 km/s) are in the Pe-ninsular Ranges west of the Elsinore fault and inthe Sierra Nevada west of the Kern Canyon fault(26). The eastern front of the Sierra Nevada ismarked by an eastward step in wave speed fromabout 3.5 to 2.8 km/s, and the Coso geothermalregion and the sedimentary fill in Owens Valleyand Indian Wells Valley account for the slowerwave speeds. We attribute the slow (2.9 km/s)wave speeds in the easternMojave to Quaternaryvolcanism.

At 10 km depth (Fig. 4), some of the basinsare no longer visible (e.g., Los Angeles and theSalton trough), and a striking pattern of wavespeeds west of the San Andreas fault is evident.The Peninsular Ranges and a mafic layer beneaththe Salton trough (27) form a fast (3.8 km/s) re-gion that is separated by the San Andreas faultfrom slower (3.4 km/s) regions to the northeast.

The 50-km scale variations in wave speedsalong the longitudinal line 119°W illuminate, fromnorth to south, the western Sierra Nevada (fast),the southern San Joaquin basin (slow), the SanEmigdio Mountains (fast), the Ventura basin(slow), the Santa Monica Mountains (fast), andthe Santa Monica basin (slow). Wave speeds inthe Coast Ranges are slowest (3.1 km/s) east ofthe San Andreas (28) and along the coast, and aresomewhat faster (3.4 km/s) in between, whereMesozoic granitic and sedimentary rocks are ex-posed at the surface. The northwestern Mojave isslow (3.3 km/s) compared with faster (3.6 km/s)material in the southern Sierra Nevada, across theGarlock fault.

At 20 km depth (Fig. 4), the most strikingfeature is the fast wave-speed (4.1 km/s) regionbeneath the Ventura–Santa Barbara basin and theSanta Monica Mountains, also observed in fig.

S10A. This region coincides with the surface ex-pression of the western Transverse Ranges block(WTRB) (fig. S1), bound to the north by theSanta Ynez fault and to the south by the MalibuCoast fault. We interpret this feature as subduction-captured Farallon oceanic crust, on top of which theWTRB rotated clockwise by more than 90° froma position near the Peninsular Ranges (3.8 km/s)(29). It is possible that the WTRB crustal anom-aly is related to upper-mantle anomalies observedbelow this region (30).

The heterogeneity in the crust (Fig. 4) stronglyinfluences seismic wave propagation from mod-erate earthquakes (Mw = 3.5 to 5.5), such as thosein this study. Using the new crustal model, wesimulated the details of earthquake ground mo-tion at periods of 2 s and longer for hundreds ofdifferent paths in southern California. By beginningto fit complex propagation paths for moderateearthquakes, we provide hope for accurately simu-lating larger—and damaging—earthquakes thatmay occur in the future (31). An improved crustalmodel will also enable better location of earth-quakes and identification of faults. Applied at thecrustal scale, spectral-element and adjoint meth-ods provide a valuable tool for improving seismichazard assessment.

References and Notes1. J. H. Woodhouse, A. M. Dziewonski, J. Geophys. Res. 89,

5953 (1984).2. B. Romanowicz, Annu. Rev. Earth Planet. Sci. 31, 303

(2003).3. S. P. Grand, R. D. van der Hilst, S. Widiyantoro, GSA Today

7 (no. 4), 1 (1997).4. R. Montelli et al., Science 303, 338 (2004).5. A. Dziewonski, D. Anderson, Phys Earth Planet Inter 25,

297 (1981).6. D. Komatitsch, J. Ritsema, J. Tromp, Science 298, 1737

(2002).7. V. Akçelik et al., Proc. ACM/IEEE Supercomputing SC2003

Conference (SC’03), 15 to 21 November 2003, Phoenix, AZ.8. P. Chen, L. Zhao, T. H. Jordan, Bull. Seismol. Soc. Am.

97, 1094 (2007).9. A. Fichtner, B. L. N. Kennett, H. Igel, H.-P. Bunge,

Geophys. J. Int. 175, 665 (2008).

−121˚ −120˚ −119˚ −118˚ −117˚ −116˚ −115˚

33˚

34˚

35˚

36˚

2.8 3.0 3.2 3.4 3.6 (3.10 ± 15 %)

Vs km/s

SA

SA

G

Depth = 2.0 km

−121˚ −120˚ −119˚ −118˚ −117˚ −116˚ −115˚

3.2 3.4 3.6 3.8 (3.50 ± 10 %)

Vs km/s

SA

SA

G

Depth = 10.0 km

−121˚ −120˚ −119˚ −118˚ −117˚ −116˚ −115˚

3.4 3.6 3.8 4.0 (3.67 ± 10 %)

Vs km/s

SA

SA

G

Depth = 20.0 km

Fig. 4. Horizontal cross sections of VS tomographic modelm16 at depths of 2, 10, and 20 km. See fig. S1 for locations of major features; Garlock (G) and SanAndreas (SA) faults are labeled for reference.

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An ideal EEW source determination system…

Ø  Treats all physical effects properly, particularly: Ø  Complex wave propagation phenomena Ø  Strongly heterogeneous crustal structures

Ø  Operates in a probabilistic framework – includes full treatment of uncertainties

Ø  Has low computational costs during operation

Achieving any two of these is reasonably straightforward – but can we have all three?

MCMC: ‘Posterior’ sampling

Sampling process cannot start until after observations have been made: infeasible for EEW scenarios

An alternative approach: ‘Prior sampling’

1.  Draw model parameter(s) at random from the prior distribution

2.  Compute synthetic data corresponding to

that model 3.  Add random noise chosen to represent

observational and modeling uncertainties

Joint data-model probability density function

Joint data-model probability density function

Learning a representation of the pdf

p(m|d0) =NX

i=1

↵i(d0) exp

� (m� µi(d0))

2

2�2i (d0)

!

Bishop, 1995. Neural networks for pattern recognition, OUP

How can we represent and store the joint distribution effectively? Ø Assume it to be smooth and continuous

Ø Represent 1D marginal distributions as Gaussian mixture models (GMMs)

Ø Coefficients of GMM are the outputs of a

neural network, called a ‘Mixture Density Network’ (MDN)

Prior sampling: Ø  Separates computationally-intensive sampling stage from time-critical

‘evaluation’ stage

Ø  Is highly inefficient for a single observation – but ideally-suited to a monitoring setting, where the same inverse problem must be solved repeatedly

Ø  Results in ‘conservative’ uncertainty estimates that could be reduced with more targeted sampling

‘Evaluation’ takes a fraction of a second!

Can we make sampling tractable for EEW?

Source parameters of interest: Ø  3 location parameters Ø  5 moment tensor components Ø  Source half-duration

9-dimensional model space

Number of samples required to achieve a given sampling density in D dimensions ~ exp(D)

Can we make sampling tractable for EEW?

Source parameters of interest: Ø  3 location parameters Ø  5 moment tensor components Ø  Source half-duration

9-dimensional model space

Strategy: 1.  Randomly sample locations; compute 6 Green’s

functions using SPECFEM3D 2.  Randomly sample moment tensors and source half-

durations at each location and construct seismograms

However: Point source seismogram can be expressed as linear combination of 6 independent Green’s functions:

s(M,x, t, ⌧,xc,�) = f(t, ⌧) ⇤

6X

i=1

Mi i(x, t,xc,�)!

Expensive sampling only needs to be done in 3 dimensions!

150 (≈ CPU allocation/(6*cost per simulation)) locations distributed randomly in box enclosing Whittier & Chino faults

Record wavefield at: Ø  1300 ‘real’ stations in Southern California, plus Ø Regular grid of 600 ‘virtual’ stations Simulate wave propagation for 200s after origin time, complete to 0.5Hz

33�N

34�N

35�N

36�N

122�W 121�W 120�W 119�W 118�W 117�W 116�W 115�W

Waveforms available for download (12Gb!): www.geo.uu.nl/~jeannot

With thanks to: ‘Cartesius’, the Dutch national supercomputer

Ø  From 150 sets of Green’s functions we generate ~2 million samples of (location, moment tensor, half duration, seismograms)

Ø Assume all source mechanisms are equally likely – but would be

straightforward to prefer alignment with fault

Ø Use only a small subset of stations; filter data at 0.2Hz

Ø Train learning algorithms to provide a smooth representation of the joint data-model distribution

Does it work? – Synthetic test

Ø Window starts when the first station ‘triggers’

Ø Wait t seconds and use recordings from all stations – some may not have recorded signal

Ø Each window length is implemented as a separate learning algorithm

�⇡/6 0 ⇡/6�

6s 15s 30s 45s

0.02 0.06 0.44 0.20

0 ⇡ 2⇡

(strike)

0.02 0.92 0.72 0.78

�⇡/2 0 ⇡/2� (rake)

0.10 0.28 0.63 0.56

0 0.5 1

h (cos(dip))

0.06 0.02 0.24 0.03

5 6.5 8Mw

1.74 2.04 2.81 2.55

1.5 10.75 20

depth [km]

0.24 0.30 0.81 0.86

33.79 33.92 34.05

lat [�]

0.92 1.57 1.80 1.71

�118.05 -117.81 �117.57lon [�]

0.85 1.82 1.94 1.86

0 5 10

⌧ [s]

1.63 1.66 1.87 1.87

Synthetic test

�⇡/6 0 ⇡/6�

6s 15s 30s 45s

0.02 0.06 0.44 0.20

0 ⇡ 2⇡

(strike)

0.02 0.92 0.72 0.78

�⇡/2 0 ⇡/2� (rake)

0.10 0.28 0.63 0.56

0 0.5 1

h (cos(dip))

0.06 0.02 0.24 0.03

5 6.5 8Mw

1.74 2.04 2.81 2.55

1.5 10.75 20

depth [km]

0.24 0.30 0.81 0.86

33.79 33.92 34.05

lat [�]

0.92 1.57 1.80 1.71

�118.05 -117.81 �117.57lon [�]

0.85 1.82 1.94 1.86

0 5 10

⌧ [s]

1.63 1.66 1.87 1.87

Synthetic test

Does it work? – Synthetic test

�⇡/6 0 ⇡/6�

6s 15s 30s 45s

0.02 0.06 0.44 0.20

0 ⇡ 2⇡

(strike)

0.02 0.92 0.72 0.78

�⇡/2 0 ⇡/2� (rake)

0.10 0.28 0.63 0.56

0 0.5 1

h (cos(dip))

0.06 0.02 0.24 0.03

5 6.5 8Mw

1.74 2.04 2.81 2.55

1.5 10.75 20

depth [km]

0.24 0.30 0.81 0.86

33.79 33.92 34.05

lat [�]

0.92 1.57 1.80 1.71

�118.05 -117.81 �117.57lon [�]

0.85 1.82 1.94 1.86

0 5 10

⌧ [s]

1.63 1.66 1.87 1.87

Synthetic test

Does it work? – Mw 5.4, Chino Hills, 2008

�⇡/6 0 ⇡/6�

USGS CMT USGS BW GCMT SCSN SCSN DC Hauksson

0.01 0.09 0.37 0.40

0 ⇡ 2⇡

(strike)

0.18 0.41 0.83 0.70

�⇡/2 0 ⇡/2� (rake)

0.07 0.12 0.12 0.38

0 0.5 1

h (cos(dip))

0.02 0.01 0.09 0.07

5 6.5 8Mw

1.66 1.89 2.38 2.76

1.5 10.75 20

depth [km]

0.23 0.68 0.79 1.13

33.79 33.92 34.05

lat [�]

0.82 1.41 1.45 1.35

�118.05 -117.81 �117.57lon [�]

0.88 1.38 1.77 1.73

0 5 10

⌧ [s]

1.46 1.64 1.70 1.80

2008 Mw 5.4 Chino Hills

Should we bother with the source at all?

If we have seismic observations at 10 randomly-chosen locations, what can we say about regional peak ground acceleration?

Inputs to system: Ø  N receiver locations Ø  N seismograms, at those locations Ø  Point(s) at which PGA estimation is desired

Output:

P�log10 (PGA)

��d1, . . . ,dN ,x1, . . .xN

�

�T

=4s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

0.00.51.01.52.02.53.03.5

�T

=6s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345

�T

=8s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345

�T

=10

s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345

�T

=20

s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345678

�6.4 �6.0 �5.6 �5.2 �4.8 �4.4 �4.0 �3.6log(PGD [m])

1.0 1.2 1.4 1.6 1.8 2.0 2.2� [log(PGD [m])]

�T

=4s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

0.00.51.01.52.02.53.03.5

�T

=6s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345

�T

=8s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345

�T

=10

s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345

�T

=20

s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345678

�6.4 �6.0 �5.6 �5.2 �4.8 �4.4 �4.0 �3.6log(PGD [m])

1.0 1.2 1.4 1.6 1.8 2.0 2.2� [log(PGD [m])]

�T

=4s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

0.00.51.01.52.02.53.03.5

�T

=6s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345

�T

=8s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345

�T

=10

s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345

�T

=20

s

32�N

33�N

34�N

118�W 116�W32�N

33�N

34�N

118�W 116�W �10 �8 �6 �4 �2 0log(PGD [m])

012345678

�6.4 �6.0 �5.6 �5.2 �4.8 �4.4 �4.0 �3.6log(PGD [m])

1.0 1.2 1.4 1.6 1.8 2.0 2.2� [log(PGD [m])]

Summary

Ø  By making use of learning algorithms in a ‘prior sampling’ framework, EEW results can be made available within milliseconds.

Ø  It is becoming feasible to take advantage of state-of-the-art numerical wave propagation codes and heterogeneous 3D crustal models

Ø  The approach can be extended to allow direct inversion for almost any

quantity of interest

a.p.valentine@uu.nl www.geo.uu.nl/~andrew

Waveform database: Ø  Download from www.geo.uu.nl/~jeannot References: Ø Käufl, Valentine, de Wit & Trampert, BSSA, 2015. (Waveform inversion) Ø Käufl, Valentine, de Wit & Trampert, GJI, in press. (Prior sampling) Ø Käufl, Valentine & Trampert, in prep. (EEW in 3D media)