Probabilistic earthquake early warning in complex earth models using prior sampling

Transcription

1 Probabilistic earthquake early warning in complex earth models using prior sampling Andrew Valentine, Paul Käufl & Jeannot Trampert EGU st April

2 A case study: The Whittier and Chino faults

3 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?

4 Treating physical effects properly COMPUTATIONAL INFRASTRUCTURE FOR GEODYNAMICS (CIG) PRINCETON UNIVERSITY (USA) CNRS and UNIVERSITY OF MARSEILLE (FRANCE) ETH ZÜRICH (SWITZERLAND) SPECFEM 3D Cartesian User Manual Version 3.0 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 REPORTS G 35 Depth = 10.0 km Depth = 20.0 km Vs km/s (3.10 ± 15 %) SA SA Depth = 2.0 km G G SA SA SA SA 36 Vs km/s (3.50 ± 10 %) Vs km/s (3.67 ± 10 %) Fig. 4. Horizontal cross sections of V tomographic model m at depths of 2, 10, and 20 km. See fig. S1 for locations of major features; Garlock (G) and San

5 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?

6 MCMC: Posterior sampling Sampling process cannot start until after observations have been made: infeasible for EEW scenarios

7 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

8 Joint data-model probability density function

9 Joint data-model probability density function

10 Learning a representation of the pdf 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) p(m d 0 )= NX i (d 0 )exp i=1! (m µ i (d 0 )) i (d 0) Bishop, Neural networks for pattern recognition, OUP

11 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!

12 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)

13 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 However: Point source seismogram can be expressed as linear combination of 6 independent Green s functions:! 6X s(m, x,t,, x c, )=f(t, ) M i i (x,t,x c, ) i=1 Expensive sampling only needs to be done in 3 dimensions! Strategy: 1. Randomly sample locations; compute 6 Green s functions using SPECFEM3D 2. Randomly sample moment tensors and source halfdurations at each location and construct seismograms

14 150 ( CPU allocation/(6*cost per simulation)) locations distributed randomly in box enclosing Whittier & Chino faults

15 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 Waveforms available for download (12Gb!): 36 N 35 N With thanks to: Cartesius, the Dutch national supercomputer 34 N 33 N 122 W 121 W 120 W 119 W 118 W 117 W 116 W 115 W

16 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

17 Does it work? Synthetic test Synthetic test 6s 15s 30s 45s apple (strike) 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

18 Does it work? Synthetic test Synthetic test 6s 15s 30s 45s /6 0 / apple (strike) /2 0 /2 (rake) h (cos(dip)) M w depth [km] lat [ ] lon [ ] [s]

19 Does it work? M w 5.4, Chino Hills, 2008 USGS CMT USGS BW GCMT SCSN SCSN DC Hauksson /6 0 / apple (strike) /2 0 /2 (rake) h (cos(dip)) M w depth [km] lat [ ] lon [ ] [s]

20 T = 10s T =8s 34 N Should we bother with the source at all? 33 N 33 N 5 log(pgd [m]) 1 If we have seismic observations at 10 randomly-chosen locations, 32 N 32 N what can we say about regional peak ground acceleration? W 118 W 116 W Inputs to system: log(pgd [m]) 34 N 34 N 34 N 34 5 N 5 Ø N receiver locations 4 4 Ø N seismograms, at those locations 3 3 Ø Point(s) at 33 which N 33PGA N estimation is desired 33 N 33 N Output: P 32 logn 10 (P32GA) N d 1,...,d N, x 1,...x N 32 N 32 0 N W W 116 W 118 W W W 116 W N 34 N 5 5 log(pgd 5 log(pgd [m]) log(pgd [m]) 34 4 N 34 4 N N 33 N 33 2 N 33 2 N W W 32 N 32 N 32 0 N 32 0 N W 118 W W W 116 W N 4 3 2

21 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 Waveform database: Ø Download from References: Ø Käufl, Valentine, de Wit & Trampert, BSSA, (Waveform inversion) Ø Käufl, Valentine, de Wit & Trampert, GJI, in press. (Prior sampling) Ø Käufl, Valentine & Trampert, in prep. (EEW in 3D media) a.p.valentine@uu.nl