Bayesian ISOLA: new tool for automated centroid moment tensor inversion

Transcription

1 Bayesian ISOLA: new tool for automated centroid moment tensor inversion A CMT catalog automatically generated for Swiss data Jiří Vackář 1,2 Jan Burjánek 2 František Gallovič 1 Jiří Zahradník 1 John Clinton 3 1 Charles University in Prague 2 Czech Academy of Sciences 3 SED, ETH Zurich February 21, 2017

2 Index 1 Introduction 2 Bayesian formulation of mixed linear non-linear problem 3 Data covariance matrix 4 Synthetic tests 5 Comparison with Swiss MT catalog 6 Software 7 Conclusions

3 Aim of the project Main goals Bayesian method for centroid moment tensor (CMT) solution Open-source code solving the problem automatically Designed for Near real-time data flow processing Processing existing datasets into moment-tensor catalogs

4 Aim of the project Main goals Bayesian method for centroid moment tensor (CMT) solution Open-source code solving the problem automatically Designed for Near real-time data flow processing Processing existing datasets into moment-tensor catalogs

5 Brief history since 2012 PhD in Prague: Automated determination of earthquake source parameters 2015 SCIEX in ZH: Automated moment tensor inversion code 2016 paper under revision: Bayesian ISOLA: new tool for automated centroid moment tensor inversion 2016 stable version of the code 2017 PhD defence (hopefully)

6 Index 1 Introduction 2 Bayesian formulation of mixed linear non-linear problem 3 Data covariance matrix 4 Synthetic tests 5 Comparison with Swiss MT catalog 6 Software 7 Conclusions

7 Bayesian formulation Applied to many problems in seismology: MT inversion from W-phase [Duputel et al., 2012] CMT inversion [Mustać and Tkalčić, 2016] finite fault (slip) inversion [Minson et al., 2013] see floor dislocation (tsunami source) [Dettmer et al., 2016] Different approaches: Analytical solution (MT with known STF linear problem) Stochastic search (CMT non-linear problem)

8 Bayesian formulation our approach CMT problem linear in MT components (6 variables) but non-linear in centroid position and time (4 variables) Grid search over space and time Least-square solution of MT components in each grid point

9 Bayesian formulation our approach CMT problem linear in MT components (6 variables) but non-linear in centroid position and time (4 variables) Grid search over space and time Least-square solution of MT components in each grid point

10 Least-square solution in a grid point Solution in a grid point i (x i, y i, z i, t i ) Inverse problem with no a priori information [Tarantola, 2005]: ( ) 1 m = G T 1 C D G G T 1 C D dobs model parameters (result) data vector forward problem matrix (Green s functions) data covariance matrix

11 Least-square solution in a grid point Solution in a grid point i (x i, y i, z i, t i ) ( m i = G T i C 1 D G i ) 1 G T i C 1 D d obs, (1) Uncertainties given by model parameters covariance matrix C M i ( 1 C M i = G T i C 1 D i) G. (2) The misfit value misfit i = ( ) T d obs G i m i C 1 ( ) D dobs G i m i. (3)

12 Putting PPD in grid-points together Posterior probability density (PPD) integrated over all MT parameters in a given space-time grid point i c i = 1 ( (2π) c 6 det C M i exp 1 ) 2 misfit i. (4) To visualize, we generate c i random samples from a multivariate normal (Gaussian) distribution (numpy.random.multivariate normal) in each grid point

13 Putting PPD in grid-points together Posterior probability density (PPD) integrated over all MT parameters in a given space-time grid point i c i = 1 ( (2π) c 6 det C M i exp 1 ) 2 misfit i. (4) To visualize, we generate c i random samples from a multivariate normal (Gaussian) distribution (numpy.random.multivariate normal) in each grid point

14 Plotting uncertainty of the solution # of station noise strong weak weak DC uncert. CLVD %

15 Index 1 Introduction 2 Bayesian formulation of mixed linear non-linear problem 3 Data covariance matrix 4 Synthetic tests 5 Comparison with Swiss MT catalog 6 Software 7 Conclusions

16 Covariance matrix (to down-weight noisy data) Inverse problem with no a priori information [Tarantola, 2005]: m = ( G T C D 1 G ) 1 G T C D d obs (5) The data covariance matrix should reflect both theory and data errors: Green s function uncertainty Limitation of model parametrization Measuring errors Seismic noise Correlation of samples

17 Covariance matrix (to down-weight noisy data) Inverse problem with no a priori information [Tarantola, 2005]: m = ( G T C D 1 G ) 1 G T C D d obs (5) The data covariance matrix should reflect both theory and data errors: Green s function uncertainty Limitation of model parametrization Measuring errors Seismic noise Correlation of samples

18 Many approaches to deal with these errors... Noise, correlation of samples and mislocation estimation [Duputel et al., 2012] Hiearchical estimation of noise [Bodin et al., 2012; Dettmer et al., 2012] Green s function uncertainty [Hallo and Gallovič, 2016] Our assumption: Seismic noise is the most important source of the errors The data covariance matrix is calculated from auto-/crosscovariance of before-event noise. The data covariance matrix works as automated frequency filter and station weighting to emphasize the high-snr data.

19 Covariance matrix from before-event noise

20 Covariance matrix from before-event noise

21 Covariance matrix from before-event noise

22 Covariance matrix from before-event noise autocovariance

23 Covariance matrix from before-event noise autocovariance

24 Covariance matrix from before-event noise crosscovariance

25 Index 1 Introduction 2 Bayesian formulation of mixed linear non-linear problem 3 Data covariance matrix 4 Synthetic tests 5 Comparison with Swiss MT catalog 6 Software 7 Conclusions

26 White noise synthetic test true solution without C D noisy noisy noisy without C D

27 White noise synthetic test true solution without C D with C D noisy noisy noisy without C D with C D

28 White noise synthetic test true solution without C D with C D noisy downweighted noisy noisy downweighted downweighted without C D with C D with C D (filtered)

29 Color noise synthetic test true solution without C D without C D

30 Color noise synthetic test true solution without C D with C D without C D with C D

31 Color noise synthetic test true solution without C D with C D without C D with C D with C D (filtered)

32 Index 1 Introduction 2 Bayesian formulation of mixed linear non-linear problem 3 Data covariance matrix 4 Synthetic tests 5 Comparison with Swiss MT catalog 6 Software 7 Conclusions

33 Reference catalog Created manually by SCMTV module of SeisComP3

34 GIMEL OG02 BRANT CHMF RSL EMV TORNY AIGLE MRGE MTI02 BOURR REMY LSD SENIN RSP DIX OTER1 VANNI CIRO WIMIS LKBD BALST LAUCH TRAV KIZ EMBD SATI ROTHE EMMET MMK DAGMA SIMPL SULZ FIESA BERGE HASLI METMA ACB BFO GRIMS SLE BNALP ZUR MUO FUSIO NALPS EMING PIORA VARE WILA LLS GUT WALHA PANIX MUGIO SGT02 SGT03 SGT01 SGT05 SGT04 PLONS TUE VDL LIENZ MDI DAVA DAVOX BERNI UBR FUORN BRMO MOSI MABI SALO RETA FETA LUSI Automated solutions Analyzed 16 years of M > 3 events from Swiss Digital Seismic Network (113 events) km

35 Comparison between automated and manual processing Mostly good agreement, differences can be easily explained Quality comparable to manual processing Capable to invert slightly weaker events

36 Sargans, Switzerland M W = 3.7 EQ and its M W = 3.4 aftershock I main shock perfect agreement with manual solution aftershock no manual solution available

37 Sargans, Switzerland M W = 3.7 EQ and its M W = 3.4 aftershock II aftershock waveforms

38 Sargans, Switzerland M W = 3.7 EQ and its M W = 3.4 aftershock III aftershock waveforms: filtered by C D

39 Auto-generated HTML catalog

40 Index 1 Introduction 2 Bayesian formulation of mixed linear non-linear problem 3 Data covariance matrix 4 Synthetic tests 5 Comparison with Swiss MT catalog 6 Software 7 Conclusions

41 Main features Fully automated tool for CMT inversion. Besides previously mentioned features... Disturbance detection: MouseTrap code [Vackář et al., 2015] MT results accompanied by their uncertainties Rich graphic output: optional visual inspection

42 Main features Fully automated tool for CMT inversion. Besides previously mentioned features... Disturbance detection: MouseTrap code [Vackář et al., 2015] MT results accompanied by their uncertainties Rich graphic output: optional visual inspection

43 Main features Fully automated tool for CMT inversion. Besides previously mentioned features... Disturbance detection: MouseTrap code [Vackář et al., 2015] MT results accompanied by their uncertainties Rich graphic output: optional visual inspection

44 Main features Fully automated tool for CMT inversion. Besides previously mentioned features... Disturbance detection: MouseTrap code [Vackář et al., 2015] MT results accompanied by their uncertainties Rich graphic output: optional visual inspection

45 Technical solution multiprocessing, pyproj (geodetics), psycopg2 (PostgreSQL) Green s functions: AXITRA [Bouchon and Coutant, 1994]

46 Availability ISOLA-ObsPy code: open-source (GNU/GPL licence) vackar/isola-obspy/

47 Index 1 Introduction 2 Bayesian formulation of mixed linear non-linear problem 3 Data covariance matrix 4 Synthetic tests 5 Comparison with Swiss MT catalog 6 Software 7 Conclusions

48 Conclusions New method and code for automated centroid moment tensor (CMT) inversion developed Bayesian approach is used: we get the posterior probability density function Data covariance matrix calculated from before-event noise It works as an automated frequency filter and station weighting according to the noise level A space-time grid search combined with the least-squares inversion speeds up the inversion Tested against 16 years of manually processed MT data from Swiss Seismic Network Quality of the results careful manual processing Can be used for everyday data processing vackar/isola-obspy/

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