Bayesian ISOLA: new tool for automated centroid moment tensor inversion Jiří Vackář 1,2,3 Jan Burjánek 1,3 František Gallovič 2 Jiří Zahradník 2 1 Swiss Seismological Service, ETH Zurich 2 Charles University in Prague 3 Czech Academy of Sciences September 5, 2016
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
Goals of the project Bayesian method for centroid moment tensor (CMT) solution Open-source code solving the problem automatically
Applications (Near) real-time data flow processing Processing existing datasets into moment-tensor catalogs
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
Bayesian formulation 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
Bayesian formulation 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
Bayesian formulation 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
Bayesian formulation 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
Least-square solution of a linear problem 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
Least-square solution of a linear problem 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
Least-square solution of a linear problem Inverse problem with no a priori information [Tarantola, 2005]: ( ) m = G T 1 1 C D G G T 1 C D dobs model parameters (result) data vector forward problem matrix (Green s functions) data covariance matrix
Least-square solution of a linear problem Inverse problem with no a priori information [Tarantola, 2005]: ( ) 1 m = G T C 1 D G G T C 1 D d obs model parameters (result) data vector forward problem matrix (Green s functions) data covariance matrix
Putting PPD in grid-points together 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) 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: mean m i and covariance matrix C M i (determined in Eqs. 1 and 2).
Plotting uncertainty of the solution # of station 3 3 8 noise strong weak weak DC uncert. CLVD %
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
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) Assumption: Seismic noise is the most important source of the errors 1 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. 1 Green s function modeling error can be incorporated; see talk by Hallo and Gallovič
Covariance matrix from before-event noise
Covariance matrix from before-event noise
Covariance matrix from before-event noise
Covariance matrix from before-event noise autocovariance
Covariance matrix from before-event noise autocovariance
Covariance matrix from before-event noise crosscovariance
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
White noise synthetic test true solution without C D noisy noisy noisy without C D
White noise synthetic test true solution without C D with C D noisy noisy noisy without C D with C D
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)
Color noise synthetic test true solution without C D without C D
Color noise synthetic test true solution without C D with C D without C D with C D
Color noise synthetic test true solution without C D with C D without C D with C D with C D (filtered)
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
Reference catalog Created manually by SCMTV module of SeisComP3
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) 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 48 48 47.5 47.5 47 47 46.5 46.5 46 46 45.5 45.5 km 0 100 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11
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
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
Main features Fully automated MT solution Scalable and universal (local regional events) Disturbance detection: MouseTrap code [Vackář et al., 2015] The C D serves as an automated objective data weighting/filtering according to the noise level/spectrum MT results accompanied by their uncertainties Rich graphic output: optional visual inspection Tested on both synthetic and real data
Main features Fully automated MT solution Scalable and universal (local regional events) Disturbance detection: MouseTrap code [Vackář et al., 2015] The C D serves as an automated objective data weighting/filtering according to the noise level/spectrum MT results accompanied by their uncertainties Rich graphic output: optional visual inspection Tested on both synthetic and real data
Main features Fully automated MT solution Scalable and universal (local regional events) Disturbance detection: MouseTrap code [Vackář et al., 2015] The C D serves as an automated objective data weighting/filtering according to the noise level/spectrum MT results accompanied by their uncertainties Rich graphic output: optional visual inspection Tested on both synthetic and real data
Main features Fully automated MT solution Scalable and universal (local regional events) Disturbance detection: MouseTrap code [Vackář et al., 2015] The C D serves as an automated objective data weighting/filtering according to the noise level/spectrum MT results accompanied by their uncertainties Rich graphic output: optional visual inspection Tested on both synthetic and real data
Main features Fully automated MT solution Scalable and universal (local regional events) Disturbance detection: MouseTrap code [Vackář et al., 2015] The C D serves as an automated objective data weighting/filtering according to the noise level/spectrum MT results accompanied by their uncertainties Rich graphic output: optional visual inspection Tested on both synthetic and real data
Main features Fully automated MT solution Scalable and universal (local regional events) Disturbance detection: MouseTrap code [Vackář et al., 2015] The C D serves as an automated objective data weighting/filtering according to the noise level/spectrum MT results accompanied by their uncertainties Rich graphic output: optional visual inspection Tested on both synthetic and real data
Main features Fully automated MT solution Scalable and universal (local regional events) Disturbance detection: MouseTrap code [Vackář et al., 2015] The C D serves as an automated objective data weighting/filtering according to the noise level/spectrum MT results accompanied by their uncertainties Rich graphic output: optional visual inspection Tested on both synthetic and real data
Technical solution multiprocessing, pyproj (geodetics), psycopg2 (PostgreSQL) Green s functions: AXITRA [Bouchon and Coutant, 1994]
Availability ISOLA-ObsPy code: open-source (GNU/GPL licence) http://geo.mff.cuni.cz/ vackar/isola-obspy/
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
Conclusions We developed a new method and code for automated centroid moment tensor (CMT) inversion Detection of disturbances 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 http://geo.mff.cuni.cz/ vackar/isola-obspy/
Conclusions We developed a new method and code for automated centroid moment tensor (CMT) inversion Detection of disturbances 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 http://geo.mff.cuni.cz/ vackar/isola-obspy/
Sargans, Switzerland M W = 3.7 EQ and its M W = 3.4 aftershock I main shock perfect agreement manual solution aftershock no manual solution available
Sargans, Switzerland M W = 3.7 EQ and its M W = 3.4 aftershock II aftershock waveforms
Sargans, Switzerland M W = 3.7 EQ and its M W = 3.4 aftershock III aftershock waveforms: filtered by C D