Joint inversion of InSAR and broadband teleseismic waveform data with ABIC: application to the 1997 Manyi, Tibet earthquake

Transcription

1 Joint inversion of InSAR and broadband teleseismic waveform data with ABIC: application to the 1997 Manyi, Tibet earthquake Gareth Funning 1, Yukitoshi Fukahata 2, Yuji Yagi 3 & Barry Parsons 4 1 University of California, Berkeley, USA 2 University of Tokyo, Japan 3 University of Tsukuba, Japan 4 COMET, University of Oxford, UK

2 Overview Introduction Rationale for joint inversions The 1997 Manyi, Tibet earthquake Properties of the earthquake source model Inverting for source parameters with ABIC Brief description of the method InSAR-only, seismology-only and joint inversion results

3 Why attempt a joint inversion? InSAR has excellent spatial resolution (< 100 m) can map and model deformation in fine detail

4 Example: the Bam earthquake Deformation pattern consistent with slip on two parallel faults. Bam, Iran: track 385 (ascending), frame 0575 (detail) Funning et al., 2005, JGR

5 Why attempt a joint inversion? InSAR has excellent spatial resolution (< 100 m) can map deformation in fine detail but temporal resolution is poor ( 35 days) no information on timing.

6 Why attempt a joint inversion? InSAR has excellent spatial resolution (< 100 m) can map deformation in fine detail but temporal resolution is poor ( 35 days) no information on timing. Body wave seismology has good temporal resolution, and is also sensitive to location.

7 Deformation pattern consistent with slip on two parallel faults. Jackson et al., 2005, submitted to GJI

8 Deformation pattern consistent with slip on two parallel faults. Jackson et al., 2005, submitted to GJI

9 Why attempt a joint inversion? InSAR has excellent spatial resolution (< 100 m) can map deformation in fine detail but temporal resolution is poor ( 35 days) no information on timing or sequence of events. Body wave seismology has good temporal resolution, and is also sensitive to location. Aim is to generate a solution that is well constrained in space and time.

10 The 1997 Manyi, Tibet earthquake 11th November 1997, M w 7.5 largest event of that year Occurred in a remote area of N Tibet; no casualties reported, no field analysis. Ideal remote earthquake to study in this way both InSAR and seismology require no field visits.

11 The 1997 Manyi, Tibet earthquake 36 8th November 1997, M w 7.5 Aftershock pattern spans 3 satellite tracks 35 SRTM topography in 34 shaded relief

12 The 1997 Manyi, Tibet earthquake Peak LOS offset is 2.4 m ( 7 m of left-lateral offset)

13 Earthquake source model properties Define a fault geometry using the InSAR data.

14 The fault geometry Assumed fault geometry: Strike 258 Dip 90 Rake -5 Length 180 km Width 18 km 180 km 18 km (schematic)

15 The fault model Assumed fault geometry: Strike 258 Dip 90 Rake -5 Length 180 km Width 18 km 180 km Fault is divided into 6 6 km patches. 18 km (schematic)

16 Earthquake source model properties Define a fault geometry using the InSAR data. Define a source model with multiple time steps.

17 The source model The amount of slip is solved for at each of five time steps. t 1 t 2 Commencement of slip on each patch occurs after a rupture front has reached the patch. t 3 t 4 t 5 Each time step has a duration of 2 seconds. increasing time

18 Earthquake source model properties Define a fault geometry using the InSAR data. Define a source model with multiple time steps. Model must be smooth in space oscillations imply unphysical strains on the fault.

19 Spatial smoothing The total slip on a given patch a 1 a 4 a 7 a M a 2 a 5 a 8 a 3 a 6 a 9 (schematic)

20 Spatial smoothing The total slip on a given patch is related to that of patches adjacent to it, by a finitedifference Laplacian approximation. (a 2 a 5 ) (a 5 a 8 )+(a 4 a 5 ) (a 5 a 6 ) = 0 a 2 + a 4 4a 5 + a 6 + a 8 = 0 a 1 a 4 a 7 a 2 a 5 a 8 a M a 3 a 6 a 9 (schematic)

21 Earthquake source model properties Define a fault geometry using the InSAR data. Define a source model with multiple time steps. Model must be smooth in space oscillations imply unphysical strains on the fault Model must be smooth in time oscillations imply changes in acceleration.

22 Temporal smoothing The slip on a given patch, at a given time step t 2 a 95 (schematic)

23 Temporal smoothing The slip on a given patch, at a given time step t 1 t 2 a 5 is related to that for the same patch at the previous and subsequent time steps. a 95 a 185 t 3 increasing time (schematic)

24 Temporal smoothing The slip on a given patch, at a given time step is related to that for the same patch at the previous and subsequent time steps. a 5 a 95 a 185 t 1 t 2 t 3 Laplacian smoothing in 1D is used here (a 5 a 95 ) (a 95 a 185 ) = 0 a 5 2a 95 + a 185 = 0

25 Earthquake source model properties Define a fault geometry using the InSAR data. Define a source model with multiple time steps. Model must be smooth in space oscillations imply unphysical strains on the fault Model must be smooth in time oscillations imply changes in acceleration Model must also be consistent with the available data, of course

26 Inverting data using ABIC Akaike s Bayesian Information Criterion (Akaike, 1980) What level of resolution is appropriate, given the input data and fault geometry? Calculation of ABIC allows the optimal estimation of the relative weighting of different constraints on the inversion.

27 Inversions using ABIC Model, a, has two types of constraints: Observations: d = Ha + e o d = observed data H = data kernels a = fault slip e o = errors in observations Smoothing: Sa + e s = 0 Ta + e t = 0 S = 2D Laplacian operator e s = errors in smoothing T = 1D Laplacian operator e t = errors in smoothing

28 Inversions using ABIC Observation equation: Smoothing equations: d = Ha + e o Sa + e s = 0 Ta + e t = 0

29 Inversions using ABIC Data distribution: Prior distribution: p(d a;σ 2,γ 2 ) = (2πσ 2 ) -N/2 E -1/2 exp[-(1/2σ 2 )(d-ha) T E -1 (d-ha)] p(a;ρ s2, ρ t2 ) = (2π) -M/2 (1/ρ s2 )G s + (1/ρ t2 )G t 1/2 exp{-a T [(1/2ρ s2 )G s + (1/2ρ t2 )G t ]a}

30 Inversions using ABIC Data distribution: Prior distribution: p(d a;σ 2,γ 2 ) = (2πσ 2 ) -N/2 E -1/2 exp[-(1/2σ 2 )(d-ha) T E -1 (d-ha)] p(a;ρ s2,ρ t2 ) = (2π) -M/2 (1/ρ s2 )G s + (1/ρ t2 )G t 1/2 exp{-a T [(1/2ρ s2 )G s + (1/2ρ t2 )G t ]a} Combined (posterior) distribution: p(a;σ 2,α 2,β 2,γ 2 d) = cp(d a;σ 2,γ 2 ) p(a;ρ s2,ρ t2 )

31 Inversions using ABIC Data distribution: Prior distribution: p(d a;σ 2,γ 2 ) = (2πσ 2 ) -N/2 E -1/2 exp[-(1/2σ 2 )(d-ha) T E -1 (d-ha)] p(a;ρ s2,ρ t2 ) = (2π) -M/2 (1/ρ s2 )G s + (1/ρ t2 )G t 1/2 exp{-a T [(1/2ρ s2 )G s + (1/2ρ t2 )G t ]a} Combined (posterior) distribution: p(a;σ 2,α 2,β 2,γ 2 d) = cp(d a;σ 2,γ 2 ) p(a;ρ s2,ρ t2 ) ABIC: ABIC(α 2,β 2,γ 2 )= -2 log p(a;σ 2,α 2,β 2,γ 2 d) da

32 Inverting data using ABIC ABIC is a function of (in this case) up to three hyperparameters, α 2, β 2 and γ 2. Evaluate ABIC numerically for a range of values. The hyperparameter values that give a minimum are the optimum values. Recover best-fitting set of model parameters, a*, for each model, as part of this process.

33 Modelling the Manyi earthquake I calculate three models for the earthquake, using the ABIC technique: 1. InSAR data only 2. Seismic data only 3. Both datasets jointly In all cases I use the same simplified fault geometry

34 InSAR data inversion Simplest case 1 time step. No temporal smoothing. Only 1 hyperparameter α 2, the relative weighting of data and smoothing.

35 ABIC for the InSAR model Evaluate ABIC for a range of values of α 2 until a minimum is obtained

36 InSAR model results Majority of significant slip occurs in the upper 12 km of the fault

37 InSAR model fit to data Fit to data is reasonable for this very crude geometry.

38 Seismic data inversion 5 time steps, temporal smoothing is required. 2 hyperparameters α 2 and β 2, controlling spatial and temporal smoothing, respectively. Seismic kernels calculated by Yuji Yagi using the method of Kikuchi and Kanamori (1991).

39 Broadband teleseismic data Broadband vertical component data used from 10 GSN stations

40 Broadband teleseismic data 80 s time window, Band-pass filtered between 0.01 and 0.8 Hz Sample interval 0.25 s.

41 ABIC for the seismic model Minimum at α 2 = 0.008, β 2 =0.8, again obtained numerically

42 Seismic model results Greater slip in the lower 6 km of the fault, and less at the upper 6 km than for the InSAR model.

43 Fit to data of the seismic model The fit to the waveforms is generally good.

44 Fit to data of the seismic model Total slip gives a poor fit to the InSAR data

45 Joint inversion 5 time steps; temporal smoothing required. 3 hyperparameters α 2, β 2 and γ 2 controlling spatial smoothing, temporal smoothing and relative weighting of the datasets.

46 ABIC for the joint model Minimum at α 2 = , β 2 =0.0006, γ 2 =117

47 Joint model results Less slip in the lower 6 km than for the seismic-only inversion it is relocated to the surface.

48 Fit to data of the joint model Total slip gives a fit comparable to that for the InSAR-only inversion

49 Fit to data of the joint model The fit to the waveforms is very similar to that of the seismic-only inversion. (degradation of 2% in misfit)

50 Slip history of the Manyi earthquake

51 Comparison of model results InSAR Seis. Joint

52 Conclusions It is possible to find a solution with ABIC which satisfies both InSAR and seismic datasets. InSAR is the main control on the spatial location of slip, which occurred mainly at shallow depths. This is a viable technique to apply to other large continental earthquakes where near-source information is not available.

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