Improved Location Procedures at the International Seismological Centre

István Bondár

ESC 32nd General AssemblyMontpellier, September 6-10, 2010

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Outline• Motivation• Current ISC locator• Proposed ISC locator• Validation tests

• Relocation of ~7,000 GT0-5 events• Comparison with EHB

• Conclusions

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Motivation• Correlated travel-time prediction errors along similar ray paths introduce location bias and result in underestimated error ellipses

• Example: • The effect of USArray on event locations in South America• Without accounting for correlated errors, locations get worse!

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Current ISC Locator• ak135, P[g|b|n], S[g|b|n] up to 100º• Jeffrey’s uniform reduction algorithm

• Iterative reweighting, all phases are equal• Reidentifies phases in each iteration (S could become pP!)• Duplicates are explicitly down-weighted

• Uncertainties are scaled to 95% confidence level• Attempts free-depth solution and cycles through all reported hypocentres until a convergent solution is found

• If fails, fixes depth to that of the trial hypocentre• If fails, fixes depth to region-dependent default depth (10/35 km)

• Depth-phase depth solution is obtained by inverting pP-P times

• Network magnitude can be obtained from a single station magnitude; no magnitude uncertainties are calculated

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New ISC Locator• Uses all ak135 predicted phases (including depth phases) in location

• Ellipticity, elevation corrections• Bounce point and water depth corrections for depth phases

• Attempts free-depth solution only if there is depth resolution• Accounts for correlated model error structure • Obtains initial guess via neighbourhood algorithm search• Performs iterative linearized inversion using a priori estimate of data covariance matrix

• Scales uncertainties to 90% confidence level• Obtains depth-phase depth via depth-phase stacking• Provides robust network magnitude estimates with uncertainties

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Data Covariance MatrixWhen correlated errors are present, the data covariance matrix is no longer diagonal

The network covariance matrix accounts for correlated travel-time prediction errors due to similar ray paths

Estimated by an isotropic stationary variogram (Bondár and McLaughlin, 2009) derived from GT residuals

The a priori picking error variances add to the diagonalCD = CN + CR

)),((),( 2jisillN stastaji C

Generic variogram model

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Depth Resolution• Attempt free-depth solution if and only if there is depth resolution

• We have depth resolution if• There is a local network

• one or more defining stations within 0.2º• Or there are sufficient number of depth phases

• 5 or more defining depth phases reported by at least two agencies

• Or there are sufficient number of core reflections• 5 or more defining core reflections (PcP et al)

• Or there are sufficient number of local/near-regional S• 5 or more defining S and P pairs within 5º

• Otherwise fix the depth to regional default depth• Explosions are fixed to zero depth

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Neighbourhood Algorithm Grid Search• The prime location may or may not be close to the global optimum in the search space

• Reported hypocentres may exhibit a large scatter• Neighbourhood Algorithm (Sambridge and Kennett, 2001) to get an initial hypocentre

• Grid search around the median of reported hypocentre parameters• NA explores the search space and rapidly closes in on the global optimum

• Once close to the global minimum, we switch to the linearized inversion algorithm to obtain the final solution and formal uncertainties

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Location Algorithm•Minimize by solving –G is the design matrix containing the travel-time derivatives for an

event-station path, m is the model adjustment vector [Δx, Δy, Δz, ΔT]T and d is the vector of time residuals. –W is the projection matrix that orthogonalizes CD and projects

redundant observations into the null space (Bondár and McLaughlin, 2009).• The SVD of CD is • We keep only the first p largest eigenvalues from the eigenvalue spectrum

such that 95% of the total variance is explained. • This reduces the effective number of degrees of freedom of the data from N

to p, with N-p dimensions of null space.• Let then

•Solution via singular value decomposition

•A posteriori model covariance matrix

WdWGm

wwestTwwwwww dGmUΛVGdmG 111 ;; estjj mmm 1

GmdCGmd DT 1

TwwwDM VΛVGCGC

T 211

TDDDD VΛUC

95.0 N

i i

p

j j

TDpp BBCΛUB ,2/1 WddWGGUΛBW ww

Tpp ,;2/11

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Depth-phase Depth

Depth-phase stack (Murphy and Barker, 2006)

• Generate predicted moveout curves

• TTdepth-phase – TTfirstP

• Parametric on delta• Generate depth traces for each station

• Boxcar at the corresponding depth for the observed moveout

• The width of boxcar is the prior measurement error estimate

• Stack depth traces• Calculate median and SMAD

2001/01/28 17:15:27.363, 23.28, 70.04, 28.5

depdp=26.0 ± 8.9

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Validation Tests• Relocation of some 7,200 GT0-5 events

• Earthquakes and explosions• Some explosions are poorly recorded

• Mimic automatic ISC location• ISC associations• Use only reported hypocentres• Ignore GT, EHB and ISC hypocentres

• Cases• Baseline: current ISC locator (isc)• Independent errors, current ISC phases (ii)• Independent errors, all ak135 phases (ia)• Independent errors, all phases, grid search (iag)• Correlated errors, current ISC phases (ci)• Correlated errors, all ak135 phases (ca)• Correlated errors, all phases, grid search (cag)

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Explosions

• Abysmal coverage when correlated error structure is ignored

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Test Sites

• Correlated errors• Significant improvements in French Polynesia• Deterioration in Novaya Zemlya

• When the effect of conspiring stations is taken out, the poor ak135 regional TT predictions become apparent

• Grid search• Does a good job in rectifying poor initial

hypocentres

French PolynesiaLop Nor NTSSemipalatinsk

Novaya Zemlya

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GT5 Earthquakes (free-depth)

Improved locations, depth and OT

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GT5 Earthquakes (depth-phase depth)

Significant improvements in location, depth and OT

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Regional Default Depth• Get a reasonable default depth where there is seismicity

• First attempt:• 1x1 degree grid of EHB free-depth solutions

• Second attempt:• Improvements were shown for free-depth hypocentres of GT events with

the new locator• Relocated the entire ISC bulletin with the new locator• 0.5x0.5 degree grid from relocated free-depth solutions + EHB free-depth

and EHB reliable depth solutions (~800K events) • Otherwise use CRUST2.0

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GT5 Earthquakes (fixed depth)

• Default depth grid: version2 vs version1• Significant improvements in depth• Improvements in location w.r.t. EHB grid• Most of the events now have a default depth based on seismicity

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Effect of Correlated Errors

• Area of error ellipse does not vanish with increasing number of stations

• Actual coverage is maintained• Location and depth bias is

reduced for large number of stations

50% percentile

90% percentile

All events

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Comparison with EHB

• EHB earthquakes in IASPEI Reference Event List

• Overall improvements in location

• Depth estimation is consistent with EHB

• Results are comparable or better than EHB

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Conclusions• Accounting for correlated errors

• Provides honest ~85-90% actual coverage• Reduces location bias due to correlated travel-time

prediction errors• Improvements in location, depth and origin time for free-depth solutions are due to

• Using all phases (including depth phases) in location• Testing for depth resolution

• Default depth grid provides reasonable depth for fixed-depth earthquakes

• Initial guess by neighbourhood algorithm grid search • Crucial for poorly recorded events with unreliable

reported hypocentres• Location and depth accuracy is comparable to EHB