Teleseismic surface wave tomography
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Transcript of Teleseismic surface wave tomography
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From data to model: how should we handle uncertainties in a chain mixing model and data
uncertainty?
Helle A. Pedersen and Gwenaelle SalaunISTERRE, University of Grenoble and CNRS
Presentation based mainly on results from the Simbaad experiment: A. Paul, H. Karabulut, D. Hatzfeld, C. Papazachos, D. M.
Childs, C. Pequegnat and Simbaad Teamas well as close collaboration with:
V. Farra, M. Bruneton, S. Fishwick, D. Snyder, and others
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Teleseismic surface wave tomography• Give me an array of stations
• Give me recordings of distant seismic events
• I will give you the (=some) model of Vs(x,y,z)
• Can I give you a sensible estimate of the error on Vs(x,y,z)?
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What we do• Preprocessing
• At each frequency:• Measure time delays between pairs of stations• Invert for phase velocity maps C(x,y)
• Assemble phase velocities to obtain C(x,y,period)
• For each grid point, invert for Vs(z)
• Assemble shear wave profiles to obtain Vs(x,y,z)
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Teleseismic surface wave tomography – different types of difficulties
1) Input data : data quantity and uncertainty
2) Out of array propagation : simplistic models of the incoming waves
3) Propagation effects inside the array: simplistic theory
4) Phase velocity uncertainty: resolution issue
5) Depth inversions uncertainty: resolution issue
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Data quality
Data heterogeneity is the norm rather than the exception
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Data quality
Data heterogeneity is the norm rather than the exception
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Data quality
1) Input data : data quantity and uncertainty – what can we reasonably do
• Available events : long recording period (2 years)
• Signal to noise ratio of signals : strict quality control and rejection of faulty signals …but choices remain subjective
• Systematic errors (glitches, mass centerings, …): we pick up automatically as much as possible, but not all is visible after preprocessing
• Timing errors : regular checks on P-wave arrivals (but what about small and/or random errors?).
• Errors in metadata (instrument response) : big effort => OK phases, amplitudes within ±30% (!)
A thorough (but is it satisfying?) analysis of remaining time delay errors
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Data quality
Question:
Can we assume that the remaining data errors follow a normal distribution?
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Out of array propagation : great-circle deviation
Maupin, GJI 2011
• Major deterministic diffractions : systematic effects• Multiple diffraction and coda• Presence of higher modes (and body waves)• Great-circle deviation• Finite frequency effects
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Out of array propagation : great-circle deviation
Maupin, GJI 2011
50s 25s
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Out of array propagation : finite frequency effects
Zhou, Dahlen and Nolet, GJI 2004 (Born)
100s Love wave, phase and arrival angle kernels 100s Rayleigh wave, phase kernel
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Chevrot and Zhao, GJI 2007
100s & 150km depth
Out of array propagation : finite frequency effects
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Out of array effects
Actions:- Carry out frequency-time filtering - Allow for great circle deviation- Allow for non plane wavefronts
Bruneton et al., GJI, 2002
Question:
Can we create a model of the errors associated with our approximations on wave propagation?
Is it enough to have sensible ‘garbage parameters’ to avoid to project out of array effects into the model?
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Snieder, GJRaS, 1986
Scattering by a mountain root Phase velocity at T=50s observed across a circular heterogeneity of 40 km diameter
Bodin and Maupin, GJI, 2008
Inside array propagation : possible to extract useful information from fundamental mode Rayleigh waves using strong approximations
(no scattering, no finite frequency effects)
R->R
R->L
L->L
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Phase velocity maps and uncertainty
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Without oceanic slab
With oceanic slab
Phase velocity maps and uncertainty: data distribution
Example from teleseismic P wave tomography
But we are fine – aren’t we?
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Phase velocity uncertainty: data distribution
With back azimuth weighting
Without back azimuth weighting
Input
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Phase velocity uncertainty: a posteriori error maps (of last inversion step)
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Questions:
1) Simple, objective tools for regularisation?
2) How can we develop tools to better assess the impact of input data weighting?
Phase velocity uncertainty
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Vs(z) uncertainty
- Smooth over depth (correlation length)
- Importance of interfaces
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Vs(x,y,z) uncertainty
Questions: 1) Laterally varying depth smoothing? On which criteria?2) Usual resolution issues
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Putting the pieces together again
Data processing and delay measurementsEstimate of measurement error (Gaussian?)
Iterative inversion for phase velocity mapsResolution : managed, but partly unsatisfactory trade-off between spatial resolution and parameter resolution
Iterative inversion for Vs(z)Resolution: managed, but partly unsatisfactory trade-off between spatial resolution and parameter resolution
Ignored out of array effects
Ignored inside array effects
?
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Going back to where we started• Give me an array of stations• Give me recordings of distant seismic events• I will give you the (=some) model of Vs(x,y,z)• It is possible to give you some estimate of the error on Vs(x,y,z)
BUT• All this careful work boils down to: which features of the model are resolved –
and our tools for error analysis may not be adequate• Many open issues, forcing us to make conservative choices at each step, thereby
reducing vertical and lateral resolution
• What we need is the uncertainty estimate on parameters of our interpretation, not the uncertainty on the parameters themselves• We therefore have got a strong communication problem of error issues towards
the end-users (geology/tectonics)
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What do end users do to the output models?
Dipping slab beneith Anatolia (?)
Top of slab geometry
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What I would like to learn?
What I am expecting from uncertainty analysis:• Estimate of the probability function of parameters relating to the interpretation• Tools for others to estimate the probability function of their interpretation• Tools to decide how to decrease uncertainties : where will an effort (data,
physics, inversion) be the most efficient?
Can statistical analysis alone solve these issues?• Can we create a library synthetic seismograms for different test structures and
array geometries?• Such a library must make us able to use different analysis techniques• Which hypothesis can we sensibly test?• How can such a library be hypothesis driven (?)• How can we create models of data uncertainty?