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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?