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Uncertainty and MT: Processing, inversion and interpretationKate Robertsonwith contributions from Stephan Thiel, Hoel Seille
Forum on the relevance of geophysicaluncertainty in exploration at the AEGC, Perth
2nd September, 2019
The Magnetotelluric Technique
𝐸𝐸𝑥𝑥 𝐸𝐸𝑦𝑦 =𝑍𝑍𝑥𝑥𝑥𝑥 𝑍𝑍𝑥𝑥𝑦𝑦𝑍𝑍𝑦𝑦𝑥𝑥 𝑍𝑍𝑦𝑦𝑦𝑦
𝐵𝐵𝑥𝑥𝐵𝐵𝑦𝑦
With an apparent resistivity 𝜌𝜌𝑎𝑎 and phase 𝜙𝜙
𝜌𝜌𝑎𝑎(𝜔𝜔) =1𝜇𝜇0𝜔𝜔
𝑍𝑍𝑖𝑖𝑖𝑖(𝜔𝜔) 2
𝜙𝜙𝑖𝑖𝑖𝑖(𝜔𝜔) = tan−1 𝑍𝑍𝑖𝑖𝑖𝑖(𝜔𝜔)
The MT method
interpretation
Some applications of MT
Processing
Processing (and acquisition)
• Careful acquisition can make processing (and inversion) easier/better
• Improving signal-to-noise ratios by:• Minimising noise sources (anthropological, geological)• Maximising signal (recording time; MT and AMT deadbands
(time of day), solar activity)• Keeping the ‘good’ data (subjective)• User errors (incorrect rotations, dipole lengths, calibrations etc)
• Need to consider the assignment of appropriate uncertainties to the data- used to weight data (or components) during inversion.
• Commonly the data weighting matrix is based upon the inverse of the error estimates of the measured data.
• Therefore, error estimates (and error floors) are as important as the actual data estimate and should not be applied blindly.
Processing (and acquisition)
Tietze 2015
MT processing workflow• Noise mitigation through:
• Remote reference processing (attenuate uncorrelated noise between local and remote sites)• Robust statistical estimation of the impedances
• However bias can still exist!• Assumptions made on the distribution of the data (Gaussian distribution,
stationarity of the signal, …) can sometimes be severely violated• With low signal-to-noise ratios, repeated measurements improve statistics but
do not remove the bias biased estimate with underestimated error!• Prior to modelling it is recommended to:
• Use different processing algorithms• Test different types of processing parameters (e.g. window length and shape) • Perform data pre-selection (time consuming)
Image courtesy of Alan Jones
MT processing workflow
a) MT data processing workflow
b) Processing results
𝐸𝐸𝑥𝑥𝑖𝑖 = 𝑍𝑍𝑥𝑥𝑥𝑥𝐵𝐵𝑥𝑥𝑖𝑖 + 𝑍𝑍𝑥𝑥𝑦𝑦𝐵𝐵𝑦𝑦𝑖𝑖 + 𝛿𝛿𝐸𝐸𝑥𝑥𝑖𝑖
𝐸𝐸𝑦𝑦𝑖𝑖 = 𝑍𝑍𝑦𝑦𝑥𝑥𝐵𝐵𝑥𝑥𝑖𝑖 + 𝑍𝑍𝑦𝑦𝑦𝑦𝐵𝐵𝑦𝑦𝑖𝑖 + 𝛿𝛿𝐸𝐸𝑦𝑦𝑖𝑖𝑍𝑍𝑥𝑥𝑦𝑦 =
𝐵𝐵𝑥𝑥𝐵𝐵𝑥𝑥∗ 𝐸𝐸𝑥𝑥𝐵𝐵𝑦𝑦∗ − 𝐵𝐵𝑥𝑥𝐵𝐵𝑦𝑦∗ 𝐸𝐸𝑥𝑥𝐵𝐵𝑥𝑥∗
𝐵𝐵𝑥𝑥𝐵𝐵𝑥𝑥∗ 𝐵𝐵𝑦𝑦𝐵𝐵𝑦𝑦∗ − 𝐵𝐵𝑥𝑥𝐵𝐵𝑦𝑦∗ 𝐵𝐵𝑦𝑦𝐵𝐵𝑥𝑥∗
Z + variance (EDI file)
and Sources of uncertainty
Windowing (non-stationarity?) Cross reference (coherent noise ?)
Robust statisticsPresence of EM noise (especially in dead bands)
adapted from (Myer et al., 2011)
Inversion
Inversion - What are we really modelling?
• Non-unique, under-parameterised problem• How do we find the best model? • Needs to be useful to the interpreter
‘All models are wrong, but some are useful’George E.P. Box
Inversion- General considerations
• Best fit does not mean geologically true model• Assumption on scalar vs anisotropic resistivity• Dimensionality consideration of your data (1D,2D,3D)• Have the data outliers been accounted for?• Data preparation, mesh design, model parameters• Trade-off between computational costs and image quality• Assignment of relative errors or error floors (propagation of noise amongst components)• Distortion (static shift accounted for)
Modelling issues: Distortion• Corrected prior to modelling? (Becken, strike, very short period correction or very long period correction from other data)
• Model within the inversion code (e.g. Avdeev, CGG)
• Phase tensor – unaffected by distortion Impedances
+ magnetic transfer functionsPhase tensors
+ magnetic transfer functions
K. Tietze, pers. Comm 2018
Inversion – Different codes, different models
• Miensopust 2013
Miensopust 2013
Inversion – 1D• Quick and simple probabilistic inversion codes available and regularly used to provide an
ensemble of solutions• Uncertainty is provided with these codes and good exploration of model space. But only useful if
actually 1D..
Inversion - 2D• Well-tested 2D inversion deterministic codes (a couple
of 2D anisotropy codes). • Probabilistic methods are computationally feasible but
not well used. • Dimensionality and strike considerations are important
for 2D profile data- is 2D appropriate?
An example of uncertainty analysis in 2D
Schnaidt & Heinson 2015
The transition from 2D to 3D
Inversion – 3D • Computationally expensive (probabilistic not
a reality) • Different codes can give different results
(and for 1D and 2D) • The absence of an equidistant site
distribution makes the 3-D inverse problem more unstable.
• 3D inversions do not strictly need to be rotated, as the full impedance tensor is inverted.
• 3D inversion of transects now common too (discretization problem)
Miensopaust 2018
The transition from 2D to 3D
• Profile of MT data where bright colours show 3D data (|skew| > 5)
• Technically shouldn’t be modelled using a 2D code)
• Can model profiles in 3D now, or collect in arrays3D 3D
1D or 2D
Image from Ben Kay
Exploring the search space (in a deterministic inversion scheme)
Bedrosian, P.A., et al (2018) Nature Geoscience, Janelle Simpson, pers. Comm 2018
Example of testing model paramaters: starting resistivity)Exploring the search space (in a deterministic inversion scheme)
Interpretation
How do we know which is the best?NOT from the global RMS…
Bedrosian, P.A., et al (2018) Nature Geoscience,
How do we know which is the best?
How do we know which is the best?• Global RMS NOT enough!
Mount St Helens example, Bedrosian et al 2018, supp. informatio
Interpreting the models
Averaged resistivity across the model region for different starting resistivity models
100
200
300
400
0
Dep
th (k
m)
104
103
102
10
1R
esistivity (Ωm
)
Interpreting the models
Water content (wt%)~0.001 wt%
~5 wt%
Two models that both fit the data can provide completely different water content estimates:
10 Ωm, RMS 1.17, 5wt%1000 Ωm, RMS 1.57, 0.001 wt%
10 Ωm starting
1000 Ωm starting
Summary• Processing – robust and reliable• Inversion –
• 1D good, uncertainty well defined. • 2D inversion codes good, probabilistic tools available,
not readily used. • 3D – less codes available, most room for improvement,
probabilistic not a reality• Interpretation – qualitative good, quantitative- more model
appraisal required.
ContactsDr Kate Robertson, Senior Geophysicist- Lithospheric Architecture
Department for Energy and Mining11 Waymouth StreetAdelaide, South Australia 5000GPO Box 320Adelaide, South Australia 5001E: [email protected]
DisclaimerThe information contained in this presentation has been compiled by the Department for Energy and Mining (DEM) and originates from a variety of sources. Although all reasonable care has been taken in the preparation and compilation of the information, it has been provided in good faith for general information only and does not purport to be professional advice. No warranty, express or implied, is given as to the completeness, correctness, accuracy, reliability or currency of the materials.
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