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: Kate.Robertson2@sa.gov.au

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.

DEM and the Crown in the right of the State of South Australia does not accept responsibility for and will not be held liable to any recipient of the information for any loss or damage however caused (including negligence) which may be directly or indirectly suffered as a consequence of use of these materials. DEM reserves the right to update, amend or supplement the information from time to time at its discretion.