... Razorback, an open source python library for magnetotelluric robust processing, in preparation. Image Project Final Conference, Akureyri, Iceland, 4-5/10/2017.
MT and CSEM data robust processing techniques. New developments. 1
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Pierre Wawrzyniak , Farid Smai , Mathieu Darnet , Nicolas Coppo , François 1 Bretaudeau 1
BRGM, 3 av ; Claude Guillemin, BP 36009, 45060 Orléans 7 Cedex2, France
matrix is enhanced to provide protection against leverage points.
Introduction An open source Python library, named Razorback, was developed for transfer function estimation in Magnetotellurics and Controlled Source Electromagnetism (CSEM). Combination of elementary bricks performs robust processing of transfer function estimates with standard leastsquare methods, M-estimator and Bounded Influence methods. Remote Reference processing is performed using the two stage method. After validation of the algorithm with Alan Chave’s Birrp code, we show a useful application of the code: testing all possible combination of Remote reference station in a synchronous MT array, from a survey executed in the framework of the Image Project. The Razorback library is available at:
Validation Comparison of Birrp and Razorback results using the same parameters for M-estimator and Bounded Influence (Single Site and Two-stage RR) for a set of 2 synchronous station on La Fournaise volcano (1-year of data, sampling 50 mHz). A deeper analysis of the data has been published in Wawrzyniak et al.,2017a;
Figure 5: Map of the MT stations deployed in the western side of Strasbourg. Black dots: complete station set. Red crosses: "local" station inserted in the Signal Set object
https://github.com/BRGM/razorback
MT Transfer Function Theory and Processing Methods
Figure 1: M-estimator results in SS (left side) and two-stage RR (right side). Comparison of estimated apparent resistivity and phases: a) crosses: Birrp code b) circles: Razorback.
MT Theory Assuming a set of N data (I.e. fourier transform of MT fields) at a fixed frequency, one component of the horizontal electric and magnetic field components are linked by a frequency domain relationship: e i = b · zi +
(1)
Where ei is a N vector; the index i can be either direction x or y, b is a Nx2 vector describing respectively one component of the horizontal electric field (the response) and the two components of the horizontal magnetic induction (the predictor ) , zi is the magnetotelluric impedance associated with the direction i of the electric field (vector of dimension 2), expressed in millivolts per km per nanotesla (mV/(Km ∗ nT )) and is the a vector of random errors. Computing MT impedance Z Computation Z is performed using a transfer function operator O, associated residuals are written ri: zi = O(ei, b) ,
ri = ei − b · z^i +
(2)
Two Stage Remote Reference Chave et al.,2004 introduced a generalization of this method to multiple remote reference data sets. Considering a set of q remote reference horizontal magnetic field reunited in one vector Q (size pX2), the local magnetic field is linked to Q by b=Q·W+
^ = O(b, Q) W
Figure 3: Bounded Influence results in SS (left side) and twostage RR (right side). Comparison of estimated apparent resistivity and phases: a) crosses: Birrp code b) circles: Razorback.
Figure 7: Upper: Phase tensor ellipses for any combinations of RR. Lower: Ellipticity gradient for combinations of RR.
(3)
where W is a TF between local and remote magnetic field sites. Let’s consider O the operator that estimate this TF. ^ is given by The predicted local magnetic field b ^ =Q·W ^ , b
Figure 2: M-estimator results in SS (left side) and two-stage RR (right side). Relative apparent resistivity difference and phase difference between Birrp and Razorback.
Figure 6: SITE 04 with local RR 2, 6, 9 and distant RR Welschbruch and Schwabwiller. Robust MT transfer function estimates for all possible combination of Remote Reference station. Left side: Apparent resistivity for xy, yx (from top to down). Right side: phase in degrees for xy, yx (from top to down).
Figure 4: Bounded influence results in SS (left side) and two-stage RR (right side). Relative apparent resistivity difference and phase difference between Birrp and Razorback.
All processings were performed using the Razorback Library developed at BRGM on internal funding. Application to the peri-urban context has received funding from the EC Seventh Frame-work Program under agreement No. 608553 (IMAGE).
References
(4)
M-estimator OME The M-estimator is a robust TF estimator, denoted OME, designed to minimize the influence of data associated to large residuals (equation 2) in the regression. Bounded Influence estimator OBI M-estimator TFs provides a good protection against strong data residuals but are still highly sensitive to extreme values in the magnetic field (predictor), i.e. the so called leverage points. The Bounded Influence estimator method consists in a variation of the M-estimator where the diagonal weighting
Multiple RR analysis for denoising MT data in peri-urban context
[1] Chave, A.D., Thomson, D.J., 2004. Bounded influence magnetotelluric response function estimation. Geophys. J. Int. 157 (3), 988–1006.
A MT/CSEM survey was performed on the western side of Strasbourg, where new EGS doublets are under construction. In the following, we show how Razorback allows to perform multiple RR analysis in order to reduce anthropic driven bias in peri-urban context. Bounded influence results are shown. 4 synchronous local sites and 2 distant remote sites are involved in the example.
[2] a) Wawrzyniak, P., Zlotnicki, J., Sailhac, P., Marquis, G. (2017). Resistivity variations related to the large March 9, 1998 eruption at La Fournaise volcano inferred by continuous MT monitoring. Journal of Volcanology and Geothermal Research. https://doi.org/10.1016/j.jvolgeores.2017.09.011 [3] b) Wawrzyniak, P., Smai, F., Razorback, an open source python library for magnetotelluric robust processing, in preparation
Image Project Final Conference, Akureyri, Iceland, 4-5/10/2017
