1. 1 Magnetic Field Modulus Estimation Using Whisper. Comparison with FGM LPCE/CNRS 12-13 February 2007 Alban Rochel, Edita Georgescu, Jonny Gloag, Pierrette Décréau, Jean-Louis Rauch, Jean-Gabriel Trotignon, Xavier Vallières

2. 2 Outline  B Extraction Algorithm  Presentation  Spectrogram Pre-Processing  Fce Extraction Method  Results on Synthetic Spectrograms  Comparison With FGM data  2001 Data  2002 Data

3. 3 Outline  B Extraction Algorithm  Presentation  Spectrogram Pre-Processing  Fce Extraction Method  Results on Synthetic Spectrograms  Comparison With FGM data  2001 Data  2002 Data

4. 4 B Extraction Algorithm Presentation  Extraction of the electron gyro- frequencies fce in plasmaspheric passes, knowing that:  Fce varies smoothly  Fce is the fundamental for a set of harmonics

5. 5 B Extraction Algorithm Spectrogram Pre-Processing  Linear interpolation of missing frequency bins (due to on- board compression)  Dummy bins added to have a [0kHz, 80kHz] frequency range rather than [2kHz, 80kHz].

6. 6 B Extraction Algorithm Spectrogram Pre-Processing  Image processing to enhance the visibility of the resonances  Per-spectrum conversion to dB  Top-hat morphological transformation in the frequency dimension to remove the large-scale trends

7. 7 B Extraction Algorithm f ce Extraction Method  Ideas:  Assuming the temporal variation of f ce is linear locally.  Locally searching the spectrogram for sets of harmonics Technique inspired by the Radon method (image processing)

8. 8 B Extraction Algorithm f ce Extraction Method  We define a “comb” as a possible (linear) fundamental and its harmonics, defined by the ordinate of the fundamental at its origin and its slope.  For each spectrum, a portion of the spectrogram is extracted (neighbourhood of the spectrum). Origin ordinate: 1.2 Slope: 0.1 Origin ordinate: 0.5 Slope: 0.2 This spectrum

9. 9 B Extraction Algorithm f ce Extraction Method  The spectrogram intensity is averaged on each comb in an {origin x slope} domain (including various normalizations).  A weight is applied for each point, depending on its distance (in time) from the central spectrum: less sensitive to curvature. slope origin ordinate Low High

10. 10 B Extraction Algorithm f ce Extraction Method  A second, more accurate, pass is performed in a neighborhood of the (origin, slope) maximizing the previous pass.  The final (origin, slope) point defines the fce value for the spectrum.

11. 11 B Extraction Algorithm f ce Extraction Method  Post-processing: Using FGM f ce as reference  Keep the points that follow the FGM f ce variations (criteria based on the smoothness of f WHI / f FGM )  Estimation of uncertainty:  A criterion based on statistical considerations gives the order i of the highest order significant harmonic.  Whisper frequency resolution r : 163Hz  Uncertainty u defined as

12. 12 Outline  B Extraction Algorithm  Presentation  Spectrogram Pre-Processing  Fce Extraction Method  Results on Synthetic Spectrograms  Comparison With FGM data  2001 Data  2002 Data

13. 13 Results on Synthetic Spectrograms  Synthtic spectrograms generated randomly as the sum of two gaussians Generated B Corresponding f ce and harmonics Addition of noise and blur

14. 14 Results on Synthetic Spectrograms  Results on 400 synthetic spectrograms (600 spectra each) → Unbiased, accurate method Average error on ratio: 0.0005% Std Deviation on ratio: 0.3806 Average error on difference: 0.016nT Std Deviation on difference: 1.823nT

15. 15 Outline  B Extraction Algorithm  Presentation  Spectrogram Pre-Processing  Fce Extraction Method  Results on Synthetic Spectrograms  Comparison With FGM data  2001 Data  2002 Data

16. 16 Comparison With FGM Data  2001, C1

17. 17 Comparison With FGM Data  2001, C2

18. 18 Comparison with FGM Data WHI/FGM mean (x100) WHI/FGM std dev (x100) WHI-FGM mean (nT) WHI-FGM std dev (nT) 2001, C1100.22352.07791.0356.187 2001, C2100.11131.16520.4305.021 2001, C399.94311.93120.0225.395 2001, C4100.25311.27800.9456.875 2002, C1100.37571.36460.9793.015 2002, C2100.15240.69050.5102.296 2002, C3100.08210.58450.3071.973 2002, C4100.29590.61031.0392.190 33.000 to 70.000 values/year/spacecraft (most of the plasmaspheric passes) Files delivered to FGM and EDI in mid-january (AI-2)

19. 19 Perspectives  Meeting with EDI and FGM teams after the workshop  Comparison with EDI data  Possibility to deliver 2003 on a short term  Automatic production, no validation required, but the plasmasphere passes have to be determined manually