Algorithm Theoretical Basis for "Geomag Delta F"
E. Joshua Rigler <erigler@usgs.gov>
Mathematical underpinnings and general algorithm considerations are presented for estimating a so-called “Delta F” data stream. Delta F is the difference between the magnetic vector magnitude measured at a given time, and a scalar total-field measurement made by a nearby independent sensor at the same time.
Magnetic vector measurements are typically made with fluxgate sensors capable of capturing rapid variations along three orthogonal axes simultaneously. However, the same technology that allows fast and accurate measurements of magnetic field variation is generally more prone to erroneous measurements than slower, more stable total-field sensors. "Delta F" is the difference between the estimated total field, obtained from vector components, and the measured total field. Delta F provides a useful time-dependent diagnostic for magnetic observatory operators.
Delta F (∆F) is, conceptually, very simple:
...where Fs is the measured scalar total field, and Fv is the estimated total field obtained by adding vector components in quadrature:
Of course, if data are only available in hdZ (where d=(D-D0)) coordinates, as is common with USGS preliminary data, they should be converted into a Cartesian system used in ( Eq. 2). See the XYZ Algorithm for a discussion on the cartesian coordinate system(s) used.
Fluxgates and total-field sensors operate at different frequencies, with the latter typically being the slower, more stable data source. While not an issue for 1-minute data, the Intermagnet proposed 1-second standard states “Compulsory full-scale scalar magnetometer measurements with a data resolution of 0.01 nT [are required] at a minimum sample period of 30 seconds”. First, assume that the authors of this standard meant “maximum sample period of 30 seconds”. That said, this standard clearly allows scalar measurements to be made less frequently than vector measurements. If this is indeed the case, Delta F should correspond to the scalar measurement time steps, however is not clearly stated in any found references which vector measurement should be used to calculate Delta F. The library requires all inputs use the same sampling rate.
The WG V-Dat modifications to the IAGA2002 data exchange format are very specific about how to deal with “missing observations”. If Fs, or Fv and Fs are missing, assign missing data flags/values to Delta F. If only Fv is missing, set Delta F equal to -Fs.
- IAGA WG V-DAT (2011), Addition to the IAGA2002 Data Exchange Format: Quasi Definitive (q) data type and valid geomagnetic element (G), IAGA WG V-DAT business meeting held during the IUGG-2011 Assembly in Mebourne, Austrailia, 04 July 2011.
- St-Louis, B. (Ed.) (2012), INTERMAGNET Technical Reference Manual, Version 4.6, obtained from: http://www.intermagnet.org/publication-software/technicalsoft-eng.php
- Turbitt, C.; Matzka, J.; Rasson, J.; St-Louis, B.; and Stewart, D. (2013), An instrument performance and data quality standard for intermagnet one-second data exchange, IN: XVth IAGA Workshop on Geomagnetic Observatory Instruments and Data Processing, Cadiz, Spain, 4-14 June, 2012, p 186-188.