Repeat station crustal biases and accuracy determined from

Repeat station crustal biases and accuracy determined from regional field models M. Korte, E. Thébault* and M. Mandea, Geo. Forschungs. Zentrum Potsdam (*now at Institut de Physique du Globe, Paris)

Outline • The German repeat station network and data processing • R-SCHA regional magnetic anomaly modelling technique • Preparation of data - satellite data - aeromagnetic data - repeat station data • Repeat station uncertainties • Repeat station crustal biases • Conclusions blue: this talk black: details in talk by E. Thébault

The German repeat station network Ca. 45 repeat stations, subset of denser ground vector surveys established in the past. Since 2000 two classes of stations: -Variometer stations Portable LEMI variometer installed nearby, 3 to 7 days - Other stations surveyed while variometer is recording at nearest variometer station

Data processing I • Determine “local baseline” of nearest variometer from absolute measurements (like standard observatory practice) => Series of full field vector variations for a few days for each station • Use quiet night times with constant differences between recordings at the station and observatory for reduction to “annual means”. C(xi, tmean) = C(xi, ti) – C(O, ti) + C(O, tmean) Repeat station “annual mean” of component C Repeat station measurement value at time ti Observatory recording at time ti This difference determined robustly from quiet night time values Observatory annual mean of component C

Data processing II Differences between recordings of the LEMI variometer at station EBH to NGK observatory recordings for 3 days Quiet hours used for final data reduction to annual means

R-SCHA modelling Revised spherical cap harmonic analysis • Method developed by E. Thébault, based on SCHA (spherical cap harmonic analysis), a “regional spherical harmonic analysis” • Data from different altitudes can be taken into account because the vector field is modelled inside a cone • Well-suited for joint inversion of ground, aeromagnetic and satellite data • Ideally suited for regional models of the vector crustal magnetic anomaly field (first example: France by Thébault et al. ) • Details given in presentation by Erwan Thébault This work: study crustal field influence at repeat station locations (“crustal biases”) and use compatibility of different data types in modelling for estimations of data uncertainty

Data for R-SCHA anomaly models Crustal anomaly data, different data types: • Satellite data + full vector information + long wavelength information - low spatial resolution (no better than ~300 km) due to altitude of satellite • Aeromagnetic data + high spatial resolution (up to km scale) - only intensity data - long wavelength information missing • Ground data, repeat station data + full vector information - very localized information, even ground vector surveys mostly not dense enough for detailed crustal field mapping => Only combination of all data types give full information

Data preparation • Satellite data - selection of quiet night time data - corrections for external fields - subtraction of core field model up to SH degree 14 • Aeromagnetic data - existing anomaly compilation for Germany (grid) used (assumption: external variation corrections, upward-/downward continuation for individual surveys to common altitude, reductions of individual surveys to common date have been done properly before) - addition of the originally subtracted DGRF 1980 model - subtraction of core field model up to SH degree 14 • Repeat station data - Results from one year would be enough, but use as many data as possible for higher confidence and to get an idea of uncertainties

Repeat station data used in this work • All available ground survey and repeat station data within the time span for which a continuous core field model is available (CM 4 model by Sabaka et al. , valid 1960 – 2002) • Only stations, where measurements had been taken at least three times in this time interval (for statistics)

Repeat station data preparation • Subtract core field model up to SH degree 14 • Afterwards, observatory annual means show systematic variations, assumed to be external field influences which did not average out. • Correction for these influences based on a simple empirical template, using the homogeneity of these variations in a small area • Average residual is crustal field contribution (assumed to be constant over 40 years) • Standard deviation about average is good estimate of uncertainty • In most cases, standard deviation of average is reduced by the empirical external field correction

Empirical external field correction for (repeat station) annual means Left: Observatory annual means after subtraction of core field model, black line is best fit linear trend. Right: Residual variations in annual means after subtraction of linear trends, black line is average of the three = template for external field correction of all annual means Red: NGK Green: WNG Blue: FUR

Repeat station data preparation • Subtract core field model up to SH degree 14 • Afterwards, observatory annual means show systematic variations, assumed to be external field influences which did not average out. • Correction for these influences based on a simple empirical template, using the homogeneity of these variations in a small area • Average residual is crustal field contribution (assumed to be constant over 40 years) • Standard deviation about average is good estimate of uncertainty • In most cases, standard deviation of average is reduced by the empirical external field correction

Repeat station crustal biases and uncertainties Avg. 4. 7 8. 3 4. 5 These uncertainties also represent repeat station data uncertainties

Repeat station crustal biases and uncertainties Uncertainties are smaller at times and locations, where a local variometer was used. These uncertainties might contain influences from insufficient representation of core field and secular variation by the subtracted model. Systematic deviations suggesting a significant influence of such an effect could not be found. However, the data mostly come from measurements without local variometers, a study of small-scale secular variation requires highest accuracy data!

X-Anomaly The R-SCHA model Z-Anomaly Y-Anomaly

Model fit to the data Average rms: Model 1 X 33. 8 n. T Y 22. 8 n. T Z 45. 1 n. T Aerom. 13. 2 n. T Model 2 X 23. 4 n. T Y 17. 0 n. T Z 26. 0 n. T Aerom. 13. 6 n. T Rms misfit larger than uncertainty estimates, probably due to resolution limit of the model (~35 km)

Conclusions • We have obtained estimates of repeat station data uncertainties: on average 4. 7 n. T for X 8. 3 n. T for Y 4. 5 n. T for Z The misfit of a regional R-SCHA model is significantly larger, but that is probably due to the limited model resolution (~35 km) • The crustal field influence at the German repeat stations reaches up to +/-150 n. T in the different components, which has to be considered when the data are used for core field studies (see example on Poster, F in 2004 and 2006) • Repeat station data are useful for joint inversions of ground, satellite and aeromagnetic data for magnetic anomaly mapping.