LOCALIZED CRUSTAL MAGNETIC DEPTH ESTIMATIONS OF EARTH AND MARS

The power spectral signature of the magnetic field strength, in consideration with other information, bears on source depth. In this present study, we attempt to isolate hemispheric-scale differences in magnetization depth using: 1) observations from the magnetometer experiment on the Mars Global Surveyor (MGS) spacecraft data from Connerney et al. and from the Sabaka et al. CM3 magnetic model for Earth, 2) power spectral relations from Voorhies et al, and 3) a spatio-spectral localization technique by Simons. The Connerney and Sabaka data sets were chosen for their nearly uniform coverage, while the Voorhies equations give an estimate of the source depth of magnetization from the magnetic power spectrum, and, finally, the localization technique by Simons enables the veridical isolation or filtering of magnetic spectral data from arbitrary locations of variable spatial sizes about a planet.

CONNERNEY GLOBAL POWER SPECTRUM WITH VOORHIES FIT

Before we applied Voorhies analytical solution to any localized data, we first derived a global magnetic depth estimate from the global data set of Connerney et al. Figure 1 is a field plot of the global power spectrum of Mars that has been downward continued to the surface and its corresponding Voorhies analytical fit. The maximum harmonic degree is 52, which equates to a full wavelength resolution of just over 400 km. Our preliminary fit gives a predicted depth of 22 ± 6 km, as Voorhies points out this depth may overestimate the true depth of laterally correlated sources, such as the those from the very strong magnetic features in Mars southern highlands. The corresponding global depth estimate from Voorhies, based on Purucker et al data, is 46 km ± 10 km.

Figure 1. Connerney et al. Global Power Spectrum with Voorhies et al. Fit

HEMISPHERIC MAGNETIC DEPTH ESTIMATIONS

The next step we took was to look at magnetic spectra from different spatial locations and sizes. After expanding the field into spherical harmonic coefficients, we applied the localization technique of Simons that effectively produced magnetic power spectra for specific spatial regions about the planet. Finally, we fit the individual spectrum with Voorhies analytical expression, to get a predicted depth for that region. For hemispheric scale regions, we predict a magnetization depth of 19 ± 8 km for the southern hemisphere and 25 ± 7 km for the northern hemisphere (see Figs 2a & b, respectively). These values are at depths less than or equal to the elastic thickness, which scales with the Curie depth, between 20-30 km, predicted by Zuber.

Figure 2. a) (Top) Southern Hemispher Power Spectrum with Voorhies et al. Fit, and its b) (Bottom) Northern Hemispheric counterpart.

Verification of Depth Prediction

To confirm our depth predictions for the localized spectra, we derived a global synthetic spectrum of random orientations and random polarities in which the Voorhies expression would predict a magnetization depth of 22 km. From this spectrum, we calculated its spherical harmonic representation. Then we sampled various spatial regions, determined their respective power spectra and then predicted their associated magnetic depths. Figure 3 displays the results for 82 samples. From this plot, it is shown that as the spatial diameter of the widow filter is reduced to approximately 100 degrees, the predicted depth and its associated standard deviation are roughly equal. Presumably below this diameter, as the spatial input is further reduced the spectral content varies and, in turn, so does the predicted depth estimates. For predictions of actual data, the desire is to spatially reduce the filter window as much as possible in order to achieve the highest resolution and to mitigate contributions far from the window’s center that may obscure or dilute the depth estimates. However, real data contains correlated along with uncorrelated magnetic dipoles and therefore, the reliable depth prediction limit is reached when the spatial scale of the correlated regions and the filter window diameter become roughly equal.

Figure 3. Verification of Localized Depth Predictions.

SABAKA GLOBAL POWER SPECTRUM WITH VOORHIES FIT

We applied the same global analysis used for Mars to the Sabaka’s CM3 magnetic Earth model. From Fig. 6, the global depth estimate is 16 ± 14 km, which compares to Voorhies CMP3 (the CM3 model is an improved CMP3 model) estimate of 4.5 ± 13.5 km.

Figure 6. Sabaka et al. Global Power Spectrum with Voorhies et al. Fit.

REFERENCES

Connerney, J.E.P., et al., The Global Magnetic Field of Mars and Implications for Crustal Evolution, Geophys. Res. Lett., in press.

Purucker, M., et al., An altitude-normalized magnetic map of Mars and its interpretation, Geophys. Res. Lett., 27, 2449-2452, 2000.

Sabaka, T. J., N. Olsen, and R. A. Langel, A comprehensive model of the near-Earth magnetic field: Phase 3, NASA Tech. Memo. 2000-209894, 75 pp., 2000.

Sabaka, T.J., N. Olsen, and R. A. Langel, A Comprehensive model of quiet-time, near-Earth magnetic field: Phase 3, Geophysical Journal International, in press

Simons, M., S. C. Solomon, and B. H. Hager, Localization of grav ity and topography: Constraints on the tectonics and mantle dynamics of Venus, Geophys J. Int., 131, 24–44, 1997.

Voorhies, C. V., T. J. Sabaka and M. Purucker, On magnetic spectra of Earth and Mars, J. Geophys. Res., 107, No. E6, 2002