GEOPHYSICS, VOL. 64, NO. 3 (MAY-JUNE1999);P. 785–794, 15 FIGS., 2 TABLES. Variogram analysis of helicopter magnetic data to identify paleochannels of the Omaruru River, Namibia Stefan Maus ∗ , K. P. Sengpiel ‡ , B. R ¨ ottger ‡ , B. Siemon ‡ , and E. A. W. Tordiffe ∗∗ ABSTRACT The geomagnetic field over sedimentary basins is very sensitive to variations in basement depth. Therefore, magnetic surveys are widely used to map basement to- pography in petroleum and groundwater exploration. We propose variogram analysis as a more accurate al- ternative to power spectral methods. Data variograms are computed from aeromagnetic flight-line data. To es- timate depth, the data variograms are compared with model variograms for a range of source depths. We use the exact space domain counterparts of a fractal power spectral model as model variograms. To demonstrate the utility of this method for groundwater exploration, we map the basement topography of the Omaruru Alluvial Plains in Namibia. A comparison with electromagnetic (EM) resistivities and drilling information confirms the high accuracy—but also the limitations—of variogram analysis depth. Variogram analysis makes maximum use of short-wavelength contributions to the magnetic sig- nal, which is the key to the resolution of shallow base- ment topography. Moreover, by using a realistic source model and avoiding extensive data preconditioning and the transform to wavenumber domain, variogram anal- ysis is likely to provide improved magnetic depth esti- mates even for deep basins. INTRODUCTION Because of the instability of magnetic minerals in oxidizing environments, the magnetization of sediments is usually weak compared with the magnetization of the crystalline basement. In this case, the crystalline basement is equivalent to the mag- netic basement, being defined as the uppermost occurrence of rocks carrying a significant magnetization. Manuscript received by the Editor September 24, 1996; revised manuscript received September 18, 1998. ∗ Institut f ¨ ur Geophysik and Meteorologie der Technischen Universit¨ at Braunschweig, Mendelssohnstr. 3, 38106 Braunschweig, Germany. E-mail: smaus@gwdg.de. ‡Bundesanstalt f ¨ ur Geowissenschaften und Rohstoffe, Stilleweg 2, D-30655 Hannover, Germany. E-mail: heli@bgr.de. ∗∗ Department of Water Affairs, Private Bag 13193, Windhoek, Namibia. c  1999 Society of Exploration Geophysicists. All rights reserved. T magnetic maps are the smoother the greater the height of the observation plane above the magnetic basement. This effect is quite prominent, as illustrated in Figure 1. The smooth- ness/ruggedness of the magnetic field is reflected in its power spectrum P (s), where s is the 2-D horizontal wavevector. The higher the relative power for small wavenumbers |s|, the more rugged the appearance of the field. The power P (s) of the mag- netic field in the observation plane is related to the power of the field at basement level P 0 (s) by P (s) = P 0 (s) e −2z|s| , (1) where z is the depth to the basement, hence, the parameter of interest. To obtain z from equation (1), we require a model for the power spectrum P 0 (s) of the field at basement level. As- suming that the e −2z|s| term dominates the shape of the power spectrum, spectral slope methods (Spector and Grant, 1970) are based on the implicit assumption P 0 ≡ constant. Hahn et al. (1976) propose subtracting 10% from these white depths for a more reliable depth estimate. A breakthrough in our under- standing of magnetic power spectra was the finding that the magnetic field at source level is self-similar (fractal) and can be described by a model P 0 (s) ∝|s| −γ , with γ ≈ 3 (Gregotski et al., 1991; Pilkington and Todoeschuck, 1993). To correct for self-similar source, Pilkington et al. (1994) suggest dividing the power spectrum by |s| −3 before applying a spectral slope method. However, even with this correction, depth estimates remain unreliable (Maus and Dimri, 1996) for several reasons. For spectral analysis the magnetic flight-line data must be transformed to a regular grid. Since data density is typically 50 times higher along- than across-line, gridding invariably leads to a loss of information. Furthermore, gridded data are likely to be smoother than the actual magnetic field. The subsequent steps—making the grid periodic, fast Fourier transform, and azimuthal averaging—again lead to distortions in the power spectrum. 785