The Stable Downward Continuation of Potential Field Data

Filtering methods based on the Fourier transform are routinely used in the processing of geophysical data. Because of the nature of the Fourier transform, the data must be prepared before the transform is calculated. This preparation usually takes the form of the removal of any trend from the data, combined with the padding of the data to 2^N points between the data edges. However, no data preparation procedure is perfect, and the result is that problems (in the form of edge effects) appear in the filtered data. When high-pass filters (such as derivatives or downward continuation) are subsequently used, then these edge effects become particularly apparent.

This paper suggests three methods for the stable downward continuation of geophysical data (two of which may be combined). The first method is applied to an integrated horizontal derivative of the data rather than to the data itself. Since the horizontal derivative can be calculated in the space domain where fast Fourier transform (FFT) edge effects are not present, this reduces the enhancement of the data at frequencies near the Nyquist, resulting in smaller edge effect problems. The second method measures the FFT-induced noise by comparing data that has been downward continued using both the space- and frequency-domain methods. The data is then compensated accordingly, and the compensated data may be downward continued to arbitrary distances that are not possible using space-domain operators. The final method treats downward continuation as an inverse problem, which allows the control of both FFT-induced noise and other noise that is intrinsic to the dataset. This method is computationally slow compared to the first two methods because of the inversion of large matrices that is required. The methods are demonstrated on synthetic models and on aeromagnetic data from the Bushveld igneous complex, South Africa.