Minimising noise problems when downward continuing potential field data

Abstract

Due to the nature of the Fourier transform geophysical 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 2N points at 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 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 or vertical derivative of the data rather than to the data itself. Since the derivatives can be calculated in the space domain where 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 are 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.