2D and 3D potential-field upward continuation using splines

The dominant upward‐continuation technique used in the potential‐field geophysics industry is the fast Fourier transform (FFT) technique. However, the spline‐based upward‐continuation technique presented in this paper has some advantages over the FFT technique. The spline technique can be used to carry out level‐to‐uneven surface 2D and 3D potential‐field upward continuation. An example of level‐to‐uneven surface upward continuation of 3D magnetic data using the spline technique is shown, and it is evident that the continued anomalies are very close to the theoretical values. The spacing can be irregular. Synthetic examples using the spline technique to continue noise‐contaminated gravity and magnetic data upward to an altitude of 15 km on irregular grids are shown. Gaussian noise with a zero mean and a standard deviation of 1% does not cause much error and can readily be tolerated. Through comparison with the FFT technique, it is found that for low‐altitude gravity and magnetic upward continuation, both the FFT technique and the spline technique are suitable; for high‐altitude upward continuation, the FFT technique is inaccurate, whereas the spline technique works very well. Also, upward continuation by the spline technique has a smaller edge effect than upward continuation by the FFT technique. The spline‐based upward continuation technique works fairly well even when the periphery of a grid is not quiet: it is rather robust in general. A real example shows that the spline technique can be employed to perform upward continuation of total‐field magnetic data and to de‐emphasize near‐surface noise.