引用本文: 孙文, 吴晓平, 王庆宾, 周睿, 刘晓刚. 分形插值曲面及其在重力场格网加密中的应用[J]. 武汉大学学报 ( 信息科学版), 2016, 41(3): 331-335.
SUN Wen, WU Xiaoping, WANG Qingbin, ZHOU Rui, LIU Xiaogang. Fractal Interpolating Curve Surface and Its Application in Gravity Anomaly Gridding Process[J]. Geomatics and Information Science of Wuhan University, 2016, 41(3): 331-335.
 Citation: SUN Wen, WU Xiaoping, WANG Qingbin, ZHOU Rui, LIU Xiaogang. Fractal Interpolating Curve Surface and Its Application in Gravity Anomaly Gridding Process[J]. Geomatics and Information Science of Wuhan University, 2016, 41(3): 331-335.

## Fractal Interpolating Curve Surface and Its Application in Gravity Anomaly Gridding Process

• 摘要: 为了满足规则格网重力异常加密的需求,引入分形插值曲面理论,实际算例结果表明,相比径向基函数法插值,分形插值曲面具有更高的加密精度,但在局部地区存在误差较大的情况;为解决这一问题,采用基于完全布格异常的分形插值曲面方法,进一步的结果表明,该方法不仅能够提高精度,而且避免了局部误差极值较大的缺点。

Abstract: Gravity data is always saved and used in grid format, which is also demanded for frequency domain computation as fast fourier transformation. Therefore, gridding method becomes the first and very important step of gravity data processing. Some gridding methods, such as Shepard and Kriging, were introduced into this step and improved the gridding precision. But when it comes to the case of sparse data, the gridding precision were sharply reduced. Moreover, the regular grid densification method was rarely studied. To meet the demands of regular grid densification, the fractal interpolating curve surface theory was introduced and applied in this paper. The computing formulae was deduced in detail. An experiment was carried out and result showed that, compared to the RBF method, the FIC method was better on the precision but worse on the error extremum. It means the FIC method showed bad behavior in data smoothing. Based on the Bouguer anomaly, a “remove-restore” method was applied to solve this problem. Result showed that not only was the precision improved by BAFIC method, but also was the error extremum reduced to a great extent, which made the result more reliable and applicable. The vertical scale parameter which plays a great role in BAFIC method was chosen after times of experiments in this paper, which could be optimized by better and precise methods.

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