Amethod for determining the optimal height for upward continuation of gravity anomalies
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摘要: 向上延拓方法是重力异常分离中的重要方法之一,但在应用时如何定量地选取合适的延拓高度是一直以来存在的问题。本文针对该问题展开研究,提出一种基于二乘误差的曲率分析方法来定量地给出相对合理的延拓高度。该方法对观测数据进行相邻不同高度的向上延拓,并用二乘法估算相邻高度延拓值的二乘误差,在各相邻高度延拓值二乘曲线中存在一个曲率最大值,在这个点最大程度地使局部异常衰减并尽可能地保留区域异常,可近似视为最佳延拓高度。利用理论模型数据对所提出的方法进行了测试,表明该方法能够定性给出较合适的延拓高度,从而为实际应用中延拓高度的选取提供参考。Abstract: Upward continuation is one of the important methods used to separate gravity anomalies. However, how to quantitatively select an appropriate upward-continuation height has always been a problem in the application of this method. Given this, this paper proposes a curvature analysis method based on the least square method to quantitatively determine a reasonable upward-continuation height. The steps of this method are as follows. Perform upward continuation to different adjacent heights for observation data, and then use the least square method to estimate the least square error of the upward continued value of adjacent heights.There is a maximum curvature in the least square curve of upward-continued values of all adjacent heights.At the point of the maximum curvature, the local anomalies are attenuated to the greatest extent, while the regional anomalies are preserved as far as possible. Therefore, this point can be approximately regarded as the optimal upward-continuation height. As indicated by tests using the data of a theoretical model, the method proposed in this paper can be used to qualitatively determine a suitable upward-continuation height, thus providing an important reference for the selection of upward-continuation height in practical applications.
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Key words:
- gravity anomaly /
- analytic continuation /
- upward-continuation height
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