| 基于改进泰勒级数法的总强度磁异常稳健向下延拓 |
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| 引用本文： | 卞光浪,翟国君,高金耀,朱丹,李连登,方建勋,李研.基于改进泰勒级数法的总强度磁异常稳健向下延拓[J].测绘学报,2014,43(1):30-36. |
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| 作者姓名： | 卞光浪 翟国君 高金耀 朱丹 李连登 方建勋 李研 |
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| 摘 要： | 位场向下延拓隶属于经典不适定问题，观测数据中细微的误差在向下延拓过程中都被严重放大，甚至会掩盖真实信息。如何精确地求解总强度磁异常（Bm）在垂直方向的各阶导数，是利用泰勒级数实现稳健向下延拓的关键。为此，本文首先分析了调和函数的相关性质，从理论上证明了Bm为准调和函数的结论，在精确计算各阶垂向导数基础上，提出利用改进泰勒级数实现磁场稳健向下延拓。为降低边界效应对向下延拓计算结果的影响，提出采用半余弦函数对磁场在4个方向上进行平滑扩边处理。通过球体与长方体仿真试验以及航空、船载实测磁场数据对提出方法进行了验证。结论表明，提出的技术方法可实现磁场稳健向下延拓，当观测数据无噪声时，计算结果精度要明显优于现行的FFT法、常规泰勒级数法以及积分-迭代法；当观测数据含有噪声时，本文方法和积分-迭代法计算结果精度相当。
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| 关 键 词： | 总强度磁异常 向下延拓 改进泰勒级数 拉普拉斯方程 垂向导数 扩边处理 |
| 收稿时间： | 2012-06-04 |
| 修稿时间： | 2013-12-04 |
Downward continuation of magnetic field with improved Taylor series |
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| Abstract: | The downward continuation process is inherently unstable and any high frequency noise present in the data gets strongly magnified in the transformed map in such a way to mask any useful signal. How to accurately calculate the any order vertical derivative of total field magnetic anomaly (Bm) is a crucial matter of implementing downward continuation. In this paper, we studied the properties of harmonic function and proved that Bm is a pseudo-harmonic function. Based on the use of stable vertical derivatives, a stable algorithm was presented to perform downward continuation applying improved Taylor series approximation. Furthermore, the problem of edge effects could be settled out using grid extension to the four directions with half a cosine function before the vertical derivative calculation. The effectiveness of the suggested algorithm has been illustrated by simulated sphere/prismatic examples and real magnetic data from an airborne and seaborne magnetic survey. The conclusion shows that the presented technique can be employed to perform stable downward continuation of total field magnetic data and provide better results than other techniques based on Fast Fourier Transformation (FFT) or on normal Talor’s series or integral-iteration method when the data is noise-free, and almost the same as integral-iteration method if the data contains certain noise. |
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| Keywords: | total field magnetic anomaly downward continuation improved Taylor series Laplace equation vertical derivative grid extension processing |
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