| 重力异常分离的小波域优化位变滤波方法 |
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| 引用本文： | 刘彩云,姚长利,郑元满.重力异常分离的小波域优化位变滤波方法[J].地球物理学报,2015,58(12):4740-4755. |
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| 作者姓名： | 刘彩云 姚长利 郑元满 |
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| 作者单位： | 1. 长江大学 信息与数学学院, 湖北荆州 434023;2. 中国地质大学 地球物理与信息技术学院, 北京 100083 |
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| 基金项目： | 国家高技术研究发展计划(863计划)课题(2014AA06A613),国家自然科学基金项目(61273179),湖北省教育厅科学技术研究项目(D20131206)联合资助. |
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| 摘 要： | 在重力异常分离中,频率域滤波分离方法是以全局数据频谱特征设计针对性的滤波器实现的.滤波器参数与空间位置无关,因此无法针对局部数据频谱特征动态调整滤波器参数.针对该局限性,在小波域滤波理论和优化滤波方法的基础上,本文研究提出了小波域优化位变滤波法,该方法具有空间变化滤波能力,在不同空间位置实现不同的滤波器特性,从而能实现局部数据频谱与全局数据频谱存在较大差异的重力异常分离问题.理论模型数据分离实验结果表明,在局部数据频谱与全局数据频谱差异较大的情况下,该方法相对于Butterworth滤波和优化滤波等方法具有优势.最后,用一个实例进行检验计算,体现了所提方法技术的效果和应用前景.
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| 关 键 词： | 异常分离 小波域 优化滤波 位变滤波 重力异常 |
| 收稿时间： | 2014-12-01 |
Preferential spatially varying filtering method in the wavelet domain for gravity anomaly separation |
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| LIU Cai-Yun,YAO Chang-Li,ZHENG Yuan-Man.Preferential spatially varying filtering method in the wavelet domain for gravity anomaly separation[J].Chinese Journal of Geophysics,2015,58(12):4740-4755. |
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| Authors: | LIU Cai-Yun YAO Chang-Li ZHENG Yuan-Man |
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| Institution: | 1. School of Mathematics and Information, Yangtze University, Hubei Jingzhou 434023, China;2. School of Geophysics and Information Technology, China University of Geosciences, Beijing 100083, China |
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| Abstract: | The classical frequency domain filtering method for gravity anomaly separation cannot change its frequency response at different spatial positions to adapt the frequency characteristic of local data, for the reason of lacking spatial information with Fourier transform. A preferential spatially varying filtering method in the wavelet domain (PSVF-WD) is proposed based on the scaling filtering theory and preferential filtering method, in order to overcome the limitation of the classical frequency domain filtering method mentioned above.#br#This method uses a preferential spatially varying filter to separate gravity anomalies. Firstly, it segments gravity anomaly data into several blocks after analyzing the spatial distribution characteristics of frequency components with the wavelet analysis method. Secondly, it obtains the local translation function with the preferential filtering method and calculates the local equivalent coefficients with the method derived in this paper. Thirdly, it combines the local equivalent coefficients to global ones according to the position information of them and achieves the design of PSVF-WD. Lastly, it obtains separated gravity anomalies using the global equivalent coefficients of PSVF-WD and wavelet coefficients of gravity anomalies.#br#We test the PSVF-WD with gravity-anomaly separation experiments of three synthetic data and one real data. In experiment 1, the PSVF-WD separates the composite signal of four different frequency sinusoidal signals using low-high filtering at one time. The results of this experiment show the spatially varying filtering ability of PSVF-WD. In experiment 2, the synthetic model consists of four prisms. Two of them belong to a relatively shallower layer and the other two of them belong to relatively deeper layer. However, one prism of the relatively shallower layer is deeper than another prism of the relatively deeper layer. The PSVF-WD method separates the anomalies of the relative shallower layer and deeper layer pretty well, while the preferential filtering method only separates the anomalies of the shallowest prism and remains anomalies of the rest of three prisms together. The average absolute error and standard deviation of separation results are 0.0500 nT and 0.0540, respectively for SVF-WD, while they are 0.0503 nT and 0.1079, respectively for preferential filtering. In experiment 3, the synthetic model consists of one large horizontal prism, one large vertical prism and five small prisms with different depths. The problem is more complicated because the spectrum aliasing is serious. The regional-residual separation results of PSVF-WD method are pretty well, but regional anomalies separated by the preferential filtering method still have too many residual anomalies and deform severely. The average absolute error and standard deviation of separation result are 0.0705 nT and 0.0531, respectively, while they are 0.0709 nT and 0.0867, respectively for preferential filtering.#br# In the field data separation experiment with the PSVF-WD method, the separated regional anomalies contain large- and middle- scale anomalies, which correspond to the field sources deeper than 10 km described in inversion results, and the separated residual anomalies contain small-scale anomalies, which correspond to the field sources shallower than 10 km described in inversion results. In the experiments with preferential filtering and traditional Butterworth filtering, the separated regional anomalies are both too simple and do not correspond to inversion results very well, and the separated residual anomalies both contain too many regional anomalies.#br#The proposed PSVF-WD method has the ability of spatially varying filtering, and is suitable for separating the gravity anomalies whose spectrum of local data is different from the average spectrum of global data obviously. The results of synthetic and field data separation experiments show that the proposed PSVF-WD method is superior to the classical frequency domain methods such as Butterworth filtering and preferential filtering method when the spectrum of local data is different from the average spectrum of global data obviously. In sum, this paper provides an approach to design a spatially varying filter in the wavelet domain, which can be applied to the other spatially varying filtering fields in potential data processing. |
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| Keywords: | Anomaly separation Wavelet domain Preferential filtering Spatially varying filtering Gravity anomaly |
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