﻿ 扩边尺度对重力异常分层分离处理的影响——以插值切割法为例
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 大地测量与地球动力学  2021, Vol. 41 Issue (3): 221-228  DOI: 10.14075/j.jgg.2021.03.001

### 引用本文

XU Rugang, LIANG Xiao, SUN Hongbo, et al. The Effects of Expanding Edge Length in the Processing of Gravity Anomalies Separation: An Example of Interpolation Cut Method[J]. Journal of Geodesy and Geodynamics, 2021, 41(3): 221-228.

### Foundation support

The Spark Program of Earthquake Technology of CEA, No.XH191204Y; Combination Project with Monitoring, Prediction and Scientific Research of Earthquake Technology, CEA, No.3JH-202001038.

### 第一作者简介

XU Rugang, senior engineer, majors in seismic gravity observation, E-mail: xurugang04@126.com.

### 文章历史

1. 安徽省地震局，合肥市长江西路558号，230031

1 插值切割分层分离原理及其技术流程 1.1 插值切割分层分离原理及改进

 $\begin{array}{l} A(x, y)=\frac{1}{N} \sum\limits_{i=1}^{N} G_{i}(r) \\ R(x, y)=(1-g) G(x, y)+g A(x, y) \\ S(x, y)=g[G(x, y)-A(x, y)] \end{array}$ (1)

 $f_{i}(r)=\frac{\left[G_{i}(r)-G_{i}^{o}(r)\right]^{2}}{\left[G_{i}(r)-G_{i}^{o}(r)\right]^{2}+\left\{G(x, y)-\frac{1}{2}\left[G_{i}(r)+G_{i}^{o}(r)\right]\right\}^{2}}$ (2)
 $g=1-\frac{1}{\frac{N}{2}} \sum\limits_{i=1}^{\frac{N}{2}} f_{i}(r)$ (3)

1.2 位场插值切割分层分离技术流程

2 理想模型实验 2.1 模型设计参数

 图 1 理想模型空间分布 Fig. 1 Space distribution of ideal model

 图 2 理想模型重力异常分布 Fig. 2 Gravity anomalies distribution of ideal model
2.2 理想模型计算

2.2.1 理想模型不同深度层源的理论重力异常值计算

 图 3 研究区及其扩边后的区域分布 Fig. 3 Distribution of the study area and its expanded area

 图 4 扩边后的重力异常分布 Fig. 4 Gravity anomalies distribution after edge expansion
2.2.2 理想模型重力异常值与重力场源分离计算值对比

 图 5 扩边尺度为50倍格网点距的不同深度层源重力异常差异分布 Fig. 5 The distribution of gravity anomalies at different depths of layers with an expanded edge size of 50 times grid spacing

 图 6 扩边尺度为100倍格网点距的不同深度层源重力异常差异分布 Fig. 6 The distribution of gravity anomalies at different depths of layers with an expanded edge size of 100 times grid spacing

 图 7 扩边尺度为150倍格网点距的不同深度层源重力异常差异分布 Fig. 7 The distribution of gravity anomalies at different depths of layers with an expanded edge size of 150 times grid spacing

2.2.3 扩边尺度与重力场源分离误差分析

 $\delta=\sqrt{\frac{1}{M P} \sum\limits_{m=1}^{M} \sum\limits_{p=1}^{P}\left[v_{c}(m, n)-v_{t}(m, n)\right]^{2}}$ (4)

 图 8 不同扩边尺度、不同深度层源重力异常差异均方误差 Fig. 8 The mean square error of gravity anomalies difference at different expanded edge sizes and depths

 图 9 不同扩边尺度、不同深度层源重力异常差异的均方误差 Fig. 9 The mean square error of gravity anomalies difference at different expanded edge sizes and depths

3 实际资料计算

 图 10 布格重力异常 Fig. 10 Bouguer gravity anomalies

 图 11 扩边尺度为40倍格网点距的不同深度层源重力异常在地表的空间分布 Fig. 11 The distribution of gravity anomalies at different depths of layers with an expanded edge size of 40 times grid spacing

 图 12 不同扩边尺度、不同深度层源重力异常差异的均方误差 Fig. 12 mean square error of gravity anomalies difference at different expanded edge sizes and depths
4 结语

1) 实验结果表明，数据区域的边界效应与扩边尺度、分离切割深度、异常的规模和幅度及空间位置等因素相关。当切割分离深度、异常体的规模和异常幅度、空间位置一定时，数据扩边尺度越大，分层分离结果中的边界效应越弱；扩边尺度越小，边界效应越强。

2) 扩边尺度的选择应综合考虑分析资料所需满足的精度和数据计算效率，扩边尺度不宜过大，若扩边尺度过大，且切割半径较小，分离结果中计算误差显著，扩边尺度与重力异常分层分离的最大切割深度至少应满足2∶1的要求，才能明显改善边界效应和计算误差。对含有较大重力异常的边界进行切割分离时，应在2倍扩边尺度的基础上再进一步扩边，基于此关系，根据所要分离的最大切割深度确定数据区域的扩边尺度，或根据数据区域的扩边尺度确定最大切割深度。

3) 数据区域边界效应的空间展布不是由数据区域边界向中心区域均匀分布，而与异常体的规模和空间位置有关。

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The Effects of Expanding Edge Length in the Processing of Gravity Anomalies Separation: An Example of Interpolation Cut Method
XU Rugang1     LIANG Xiao1     SUN Hongbo1     CHU Fei1
1. Anhui Earthquake Agency, 558 West-Changjiang Road, Hefei 230031, China
Abstract: Using interpolation cut method, the expanded gravity anomalies of ideal model on the surface at different scales is separated into several gravity anomalies caused by strata at different depths. Based on separated results, the effects of expanding edge length on gravity anomalies separation are studied from two aspects: the difference of gravity anomalies at different scales and depths, and the mean square deviation between the expanding edge scale and the gravity anomalies separation. The results show that 1) The region boundary effect of ideal model data is related to the expanding edge length, the depth of cutting separation, location, scale and intensity of geological abnormal bodies. 2) In selecting the expanding edge scale, accuracy and computational efficiency should be taken into consideration. The expanded edge size should not be too large, and the expanded edge size and maximum cutting depth for gravity anomalies separation should at least meet the requirements of 2 ∶1; this significantly improves the boundary effect. When cutting and separating the boundary with large gravity anomalies, it is necessary to further expand the boundary on the basis of twice the scale of expansion. 3) The spatial distribution of the boundary effect is not evenly distributed from the boundary of the data area to the central area, but is related to the scale and spatial location of the anomalous body.
Key words: expanding edge length; interpolation cut; gravity anomalies; potential field separation