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CN115393547B - An omnidirectional filtering method and system for lunar satellite gravity anomaly data - Google Patents

An omnidirectional filtering method and system for lunar satellite gravity anomaly data Download PDF

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CN115393547B
CN115393547B CN202210974724.0A CN202210974724A CN115393547B CN 115393547 B CN115393547 B CN 115393547B CN 202210974724 A CN202210974724 A CN 202210974724A CN 115393547 B CN115393547 B CN 115393547B
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郭良辉
杨婧
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China University of Geosciences Beijing
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Abstract

本发明提供了一种月球卫星重力异常数据的全方向滤波方法,包括:将月球卫星重力异常网格数据剖分成多个子区;对滤波窗口范围内的数据进行单方向去噪,滑动滤波窗口直至遍历子区内所有数据,得到各子区的单方向去噪结果;将各子区的数据按照预设角度逐次旋转,直到完成所有预设角度方向的去噪;将得到的全方向去噪的各个子区数据进行拼合,得到一次去噪结果;当本次去噪结果满足预设条件时,输出最终的去噪结果。本发明通过对滤波窗口范围内的数据按照预设角度进行单方向去噪,最终得到全方向去噪数据,可以去除月球卫星重力异常数据中的条带干扰和高频噪音,为后续重力数据处理、反演和地质构造解释等方面提供可靠的数据支撑。

Figure 202210974724

The invention provides an omnidirectional filtering method for lunar satellite gravity anomaly data, comprising: dividing the lunar satellite gravity anomaly grid data into multiple sub-areas; performing unidirectional denoising on the data within the filtering window range, and sliding the filtering window until Traverse all the data in the sub-areas to obtain the unidirectional denoising results of each sub-area; rotate the data of each sub-area successively according to the preset angle until the denoising of all preset angle directions is completed; the obtained omni-directional denoising results The data of each sub-area is combined to obtain a denoising result; when the denoising result meets the preset conditions, the final denoising result is output. The present invention denoises the data within the filter window in one direction according to the preset angle, and finally obtains the omnidirectional denoising data, which can remove the band interference and high-frequency noise in the gravity anomaly data of the lunar satellite, and provide the next step for the subsequent gravity data processing. , inversion and interpretation of geological structures and other aspects to provide reliable data support.

Figure 202210974724

Description

一种月球卫星重力异常数据的全方向滤波方法及系统An omnidirectional filtering method and system for lunar satellite gravity anomaly data

技术领域technical field

本发明涉及卫星重力数据处理技术领域,特别是涉及一种月球卫星重力异常数据的全方向滤波方法及系统。The invention relates to the technical field of satellite gravity data processing, in particular to an omnidirectional filtering method and system for lunar satellite gravity anomaly data.

背景技术Background technique

利用卫星重力测量技术获得卫星运行时的轨道摄动,可用于构建月球重力场模型。月球重力场模型由一组正则化球谐系数构成,用以近似描述月球上任意位置的重力异常,模型的阶次越高,对应描述的重力异常数据精度就越高。随着空间技术的发展,月球重力场模型球谐阶次不断提高,由月球重力场模型解算出的重力异常数据网格间距也对应变小。目前精度最高的月球重力场模型为1500阶,对应的月球重力异常数据网格间距为3.6km。然而在重力场模型球谐阶次提高的过程中,由于奇阶次项和偶阶次项间的相关性,以及飞行轨道变化及仪器震动等原因,导致解算出的重力异常数据出现严重的条带干扰与高频随机噪音,极大影响后续的数据处理和解释,所以需要首先对月球卫星重力异常数据做去噪处理,获取更为可靠的数据,为后续的处理与解释提供保障。Obtaining orbital perturbation during satellite operation using satellite gravity measurement technology can be used to construct a lunar gravity field model. The lunar gravity field model consists of a set of regularized spherical harmonic coefficients, which are used to approximately describe the gravity anomaly at any position on the moon. The higher the order of the model, the higher the accuracy of the gravity anomaly data described. With the development of space technology, the spherical harmonic order of the lunar gravity field model has been continuously improved, and the grid spacing of the gravity anomaly data calculated by the lunar gravity field model has also become smaller. At present, the lunar gravity field model with the highest accuracy is 1500th order, and the corresponding lunar gravity anomaly data grid spacing is 3.6km. However, in the process of increasing the spherical harmonic order of the gravity field model, due to the correlation between odd-order items and even-order items, as well as flight trajectory changes and instrument vibrations, serious irregularities appear in the calculated gravity anomaly data. Interference and high-frequency random noise greatly affect subsequent data processing and interpretation. Therefore, it is necessary to denoise the lunar satellite gravity anomaly data first to obtain more reliable data and provide guarantee for subsequent processing and interpretation.

当前国内外存在多种卫星重力数据去噪方法,按照实现原理可大致分为数字滤波和阶次截断两大类。数字滤波方法是应用高斯滤波(Swenson and Wahr,2002)、滑动去相关(Chambers,2006)等方法对数据进行平滑去噪,这些方法普遍被应用于地球时变重力数据领域;阶次截断方法则是将重力场模型中误差功率谱较高的阶次直接舍弃,不参与后续解算。它们存在的最主要问题均为无法有效去噪,即在不损失有效信号幅值的情况下,将条带干扰与随机噪音尽可能地去除。由于卫星重力异常数据条带干扰形态与航空地球物理数据预处理前的测线条带干扰有相似之处,因此考虑引入航空地球物理数据处理中的调平算法。其中,Beiki等人(2010)开发出了单方向的差分多项式拟合滤波方法(DPF,differential polynomial fitting method),该方法去除条带干扰效果较优,然而,该方法仅适用于测线方向,卫星重力数据没有测线排列,且其条带干扰多数情况为沿多个方向分布。因此,开发一种能够在不损失卫星重力异常数据有效信号的前提下将多方向的条带误差与高频噪音进行剔除的方法至关重要。At present, there are many satellite gravity data denoising methods at home and abroad, which can be roughly divided into two categories: digital filtering and order truncation according to the realization principle. The digital filtering method is to apply Gaussian filtering (Swenson and Wahr, 2002), sliding decorrelation (Chambers, 2006) and other methods to smooth and denoise the data. These methods are generally used in the field of earth time-varying gravity data; The higher order of the error power spectrum in the gravity field model is directly discarded, and does not participate in the subsequent calculation. The main problem they have is the inability to effectively denoise, that is, to remove the band interference and random noise as much as possible without losing the effective signal amplitude. Since the stripe interference pattern of satellite gravity anomaly data is similar to that of survey line interference before airborne geophysical data preprocessing, the leveling algorithm in airborne geophysical data processing is considered. Among them, Beiki et al. (2010) developed a unidirectional differential polynomial fitting filtering method (DPF, differential polynomial fitting method). This method has a better effect in removing band interference. However, this method is only applicable to the survey line direction. There is no survey line arrangement for satellite gravity data, and most of the band interference is distributed along multiple directions. Therefore, it is very important to develop a method that can eliminate multi-directional banding errors and high-frequency noise without losing the effective signal of satellite gravity anomaly data.

发明内容Contents of the invention

为了克服现有技术的不足,本发明的目的是提供一种月球卫星重力异常数据的全方向滤波方法及系统。In order to overcome the deficiencies of the prior art, the purpose of the present invention is to provide an omnidirectional filtering method and system for lunar satellite gravity anomaly data.

为实现上述目的,本发明提供了如下方案:To achieve the above object, the present invention provides the following scheme:

一种月球卫星重力异常数据的全方向滤波方法,包括:An omnidirectional filtering method for lunar satellite gravity anomaly data, comprising:

步骤1:获取待处理的月球卫星重力异常网格数据;Step 1: Obtain the gravity anomaly grid data of the lunar satellite to be processed;

步骤2:将所述月球卫星重力异常网格数据剖分成多个子区;Step 2: dividing the lunar satellite gravity anomaly grid data into multiple sub-areas;

步骤3:创建滤波窗口,对所述滤波窗口范围内的数据进行单方向去噪,滑动滤波窗口直至遍历子区内所有数据,得到各子区的单方向去噪结果;Step 3: Create a filtering window, perform unidirectional denoising on the data within the scope of the filtering window, slide the filtering window until all data in the sub-areas are traversed, and obtain the unidirectional denoising results of each sub-area;

步骤4:将各子区的数据按照预设角度做坐标旋转并重新网格化,返回步骤3直到完成所有预设角度方向的去噪,得到全方向去噪的各个子区数据;Step 4: Rotate the data of each sub-area according to the preset angle and re-grid, return to step 3 until the denoising of all preset angle directions is completed, and obtain the data of each sub-area denoised in all directions;

步骤5:将全方向去噪的各个子区数据进行拼合,得到第一次去噪结果;Step 5: Combine the data of each sub-area for omnidirectional denoising to obtain the first denoising result;

步骤6:判断所述第一次去噪结果是否满足误差条件,若未满足条件则将第一次去噪结果作为待处理的月球卫星重力异常网格数据,返回步骤2直到输出满足误差条件的全方向去噪数据。Step 6: Determine whether the first denoising result satisfies the error condition. If the condition is not met, take the first denoising result as the lunar satellite gravity anomaly grid data to be processed, and return to step 2 until the output meets the error condition. Omnidirectional denoised data.

优选的,所述对所述滤波窗口范围内的数据进行单方向去噪,包括:Preferably, the unidirectional denoising of the data within the filtering window range includes:

建立滤波窗口;所述滤波窗口包括纵向一维窗口和正方形二维窗口,且纵向一维窗口位于正方形二维窗口的中心;Establish a filter window; the filter window includes a vertical one-dimensional window and a square two-dimensional window, and the vertical one-dimensional window is located at the center of the square two-dimensional window;

将所述纵向一维窗口和所述正方形二维窗口内的数据分别进行多项式拟合得到数据拟合结果;Carrying out polynomial fitting to the data in the vertical one-dimensional window and the square two-dimensional window respectively to obtain a data fitting result;

根据数据拟合结果确定误差值;Determine the error value according to the data fitting result;

根据所述误差值得到相应滤波窗口内的单方向去噪数据。The unidirectional denoising data within the corresponding filtering window is obtained according to the error value.

优选的,将所述纵向一维窗口和所述正方形二维窗口内的数据分别进行多项式拟合得到数据拟合结果,包括:Preferably, the data in the vertical one-dimensional window and the square two-dimensional window are respectively subjected to polynomial fitting to obtain data fitting results, including:

采用公式:Using the formula:

Figure BDA0003797786220000031
Figure BDA0003797786220000031

Figure BDA0003797786220000032
Figure BDA0003797786220000032

得到数据拟合结果;其中,f(x)1D为纵向一维窗口的数据拟合结果,f(x,y)2D为正方形二维窗口的数据拟合结果,x、y分别为数据在网格中的坐标位置,i、j为多项式次数,n为最大次数,且i+j≤n,ai为一元多项式xi项拟合系数,bi,j为二元多项式xiyj项拟合系数。The data fitting results are obtained; among them, f(x) 1D is the data fitting result of the vertical one-dimensional window, f(x,y) 2D is the data fitting result of the square two-dimensional window, and x and y are respectively the data in the network The coordinate position in the grid, i, j are polynomial degrees, n is the maximum degree, and i+j≤n, a i is the fitting coefficient of the one-variable polynomial x i item, b i, j is the binary polynomial x i y j item fit coefficient.

优选的,所述根据数据拟合结果确定误差值,包括:Preferably, said determining the error value according to the data fitting result includes:

采用公式:Using the formula:

e(x,y)=a0-b0,0 e(x,y)=a 0 -b 0,0

确定误差值;其中,e(x,y)为(x,y)位置的误差大小,a0为纵向一维滤波窗口数据拟合常数项系数,b0,0为正方形二维滤波窗口数据拟合常数项系数。Determine the error value; among them, e(x,y) is the error size of the (x,y) position, a 0 is the coefficient of the constant term of the longitudinal one-dimensional filter window data fitting, b 0,0 is the square two-dimensional filter window data fitting coefficient Composite constant term coefficient.

本发明还提供了一种月球卫星重力异常数据的全方向滤波系统,包括:The present invention also provides an omnidirectional filtering system for lunar satellite gravity anomaly data, including:

数据获取模块,用于获取待处理的月球卫星重力异常网格数据;The data acquisition module is used to acquire the gravity anomaly grid data of the lunar satellite to be processed;

数据剖分模块,用于将所述月球卫星重力异常网格数据剖分成多个子区;A data segmentation module, configured to divide the lunar satellite gravity anomaly grid data into multiple sub-areas;

单方向去噪模块,用于创建滤波窗口,对所述滤波窗口范围内的数据进行单方向去噪,滑动滤波窗口直至遍历子区内所有数据,得到各子区的单方向去噪结果;The unidirectional denoising module is used to create a filtering window, perform unidirectional denoising to the data within the scope of the filtering window, slide the filtering window until all data in the sub-areas are traversed, and obtain the unidirectional de-noising results of each sub-area;

全方向去噪模块,用于将各子区的数据按照预设角度做坐标旋转并重新网格化,返回单方向去噪模块直到完成所有预设角度方向的去噪,得到全方向去噪的各个子区数据;The omnidirectional denoising module is used to coordinately rotate and re-grid the data of each sub-area according to the preset angle, return to the unidirectional denoising module until the denoising of all preset angle directions is completed, and obtain the omnidirectional denoising Data of each sub-area;

数据拼合模块,用于将全方向去噪的各个子区数据进行拼合,得到第一次去噪结果;The data combination module is used to combine the data of each sub-area for omnidirectional denoising to obtain the first denoising result;

检验迭代模块,用于判断所述第一次去噪结果是否满足误差条件,若未满足条件则将第一次去噪结果作为待处理的月球卫星重力异常网格数据,返回数据剖分模块重新迭代直到输出满足误差条件的全方向去噪数据。The inspection iteration module is used to judge whether the first denoising result satisfies the error condition, if the first denoising result is not satisfied, the first denoising result is used as the lunar satellite gravity anomaly grid data to be processed, and the data segmentation module is returned to Iterate until outputting omni-directional denoised data satisfying the error condition.

优选的,所述单方向去噪模块,包括:Preferably, the unidirectional denoising module includes:

滤波窗口构建单元,用于建立滤波窗口;所述滤波窗口包括纵向一维窗口和正方形二维窗口,且纵向一维窗口位于正方形二维窗口的中心;A filtering window construction unit, configured to establish a filtering window; the filtering window includes a vertical one-dimensional window and a square two-dimensional window, and the vertical one-dimensional window is located at the center of the square two-dimensional window;

多项式拟合单元,用于将所述纵向一维窗口和所述正方形二维窗口内的数据分别进行多项式拟合得到数据拟合结果;A polynomial fitting unit, configured to perform polynomial fitting on the data in the longitudinal one-dimensional window and the square two-dimensional window respectively to obtain a data fitting result;

误差值确定单元,用于根据数据拟合结果确定误差值;An error value determination unit is used to determine the error value according to the data fitting result;

去噪单元,用于根据所述误差值得到相应滤波窗口内的单方向去噪数据。A denoising unit, configured to obtain unidirectional denoising data within a corresponding filtering window according to the error value.

优选的,所述多项式拟合单元,包括:Preferably, the polynomial fitting unit includes:

数据拟合子单元,用于采用公式:Data Fitting subunit to use the formula:

Figure BDA0003797786220000041
Figure BDA0003797786220000041

Figure BDA0003797786220000042
Figure BDA0003797786220000042

得到数据拟合结果;其中,f(x)1D为纵向一维窗口的数据拟合结果,f(x,y)2D为正方形二维窗口的数据拟合结果,x、y分别为数据在网格中的坐标位置,i、j为多项式次数,n为最大次数,且i+j≤n,ai为一元多项式xi项拟合系数,bi,j为二元多项式xiyj项拟合系数。The data fitting results are obtained; among them, f(x) 1D is the data fitting result of the vertical one-dimensional window, f(x,y) 2D is the data fitting result of the square two-dimensional window, and x and y are respectively the data in the network The coordinate position in the grid, i, j are polynomial degrees, n is the maximum degree, and i+j≤n, a i is the fitting coefficient of the one-variable polynomial x i item, b i, j is the binary polynomial x i y j item fit coefficient.

优选的,所述误差值确定单元,包括:Preferably, the error value determination unit includes:

误差值确定子单元,用于采用公式:The error value determination subunit is used to adopt the formula:

e(x,y)=a0-b0,0 e(x,y)=a 0 -b 0,0

确定误差值;其中,e(x,y)为(x,y)位置的误差大小,a0为纵向一维滤波窗口数据拟合常数项系数,b0,0为正方形二维滤波窗口数据拟合常数项系数。Determine the error value; among them, e(x, y) is the error size of the (x, y) position, a 0 is the coefficient of the constant term of the longitudinal one-dimensional filter window data fitting, b 0,0 is the square two-dimensional filter window data fitting coefficient Composite constant term coefficient.

根据本发明提供的具体实施例,本发明公开了以下技术效果:According to the specific embodiments provided by the invention, the invention discloses the following technical effects:

本发明提供了一种月球卫星重力异常数据的全方向滤波方法及系统,与现有技术相比,本发明通过对滤波窗口范围内的数据按照预设角度进行单方向去噪,最终得到全方向去噪数据,可以去除月球卫星重力异常数据中的条带干扰和高频噪音,为后续重力数据处理、反演和地质构造解释等方面提供可靠的数据支撑。The present invention provides an omnidirectional filtering method and system for lunar satellite gravity anomaly data. Compared with the prior art, the present invention performs unidirectional denoising on the data within the filtering window range according to a preset angle, and finally obtains omnidirectional Denoising data can remove band interference and high-frequency noise in lunar satellite gravity anomaly data, and provide reliable data support for subsequent gravity data processing, inversion, and geological structure interpretation.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案,下面将对实施例中所需要使用的附图作简单地介绍,显而易见地,下面描述中的附图仅仅是本发明的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动性的前提下,还可以根据这些附图获得其他的附图。In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the embodiments. Obviously, the accompanying drawings in the following description are only some of the present invention. Embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without paying creative labor.

图1为本发明提供的一种月球卫星重力异常数据的全方向滤波方法流程图;Fig. 1 is a flow chart of an omnidirectional filtering method for lunar satellite gravity anomaly data provided by the present invention;

图2为本发明提供的单方向去噪原理图;其中dx、dy分别为数据x、y方向网格间距,r为滤波半窗口参数。Fig. 2 is a schematic diagram of the single-direction denoising provided by the present invention; where dx and dy are the grid spacing in the x and y directions of the data respectively, and r is the filtering half-window parameter.

图3为本发明提供的月球Rümkerregion原始卫星布格重力异常图;Fig. 3 is the Bouguer gravitational anomaly diagram of the moon Rümkerregion original satellite provided by the present invention;

图4为本发明提供的全方向滤波去噪后的月球Rümkerregion卫星布格重力异常图。Fig. 4 is a Bouguer gravity anomaly map of the lunar Rümkerregion satellite after omnidirectional filtering and denoising provided by the present invention.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅仅是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

在本文中提及“实施例”意味着,结合实施例描述的特定特征、结构或特性可以包含在本申请的至少一个实施例中。在说明书中的各个位置出现该短语并不一定均是指相同的实施例,也不是与其它实施例互斥的独立的或备选的实施例。本领域技术人员显式地和隐式地理解的是,本文所描述的实施例可以与其它实施例相结合。Reference herein to an "embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the present application. The occurrences of this phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is understood explicitly and implicitly by those skilled in the art that the embodiments described herein can be combined with other embodiments.

本申请的说明书和权利要求书及所述附图中的术语“第一”、“第二”、“第三”和“第四”等是用于区别不同对象,而不是用于描述特定顺序。此外,术语“包括”和“具有”以及它们任何变形,意图在于覆盖不排他的包含。例如包含了一系列步骤、过程、方法等没有限定于已列出的步骤,而是可选地还包括没有列出的步骤,或可选地还包括对于这些过程、方法、产品或设备固有的其它步骤元。The terms "first", "second", "third" and "fourth" in the specification and claims of the present application and the drawings are used to distinguish different objects, rather than to describe a specific order . Furthermore, the terms "include" and "have", as well as any variations thereof, are intended to cover a non-exclusive inclusion. For example, a series of steps, processes, methods, etc. are not limited to the listed steps, but optionally also include steps that are not listed, or optionally also include the inherent characteristics of these processes, methods, products or equipment. other steps.

为使本发明的上述目的、特征和优点能够更加明显易懂,下面结合附图和具体实施方式对本发明作进一步详细的说明。In order to make the above objects, features and advantages of the present invention more comprehensible, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

请参阅图1,一种月球卫星重力异常数据的全方向滤波方法,包括:Please refer to Figure 1, an omnidirectional filtering method for lunar satellite gravity anomaly data, including:

步骤1:获取待处理的月球卫星重力异常网格数据;Step 1: Obtain the gravity anomaly grid data of the lunar satellite to be processed;

步骤2:将所述月球卫星重力异常网格数据剖分成多个子区;Step 2: dividing the lunar satellite gravity anomaly grid data into multiple sub-areas;

进一步地,在步骤2中需要根据计算机实际内存情况和输入数据总网格数,确定子区的网格数;其次,为使后续子区平滑拼合,还需保证各子区之间有一定的重叠区域;再者,各子区按照其位于网格数据中x方向和y方向的顺序编号,由于总数据网格数不一定是子区网格数的整数倍,故在数据边缘的子区与其他子区的大小可能不一致。Further, in step 2, it is necessary to determine the number of grids in the sub-areas according to the actual memory of the computer and the total number of grids in the input data; secondly, in order to make the subsequent sub-areas merge smoothly, it is necessary to ensure that there is a certain distance between each sub-area. Overlapping area; moreover, each sub-area is numbered according to the order in which it is located in the x direction and y direction in the grid data. Since the total number of data grids is not necessarily an integer multiple of the number of sub-area grids, the sub-area at the edge of the data May not match the size of other subsections.

步骤3:创建滤波窗口,对所述滤波窗口范围内的数据进行单方向去噪,滑动滤波窗口直至遍历子区内所有数据,得到各子区的单方向去噪结果;Step 3: Create a filtering window, perform unidirectional denoising on the data within the scope of the filtering window, slide the filtering window until all data in the sub-areas are traversed, and obtain the unidirectional denoising results of each sub-area;

需要说明的是,本发明的步骤3,包括:It should be noted that step 3 of the present invention includes:

建立滤波窗口;所述滤波窗口包括纵向一维窗口和正方形二维窗口,且纵向一维窗口位于正方形二维窗口的中心;Establish a filter window; the filter window includes a vertical one-dimensional window and a square two-dimensional window, and the vertical one-dimensional window is located at the center of the square two-dimensional window;

在实际应用中,选取适合的滤波半窗口宽度r,建立长度为2·r+1的纵向一维窗口和边长为2·r+1的正方形二维窗口,使一维窗口位于二维窗口的中心(如图2),将两个窗口内的数据分别进行多项式拟合,由纵向一维滤波窗口数据拟合常数项系数减去对应位置正方形二维滤波窗口数据拟合常数项系数确定误差大小,从输入数据中将误差减去,获取一维滤波窗口内去噪后的数据。滤波半窗口宽度r的大小与最终去噪效果直接相关,半窗口过大会导致结果过度平滑,损失较多有效信号;半窗口过小则无法将条带干扰排除干净。故需要参考数据网格间距和条带干扰宽度等因素,采用试错法,选择最合适的滤波半窗口。In practical applications, select the appropriate filtering half-window width r, establish a vertical one-dimensional window with a length of 2·r+1 and a square two-dimensional window with a side length of 2·r+1, so that the one-dimensional window is located in the two-dimensional window (as shown in Figure 2), polynomial fitting is performed on the data in the two windows respectively, and the error is determined by subtracting the fitting constant term coefficient of the data fitting constant term of the longitudinal one-dimensional filtering window data from the corresponding position square two-dimensional filtering window data fitting coefficient Size, subtract the error from the input data to obtain the denoised data in the one-dimensional filtering window. The size of the filtering half-window width r is directly related to the final denoising effect. If the half-window is too large, the result will be over-smooth and more effective signals will be lost; if the half-window is too small, the band interference cannot be completely eliminated. Therefore, it is necessary to refer to factors such as data grid spacing and stripe interference width, and use trial and error to select the most suitable filtering half window.

特别地,由于一维窗口在二维窗口的中心位置,为使子区边缘数据正常去噪,需对子区扩边出一个滤波半窗口r的范围,扩边采用二维边界值复制法,即在扩边区域直接复制边缘的重力异常值。In particular, since the one-dimensional window is at the center of the two-dimensional window, in order to denoise the edge data of the sub-area normally, it is necessary to expand the edge of the sub-area to obtain a range of filtering half-window r, and the edge expansion adopts the two-dimensional boundary value copy method, That is, the gravity anomaly of the edge is directly copied in the edge expansion area.

进一步的,将所述纵向一维窗口和所述正方形二维窗口内的数据分别进行多项式拟合得到数据拟合结果;其计算公式如下:Further, the data in the vertical one-dimensional window and the square two-dimensional window are respectively subjected to polynomial fitting to obtain a data fitting result; the calculation formula is as follows:

Figure BDA0003797786220000071
Figure BDA0003797786220000071

Figure BDA0003797786220000072
Figure BDA0003797786220000072

其中,f(x)1D为纵向一维窗口的数据拟合结果,f(x,y)2D为正方形二维窗口的数据拟合结果,x、y分别为数据在网格中的坐标位置,i、j为多项式次数,n为最大次数,且i+j≤n,ai为一元多项式xi项拟合系数,bi,j为二元多项式xiyj项拟合系数。Among them, f(x) 1D is the data fitting result of the vertical one-dimensional window, f(x,y) 2D is the data fitting result of the square two-dimensional window, x and y are the coordinate positions of the data in the grid respectively, i and j are polynomial degrees, n is the maximum degree, and i+j≤n, a i is the fitting coefficient of the one-variable polynomial x i term, b i,j is the fitting coefficient of the binary polynomial x i y j term.

根据数据拟合结果确定误差值;误差值的计算公式为:The error value is determined according to the data fitting result; the calculation formula of the error value is:

e(x,y)=a0-b0,0 e(x,y)=a 0 -b 0,0

其中,e(x,y)为(x,y)位置的误差大小,a0为纵向一维滤波窗口数据拟合常数项系数,b0,0为正方形二维滤波窗口数据拟合常数项系数。Among them, e(x, y) is the error size of the (x, y) position, a 0 is the coefficient of the constant term of the data fitting of the vertical one-dimensional filtering window, and b 0,0 is the coefficient of the constant term of the data fitting of the square two-dimensional filtering window .

根据所述误差值得到相应滤波窗口内的单方向去噪数据。The unidirectional denoising data within the corresponding filtering window is obtained according to the error value.

步骤4:将各子区的数据按照预设角度做坐标旋转并重新网格化,返回步骤3直到完成所有预设角度方向的去噪,得到全方向去噪的各个子区数据;Step 4: Rotate the data of each sub-area according to the preset angle and re-grid, return to step 3 until the denoising of all preset angle directions is completed, and obtain the data of each sub-area denoised in all directions;

进一步的,在步骤4中,本发明可根据月球卫星重力异常数据条带干扰特征对子区数据选择多个预设角度(比如0°、30°、60°、90°、-30°、-60°),从而实现子区全方向滤波去噪。Further, in step 4, the present invention can select a plurality of preset angles (such as 0°, 30°, 60°, 90°, -30°, - 60°), so as to realize omni-directional filtering and denoising of the sub-area.

步骤5:将全方向去噪的各个子区数据进行拼合,得到第一次去噪结果;Step 5: Combine the data of each sub-area for omnidirectional denoising to obtain the first denoising result;

进一步地,在步骤5中,本发明需要将子区按照分区前对应位置复位,各重叠部分对应位置数据求平均。Further, in step 5, the present invention needs to reset the sub-area according to the corresponding position before partitioning, and average the corresponding position data of each overlapping part.

步骤6:判断所述第一次去噪结果是否满足误差条件,若未满足条件则将第一次去噪结果作为待处理的月球卫星重力异常网格数据,返回步骤2直到输出满足误差条件的全方向去噪数据。需要说明的是,误差条件可以是事先根据经验人为设置的迭代次数,也可以是均方根误差容限,即满足迭代次数限制或均方根误差限制均可通过检验,输出最终的全方向滤波去噪结果。Step 6: Determine whether the first denoising result satisfies the error condition. If the condition is not met, take the first denoising result as the lunar satellite gravity anomaly grid data to be processed, and return to step 2 until the output meets the error condition. Omnidirectional denoised data. It should be noted that the error condition can be the number of iterations artificially set in advance based on experience, or the root mean square error tolerance, that is, the limit of the number of iterations or the limit of the root mean square error can pass the test, and the final omnidirectional filtering is output Denoising results.

下面本发明结合具体的实施例对本发明的去噪过程做进一步的说明:Below the present invention is further described to the denoising process of the present invention in conjunction with specific embodiment:

步骤一:读入研究区待处理的月球卫星重力异常网格数据(见图3,数据总网格数296×108)。进一步的,本实施中的布格重力异常数据是通过月球GRGM1200B模型解算而来的。Step 1: Read in the gravitational anomaly grid data of lunar satellites to be processed in the study area (see Figure 3, the total number of grids in the data is 296×108). Furthermore, the Bouguer gravity anomaly data in this implementation is calculated through the lunar GRGM1200B model.

步骤二:将网格数据剖分成6×3的子区,除边缘子区外,子区网格数为70×70,重叠部分为25个网格;Step 2: Divide the grid data into 6×3 sub-areas, except for the edge sub-area, the number of sub-area grids is 70×70, and the overlapping part is 25 grids;

步骤三:选择滤波半窗口为8,对滤波窗口范围内的数据进行单方向去噪,在子区内滑动两个去噪窗口,进而得到各子区内全部数据的单方向去噪结果;Step 3: Select the filtering half-window as 8, perform unidirectional denoising on the data within the filtering window range, slide two denoising windows in the sub-areas, and then obtain the unidirectional de-noising results of all data in each sub-area;

步骤四:将各子区数据按照0°、30°、60°、90°、-30°、-60°的特定角度逐次旋转,重新网格化,重复子区单方向去噪步骤对其进行单方向去噪,直到完成所有特定角度的全方向去噪;Step 4: Rotate the data of each sub-area successively according to specific angles of 0°, 30°, 60°, 90°, -30°, -60°, re-grid, and repeat the sub-area unidirectional denoising steps Unidirectional denoising until omnidirectional denoising of all specific angles is completed;

步骤五:将完成全方向去噪的各个子区数据进行拼合,得到全区的第一次去噪结果;Step 5: Combine the data of each sub-area that has completed omnidirectional denoising to obtain the first denoising result of the whole area;

步骤六:检验完成第一次全方向滤波去噪结果的效果,最终在迭代3次后,均方根误差满足条件,输出全方向滤波去噪结果(见图4)。Step 6: Check the effect of the first omnidirectional filtering and denoising results. Finally, after 3 iterations, the root mean square error meets the conditions, and output the omnidirectional filtering and denoising results (see Figure 4).

根据本发明提供的具体实施例,本发明公开了以下有益效果:According to the specific embodiments provided by the invention, the invention discloses the following beneficial effects:

1)本发明实现了一种适用于含有条带干扰及随机噪音的月球卫星重力异常数据的全方向去噪方法。1) The present invention implements an omnidirectional denoising method suitable for lunar satellite gravity anomaly data containing band interference and random noise.

2)本发明利用滑动子区的剖分方案,减少了去噪过程中对计算机内存占用量,大大提升了去噪速度。2) The present invention utilizes the subdivision scheme of the sliding sub-area, which reduces the computer memory usage during the denoising process and greatly improves the denoising speed.

3)本发明采用迭代算法,对每次迭代的全方向去噪效果均进行了检验,有效提升了去噪效果。3) The present invention adopts an iterative algorithm to check the omni-directional denoising effect of each iteration, effectively improving the denoising effect.

本发明还提供了一种月球卫星重力异常数据的全方向滤波系统,包括:The present invention also provides an omnidirectional filtering system for lunar satellite gravity anomaly data, including:

数据获取模块,用于获取待处理的月球卫星重力异常网格数据;The data acquisition module is used to acquire the gravity anomaly grid data of the lunar satellite to be processed;

数据剖分模块,用于将所述月球卫星重力异常网格数据剖分成多个子区;A data segmentation module, configured to divide the lunar satellite gravity anomaly grid data into multiple sub-areas;

单方向去噪模块,用于对所述滤波窗口范围内的数据进行单方向去噪,滑动滤波窗口直至遍历子区内所有数据,得到各子区的单方向去噪结果;A unidirectional denoising module, configured to perform unidirectional denoising on the data within the filtering window range, slide the filtering window until all data in the sub-area is traversed, and obtain the unidirectional denoising results of each sub-area;

全方向去噪模块,用于将各子区的数据按照预设角度逐次旋转,返回单方向去噪模块直到完成所有预设角度的单方向去噪,得到全方向去噪的各个子区数据;The omnidirectional denoising module is used to rotate the data of each sub-area successively according to the preset angle, return to the unidirectional denoising module until the unidirectional denoising of all preset angles is completed, and obtain the data of each sub-area for omnidirectional denoising;

数据拼合模块,用于将全方向去噪的各个子区数据进行拼合,得到第一次去噪结果;The data combination module is used to combine the data of each sub-area for omnidirectional denoising to obtain the first denoising result;

检验迭代模块,用于判断所述第一次去噪结果是否满足误差条件,若未满足条件则将第一次去噪结果作为待处理的月球卫星重力异常网格数据,返回数据剖分模块直到输出满足误差条件的全方向去噪数据。The inspection iteration module is used to judge whether the first denoising result meets the error condition, if the first denoising result is not satisfied, the first denoising result is used as the lunar satellite gravity anomaly grid data to be processed, and the data segmentation module is returned until Output the omnidirectional denoising data satisfying the error condition.

优选的,所述单方向去噪模块,包括:Preferably, the unidirectional denoising module includes:

滤波窗口构建单元,用于建立滤波窗口;所述滤波窗口包括纵向一维窗口和正方形二维窗口,且纵向一维窗口位于正方形二维窗口的中心;A filtering window construction unit, configured to establish a filtering window; the filtering window includes a vertical one-dimensional window and a square two-dimensional window, and the vertical one-dimensional window is located at the center of the square two-dimensional window;

多项式拟合单元,用于将所述纵向一维窗口和所述正方形二维窗口内的数据分别进行多项式拟合得到数据拟合结果;A polynomial fitting unit, configured to perform polynomial fitting on the data in the longitudinal one-dimensional window and the square two-dimensional window respectively to obtain a data fitting result;

误差值确定单元,用于根据数据拟合结果确定误差值;An error value determination unit is used to determine the error value according to the data fitting result;

去噪单元,用于根据所述误差值得到相应滤波窗口内的单方向去噪数据。A denoising unit, configured to obtain unidirectional denoising data within a corresponding filtering window according to the error value.

优选的,所述多项式拟合单元,包括:Preferably, the polynomial fitting unit includes:

数据拟合子单元,用于采用公式:Data Fitting subunit to use the formula:

Figure BDA0003797786220000091
Figure BDA0003797786220000091

Figure BDA0003797786220000092
Figure BDA0003797786220000092

得到数据拟合结果;其中,f(x)1D为纵向一维窗口的数据拟合结果,f(x,y)2D为正方形二维窗口的数据拟合结果,x、y分别为数据在网格中的坐标位置,i、j为多项式次数,n为最大次数,且i+j≤n,ai为一元多项式xi项拟合系数,bi,j为二元多项式xiyj项拟合系数。The data fitting results are obtained; among them, f(x) 1D is the data fitting result of the vertical one-dimensional window, f(x,y) 2D is the data fitting result of the square two-dimensional window, and x and y are respectively the data in the network The coordinate position in the grid, i, j are polynomial degrees, n is the maximum degree, and i+j≤n, a i is the fitting coefficient of the one-variable polynomial x i item, b i, j is the binary polynomial x i y j item fit coefficient.

优选的,所述误差值确定单元,包括:Preferably, the error value determination unit includes:

误差值确定子单元,用于采用公式:The error value determination subunit is used to adopt the formula:

e(x,y)=a0-b0,0 e(x,y)=a 0 -b 0,0

确定误差值;其中,e(x,y)为(x,y)位置的误差大小,a0为纵向一维滤波窗口数据拟合常数项系数,b0,0为正方形二维滤波窗口数据拟合常数项系数。Determine the error value; among them, e(x,y) is the error size of the (x,y) position, a 0 is the coefficient of the constant term of the longitudinal one-dimensional filter window data fitting, b 0,0 is the square two-dimensional filter window data fitting coefficient Composite constant term coefficient.

本发明通过对滤波窗口范围内的数据按照预设角度进行单方向去噪,最终得到全方向去噪数据,可以去除月球卫星重力异常数据中的条带干扰和高频噪音,为后续重力数据处理、反演和地质构造解释等方面提供可靠的数据支撑。The present invention denoises the data within the filtering window in one direction according to the preset angle, and finally obtains the omnidirectional denoising data, which can remove the band interference and high-frequency noise in the gravity anomaly data of the lunar satellite, and provide the next step for the subsequent gravity data processing. , inversion and interpretation of geological structures and other aspects to provide reliable data support.

本说明书中各个实施例采用递进的方式描述,每个实施例重点说明的都是与其他实施例的不同之处,各个实施例之间相同相似部分互相参见即可。对于实施例公开的方法而言,由于其与实施例公开的装置相对应,所以描述的比较简单,相关之处参见装置部分说明即可。Each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other. As for the method disclosed in the embodiment, since it corresponds to the device disclosed in the embodiment, the description is relatively simple, and the related parts can be referred to the description of the device part.

本文中应用了具体个例对本发明的原理及实施方式进行了阐述,以上实施例的说明只是用于帮助理解本发明的方法及其核心思想;同时,对于本领域的一般技术人员,依据本发明的思想,在具体实施方式及应用范围上均会有改变之处。综上所述,本说明书内容不应理解为对本发明的限制。In this paper, specific examples have been used to illustrate the principle and implementation of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; meanwhile, for those of ordinary skill in the art, according to the present invention Thoughts, there will be changes in specific implementation methods and application ranges. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims (6)

1. An omnidirectional filtering method for lunar satellite gravity anomaly data is characterized by comprising the following steps:
step 1: acquiring lunar satellite gravity anomaly grid data to be processed;
step 2: dividing the lunar satellite gravity anomaly grid data into a plurality of sub-areas;
and 3, step 3: creating a filtering window, carrying out unidirectional denoising on data in the range of the filtering window, sliding the filtering window until all data in the sub-area are traversed, and obtaining a unidirectional denoising result of each sub-area;
the unidirectional denoising is performed on the data in the filtering window range, and the unidirectional denoising comprises the following steps:
establishing a filtering window; the filtering window comprises a longitudinal one-dimensional window and a square two-dimensional window, and the longitudinal one-dimensional window is positioned in the center of the square two-dimensional window;
respectively carrying out polynomial fitting on the data in the longitudinal one-dimensional window and the data in the square two-dimensional window to obtain data fitting results;
determining an error value according to the data fitting result;
obtaining unidirectional denoising data in a corresponding filtering window according to the error value;
and 4, step 4: performing coordinate rotation on the data of each sub-area according to a preset angle, rescreening the gridding, and returning to the step 3 until the denoising in all preset angle directions is completed, so as to obtain the data of each sub-area subjected to omnidirectional denoising;
and 5: splicing all sub-area data subjected to omnidirectional denoising to obtain a first denoising result;
step 6: and judging whether the first denoising result meets an error condition, if not, taking the first denoising result as lunar satellite gravity abnormal grid data to be processed, and returning to the step 2 until outputting the omnidirectional denoising data meeting the error condition.
2. The method as claimed in claim 1, wherein the performing polynomial fitting on the data in the longitudinal one-dimensional window and the square two-dimensional window to obtain a data fitting result comprises:
the formula is adopted:
Figure DEST_PATH_IMAGE002
Figure DEST_PATH_IMAGE004
get the numberAccording to the fitting result; wherein, f (x) 1D Fitting the data for a longitudinal one-dimensional window, f (x, y) 2D Is the data fitting result of a square two-dimensional window, x and y are the coordinate positions of the data in the grid respectively, i and j are polynomial times, n is the maximum time, and a i Is a univariate polynomial x i Coefficient of term fit, b i,j Is a binary polynomial x i y j The term fitting coefficient.
3. The method as claimed in claim 2, wherein the determining an error value according to the data fitting result comprises:
the formula is adopted:
Figure DEST_PATH_IMAGE006
determining an error value; wherein, is the error size of (x, y) position, a 0 Fitting constant term coefficients to longitudinal one-dimensional filter window data, b 0,0 Constant term coefficients are fitted to the square two-dimensional filter window data.
4. An omnidirectional filtering system for lunar satellite gravity anomaly data, comprising:
the data acquisition module is used for acquiring lunar satellite gravity anomaly grid data to be processed;
the data subdivision module is used for subdividing the lunar satellite gravity anomaly grid data into a plurality of sub-areas;
the unidirectional denoising module is used for creating a filtering window, performing unidirectional denoising on the data in the range of the filtering window, sliding the filtering window until all the data in the sub-area are traversed, and obtaining a unidirectional denoising result of each sub-area;
wherein, the unidirectional denoising module comprises:
the filtering window construction unit is used for establishing a filtering window; the filtering window comprises a longitudinal one-dimensional window and a square two-dimensional window, and the longitudinal one-dimensional window is positioned in the center of the square two-dimensional window;
the polynomial fitting unit is used for respectively performing polynomial fitting on the data in the longitudinal one-dimensional window and the data in the square two-dimensional window to obtain data fitting results;
an error value determination unit for determining an error value according to the data fitting result;
the denoising unit is used for obtaining unidirectional denoising data in a corresponding filtering window according to the error value;
the omnidirectional denoising module is used for performing coordinate rotation on the data of each sub-area according to a preset angle, rescreening the gridding, returning to the unidirectional denoising module until the denoising in all the preset angle directions is completed, and obtaining the data of each sub-area subjected to omnidirectional denoising;
the data splicing module is used for splicing the data of each sub-area subjected to omnidirectional denoising to obtain a first denoising result;
and the inspection iteration module is used for judging whether the first denoising result meets an error condition or not, taking the first denoising result as lunar satellite gravity abnormal grid data to be processed if the first denoising result does not meet the error condition, and returning to the data subdivision module until outputting omnidirectional denoising data meeting the error condition.
5. The system of claim 4, wherein the polynomial fitting unit comprises:
a data fitting subunit for employing the formula:
Figure DEST_PATH_IMAGE008
Figure DEST_PATH_IMAGE010
obtaining a data fitting result; wherein, f (x) 1D Fitting the data for a longitudinal one-dimensional window, f (x, y) 2D Is the data fitting result of a square two-dimensional window, x and y are respectively the coordinate positions of the data in the grid, i and j are polynomial times, n is the maximum time, and a i Is a univariate polynomial x i Coefficient of term fit, b i,j Is a binary polynomial x i y j The term fitting coefficient.
6. The system of claim 5, wherein the error value determining unit comprises:
an error value determining subunit configured to use the formula:
Figure DEST_PATH_IMAGE012
determining an error value; wherein, is the error magnitude of (x, y) position, a 0 Fitting constant term coefficients to longitudinal one-dimensional filter window data, b 0,0 Constant term coefficients are fitted to the square two-dimensional filter window data.
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