CN105334537A - Primary wave and multiple wave separation method based on alternative splitting Bregman iterative algorithm - Google Patents
Primary wave and multiple wave separation method based on alternative splitting Bregman iterative algorithm Download PDFInfo
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Abstract
本发明属于地震勘探技术中地震信号处理领域,具体公开了一种基于交替分裂Bregman迭代算法的一次波和多次波分离方法。对于基于3D匹配滤波器的多次波自适应相减方法,本发明利用交替分裂Bregman迭代算法求解对一次波施加稀疏约束的优化问题,实现3D匹配滤波器的估计,并利用估计的3D匹配滤波器自适应分离3D数据窗口中的一次波和多次波。相比于传统的迭代重加权最小二乘算法,本发明中的交替分裂Bregman迭代算法在每一个3D数据窗口估计3D匹配滤波器时,只需计算一次矩阵-矩阵相乘和矩阵求逆,能够有效地降低优化问题求解的计算复杂度,提高一次波和多次波自适应分离的计算效率。
The invention belongs to the field of seismic signal processing in seismic exploration technology, and specifically discloses a primary wave and multiple wave separation method based on an alternately split Bregman iterative algorithm. For the multiple wave adaptive subtraction method based on 3D matched filter, the present invention uses alternate splitting Bregman iterative algorithm to solve the optimization problem of applying sparse constraints to the primary wave, realizes the estimation of 3D matched filter, and utilizes the estimated 3D matched filter The detector adaptively separates primary and multiple waves in the 3D data window. Compared with the traditional iterative reweighted least squares algorithm, the alternating split Bregman iterative algorithm in the present invention only needs to calculate the matrix-matrix multiplication and matrix inversion once when estimating the 3D matched filter in each 3D data window, and can It effectively reduces the computational complexity of solving the optimization problem, and improves the computational efficiency of the adaptive separation of primary waves and multiple waves.
Description
技术领域technical field
本发明属于地震勘探技术中的地震信号处理领域,具体涉及一种基于交替分裂Bregman迭代算法的一次波和多次波分离方法。The invention belongs to the field of seismic signal processing in seismic exploration technology, and in particular relates to a method for separating primary waves and multiple waves based on an alternately split Bregman iterative algorithm.
背景技术Background technique
SRME(SurfaceRelatedMultipleElimination)是海洋地震勘探中广泛采用的多次波压制方法。SRME预测的多次波与真实多次波存在时间和空间差异,可以利用匹配滤波器将预测多次波从原始数据中自适应减去。通常,随着匹配滤波器维数的增加(从1D、2D到3D匹配滤波器),多次波能更好地从原始数据中自适应减去,但需要更多的计算时间。基于3D匹配滤波器的多次波自适应相减方法的数学模型为(Li,Z.,andW.Lu,2013,Adaptivemultiplesubtractionbasedon3Dblindseparationofconvolvedmixtures:Geophysics,78,V251-V266):SRME (SurfaceRelatedMultipleElimination) is a multiple wave suppression method widely used in marine seismic exploration. There are time and space differences between the multiples predicted by SRME and the real multiples. Matched filters can be used to adaptively subtract the predicted multiples from the original data. In general, as the dimensionality of the matched filter increases (from 1D, 2D to 3D matched filters), multiples are better adaptively subtracted from the raw data, but require more computation time. The mathematical model of the multiple wave adaptive subtraction method based on 3D matched filter is (Li, Z., and W. Lu, 2013, Adaptive multiple subtraction based on 3D blind separation of involved mixtures: Geophysics, 78, V251-V266):
v=d-Hx(1)v=d-Hx(1)
其中,v表示估计一次波,d表示原始数据,x表示3D匹配滤波器,H表示预测多次波的褶积矩阵。Among them, v represents the estimated primary, d represents the original data, x represents the 3D matched filter, and H represents the convolution matrix for predicting multiples.
基于3D匹配滤波器的多次波自适应相减方法在相互重叠的3D数据窗口内,通过估计3D匹配滤波器来自适应分离一次波和多次波。为估计3D匹配滤波器,传统的多次波自适应相减方法对估计一次波施加能量最小化约束。另外,为避免滤波器估计的不稳定性,滤波器系数也假设满足能量最小化约束。相应的优化问题为:The multiple adaptive subtraction method based on 3D matched filter adaptively separates primary and multiple by estimating 3D matched filter within overlapping 3D data windows. To estimate the 3D matched filter, the traditional multiple adaptive subtraction method imposes an energy minimization constraint on the estimated primary. In addition, to avoid instability in filter estimation, the filter coefficients are also assumed to satisfy energy minimization constraints. The corresponding optimization problem is:
其中,μ为正则化参数。方程(2)中的3D匹配滤波器可以采用最小二乘算法进行求解:Among them, μ is the regularization parameter. The 3D matched filter in equation (2) can be solved using the least squares algorithm:
x=(HTH+μI)-1HTd(3)x=(H T H+μI) -1 H T d(3)
其中,I为单位矩阵。Among them, I is the identity matrix.
最小二乘算法需要一次波和多次波的正交性假设。当一次波和多次波相互重叠或有强一次波同相轴存在时,最小二乘算法会产生残余多次波或造成一次波的损伤。为克服正交性假设的缺点,对一次波施加稀疏约束已经引入到多次波自适应相减方法中。另外,假设3D匹配滤波器系数满足能量最小化约束来确保3D匹配滤波器估计的稳定性,相应的优化问题为:The least squares algorithm requires an assumption of orthogonality for the primaries and multiples. When the primary wave and the multiple wave overlap each other or there is a strong primary wave event, the least squares algorithm will generate residual multiple waves or cause damage to the primary wave. To overcome the shortcoming of the orthogonality assumption, the sparse constraint imposed on the primary has been introduced into the multiple adaptive subtraction method. In addition, assuming that the 3D matched filter coefficients satisfy the energy minimization constraint to ensure the stability of the 3D matched filter estimation, the corresponding optimization problem is:
其中,λ为正则化参数。可以采用迭代重加权最小二乘算法(Guitton,A.,andD.J.Verschuur,2004,AdaptivesubtractionofmultiplesusingtheL1-norm:GeophysicalProspecting,52,27-38)来估计式(4)中的3D匹配滤波器。然而,迭代重加权最小二乘算法在每一步迭代均需计算一次矩阵-矩阵相乘和矩阵求逆,计算复杂度较高。Among them, λ is a regularization parameter. The 3D matched filter in equation (4) can be estimated using an iterative reweighted least squares algorithm (Guitton, A., and D.J. Verschuur, 2004, Adaptive subtraction of multiples using the L 1 -norm: Geophysical Prospecting, 52, 27-38). However, the iterative reweighted least squares algorithm needs to calculate a matrix-matrix multiplication and matrix inversion at each iteration step, and the computational complexity is relatively high.
发明内容Contents of the invention
针对现有技术中存在的上述技术问题,本发明提出了一种基于交替分裂Bregman迭代的一次波和多次波分离方法,该方法能够有效降低对一次波施加稀疏约束的优化问题求解的计算复杂度,提高一次波和多次波分离的计算效率。Aiming at the above-mentioned technical problems existing in the prior art, the present invention proposes a primary wave and multiple wave separation method based on alternately splitting Bregman iterations, which can effectively reduce the computational complexity of solving optimization problems with sparse constraints imposed on the primary wave degree, improving the calculation efficiency of primary wave and multiple wave separation.
为了实现上述目的,本发明采用如下技术方案:In order to achieve the above object, the present invention adopts the following technical solutions:
基于交替分裂Bregman迭代算法的一次波和多次波分离方法,包括如下步骤:The primary wave and multiple wave separation method based on alternate splitting Bregman iterative algorithm includes the following steps:
a设置变量初始值,需要设置初始值的变量包括3D数据窗口的时间长度T0,3D数据窗口的空间长度X0,3D数据窗口的道集个数Y0,3D匹配滤波器的时间长度K,3D匹配滤波器的空间长度R,3D匹配滤波器的道集个数G,一次波阈值sβ,阻尼因子β和迭代次数 a Set the initial value of the variable. The variables that need to be set to the initial value include the time length T 0 of the 3D data window, the spatial length X 0 of the 3D data window, the number of gathers Y 0 of the 3D data window, and the time length K of the 3D matched filter , the spatial length R of the 3D matched filter, the number of gathers G of the 3D matched filter, the primary wave threshold s β , the damping factor β and the number of iterations
b输入原始数据道集中一个待处理的3D数据窗口中的数据d,然后利用预测多次波数据以及3D数据窗口的参数T0、X0和Y0、3D匹配滤波器的参数K、R和G构造褶积矩阵H,并采用克莱斯基分解计算逆矩阵 b Input the data d in a 3D data window to be processed in the original data collection, and then use the predicted multiple wave data and the parameters T 0 , X 0 and Y 0 of the 3D data window, and the parameters K, R and G constructs the convolution matrix H, and uses Kleisky decomposition to calculate the inverse matrix
c基于交替分裂Bregman迭代算法,利用步骤b得到的逆矩阵对地震道集的所有3D数据窗口的数据d逐一进行处理;c is based on the alternate split Bregman iterative algorithm, using the inverse matrix obtained in step b Process the data d of all 3D data windows of the seismic gather one by one;
d判断原始数据道集中所有3D数据窗口内的数据d是否全部处理完毕;如果否,返回步骤c;如果全部处理完毕,则首先采用3D汉宁窗将每一个3D数据窗口中估计的一次波进行加权,并融合为一个数据体然后采用同样的方式将3D汉宁窗融合为一个数据体最终的一次波估计结果表示为:其中,/表示逐个元素的相除操作。d Determine whether all the data d in all 3D data windows in the original data gather have been processed; if not, return to step c; if all have been processed, first use the 3D Hanning window to process the primary wave estimated in each 3D data window weighted and fused into one data volume Then use the same method to fuse the 3D Hanning window into a data volume The final primary wave estimation result is expressed as: Among them, / represents an element-by-element division operation.
优选地,所述步骤c具体包括:Preferably, said step c specifically includes:
c1设置迭代数m=1,利用步骤b得到的逆矩阵求取一次波的初始估计值v(0):
c2计算向量y(m)=v(m-1)+b1 (m-1);c2 calculation vector y (m) = v (m-1) +b 1 (m-1) ;
c3对y(m)利用如下的距离算子prox计算向量u1 (m):c3 uses the following distance operator prox to calculate the vector u 1 (m) for y ( m):
其中,i=1,2,…,T0,j=1,2,…,X0,n=1,2,…,Y0,s=sβC(m),0<sβ<1;y(m)={yi,j,n (m)},yi,j,n (m)表示向量y(m)中下标为(i,j,n)的元素,C(m)=max(|yi,j,n (m)|),
c4计算向量b1 (m)=b1 (m-1)-[u1 (m)-v(m-1)];c4 calculation vector b 1 (m) = b 1 (m-1) -[u 1 (m) -v (m-1) ];
c5计算3D匹配滤波器
c6估计一次波v(m)=d-Hx(m);c6 estimates primary wave v (m) = d-Hx (m) ;
c7令m=m+1,如果返回到步骤c2;如果输出当前3D数据窗口估计的一次波结果。c7 let m=m+1, if Return to step c2; if Output the primary wave result estimated by the current 3D data window.
本发明具有如下优点:The present invention has the following advantages:
对于基于3D匹配滤波器的多次波自适应相减方法,本发明利用交替分裂Bregman迭代算法求解对一次波施加稀疏约束的优化问题,实现3D匹配滤波器的估计,并利用估计的3D匹配滤波器自适应分离3D数据窗口中的一次波和多次波。相比于传统的迭代重加权最小二乘算法,本发明中的交替分裂Bregman迭代算法在每一个3D数据窗口估计3D匹配滤波器时,只需计算一次矩阵-矩阵相乘和矩阵求逆,能有效地降低优化问题求解的计算复杂度,提高一次波和多次波自适应分离的计算效率。For the multiple wave adaptive subtraction method based on 3D matched filter, the present invention uses alternate splitting Bregman iterative algorithm to solve the optimization problem of applying sparse constraints to the primary wave, realizes the estimation of 3D matched filter, and utilizes the estimated 3D matched filter The detector adaptively separates primary and multiple waves in the 3D data window. Compared with the traditional iterative reweighted least squares algorithm, the alternating split Bregman iterative algorithm in the present invention only needs to calculate the matrix-matrix multiplication and matrix inversion once when estimating the 3D matched filter in each 3D data window, which can It effectively reduces the computational complexity of solving the optimization problem, and improves the computational efficiency of the adaptive separation of primary waves and multiple waves.
附图说明Description of drawings
图1为本发明中基于交替分裂Bregman迭代算法的一次波和多次波分离方法的流程图;Fig. 1 is the flow chart of the primary wave and the multiple wave separation method based on alternate splitting Bregman iterative algorithm among the present invention;
图2a为原始数据的共偏移距道集图;Figure 2a is the co-offset gather map of the original data;
图2b为预测多次波的共偏移距道集图;Figure 2b is the co-offset gather map of predicted multiples;
图3a为基于最小二乘算法的一次波估计结果的共偏移距道集图;Figure 3a is the co-offset gather diagram of the primary wave estimation results based on the least squares algorithm;
图3b为基于迭代重加权最小二乘算法的一次波估计结果的共偏移距道集图;Figure 3b is the co-offset gather diagram of the primary wave estimation results based on the iterative reweighted least squares algorithm;
图3c为基于交替分裂Bregman迭代算法的一次波估计结果的共偏移距道集图;Figure 3c is the co-offset gather diagram of the primary wave estimation results based on the alternate splitting Bregman iterative algorithm;
图4a为基于最小二乘算法所去除多次波的共偏移距道集图;Fig. 4a is a common offset gather diagram of multiples removed based on the least squares algorithm;
图4b为基于迭代重加权最小二乘算法所去除多次波的共偏移距道集图;Figure 4b is the image of the common offset gather with multiples removed based on the iterative reweighted least squares algorithm;
图4c为基于交替分裂Bregman迭代算法所去除多次波的共偏移距道集图;Fig. 4c is the image of the common offset gather with multiples removed based on the alternate splitting Bregman iterative algorithm;
图5a为原始数据的放大显示结果图(对应于图2a中黑色方框);Figure 5a is an enlarged display result map of the original data (corresponding to the black box in Figure 2a);
图5b为预测多次波的放大显示结果图;Fig. 5b is an enlarged display result diagram of predicted multiple waves;
图5c为基于最小二乘算法所估计一次波的放大显示结果图;Figure 5c is an enlarged display result diagram of the primary wave estimated based on the least squares algorithm;
图5d为基于迭代重加权最小二乘算法所估计一次波的放大显示结果图;Figure 5d is an enlarged display result diagram of the primary wave estimated based on the iterative reweighted least squares algorithm;
图5e为基于交替分裂Bregman迭代算法所估计一次波的放大显示结果图。Fig. 5e is an enlarged display result diagram of the primary wave estimated based on the alternate splitting Bregman iterative algorithm.
具体实施方式detailed description
本发明的基本思想是:逐个3D数据窗口地分离一次波和多次波,构建对一次波施加稀疏约束的优化问题:其中,d为原始数据,x表示3D匹配滤波器,H表示预测多次波的褶积矩阵,λ为正则化因子。求解上式中的优化问题来估计3D匹配滤波器,并采用估计的3D匹配滤波器来对3D数据窗口中一次波和多次波进行分离,最后将所有3D数据窗口内的一次波估计结果进行合并,得到最终的一次波估计结果。The basic idea of the present invention is: separate the primary wave and the multiple wave one by one 3D data window, construct the optimization problem that imposes sparse constraints on the primary wave: Among them, d is the original data, x is the 3D matched filter, H is the convolution matrix for predicting multiples, and λ is the regularization factor. Solve the optimization problem in the above formula to estimate the 3D matched filter, and use the estimated 3D matched filter to separate the primary wave and multiple wave in the 3D data window, and finally calculate the primary wave estimation results in all 3D data windows Combined to get the final primary wave estimation result.
下面结合附图以及具体实施方式对本发明作进一步详细说明:Below in conjunction with accompanying drawing and specific embodiment the present invention is described in further detail:
如图1所示,基于交替分裂Bregman迭代算法的一次波和多次波分离方法,包括步骤:As shown in Figure 1, the primary wave and multiple wave separation method based on the alternating split Bregman iterative algorithm includes steps:
a设置变量初始值,需要设置初始值的变量包括3D数据窗口的时间长度T0,3D数据窗口的空间长度X0,3D数据窗口的道集个数Y0,3D匹配滤波器的时间长度K,3D匹配滤波器的空间长度R,3D匹配滤波器的道集个数G,一次波阈值sβ,阻尼因子β和迭代次数 a Set the initial value of the variable. The variables that need to be set to the initial value include the time length T 0 of the 3D data window, the spatial length X 0 of the 3D data window, the number of gathers Y 0 of the 3D data window, and the time length K of the 3D matched filter , the spatial length R of the 3D matched filter, the number of gathers G of the 3D matched filter, the primary wave threshold s β , the damping factor β and the number of iterations
b输入原始数据道集中一个待处理的3D数据窗口中的数据d,然后利用预测多次波数据以及3D数据窗口的参数T0、X0和Y0、3D匹配滤波器的参数K、R和G构造褶积矩阵H,矩阵H的行数为T0X0Y0,列数为KRG,并采用克莱斯基分解计算逆矩阵 b Input the data d in a 3D data window to be processed in the original data collection, and then use the predicted multiple wave data and the parameters T 0 , X 0 and Y 0 of the 3D data window, and the parameters K, R and G constructs a convolution matrix H, the number of rows of the matrix H is T 0 X 0 Y 0 , and the number of columns is KRG, and the inverse matrix is calculated by Kleinsky decomposition
c利用步骤b得到的逆矩阵H对地震道集的3D数据窗口的数据d进行处理;c. Using the inverse matrix H obtained in step b to process the data d in the 3D data window of the seismic gather;
本发明采用交替分裂Bregman迭代算法求解3D匹配滤波器,实现一次波和多次波的自适应分离,即在每一步迭代,交替分裂Bregman迭代算法交替求解对一次波施加稀疏约束的优化问题和对3D匹配滤波器施加能量最小化约束的优化问题;具体地讲,在每一步迭代,交替分裂Bregman迭代算法采用距离算子求解对一次波施加稀疏约束的优化问题,采用最小二乘算法求解对3D匹配滤波器施加能量最小化约束的优化问题;同时假设正则化参数间的倍数关系对迭代步骤进行简化;最后利用估计的3D匹配滤波器自适应分离一次波和多次波。The present invention adopts the alternately split Bregman iterative algorithm to solve the 3D matched filter, and realizes the adaptive separation of the primary wave and the multiple wave, that is, in each step of iteration, the alternately split Bregman iterative algorithm alternately solves the optimization problem of applying sparse constraints to the primary wave and the The optimization problem of 3D matched filter imposing energy minimization constraints; specifically, at each iteration step, the alternately split Bregman iterative algorithm uses the distance operator to solve the optimization problem of imposing sparse constraints on the primary wave, and uses the least squares algorithm to solve the 3D The optimization problem of energy minimization constraints imposed by the matched filter; at the same time, the multiple relationship between the regularization parameters is assumed to simplify the iterative steps; finally, the estimated 3D matched filter is used to adaptively separate the primary wave and the multiple wave.
其具体处理过程为:Its specific processing process is:
c1设置迭代数m=1,利用步骤b得到的逆矩阵求取一次波的初始估计值v(0):
c2计算向量y(m)=v(m-1)+b1 (m-1);c2 calculation vector y (m) = v (m-1) +b 1 (m-1) ;
c3对y(m)利用如下的距离算子prox计算向量u1 (m):c3 uses the following distance operator prox to calculate the vector u 1 (m) for y ( m):
其中,i=1,2,…,T0,j=1,2,…,X0,n=1,2,…,Y0,s=sβC(m),0<sβ<1;y(m)={yi,j,n (m)},yi,j,n (m)表示向量y(m)中下标为(i,j,n)的元素,C(m)=max(|yi,j,n (m)|),
c4计算向量b1 (m)=b1 (m-1)-[u1 (m)-v(m-1)];c4 calculation vector b 1 (m) = b 1 (m-1) -[u 1 (m) -v (m-1) ];
c5计算3D匹配滤波器
c6估计一次波v(m)=d-Hx(m);c6 estimates primary wave v (m) = d-Hx (m) ;
c7令m=m+1,如果返回到步骤c2;如果输出当前数据窗口估计的一次波结果。c7 let m=m+1, if Return to step c2; if Output the estimated primary results for the current data window.
d判断原始数据道集中所有数据窗口内的数据d是否全部处理完毕;如果否,返回步骤c;如果全部处理完毕,则首先采用3D汉宁窗将每一个3D数据窗口中估计的一次波进行加权,并融合为一个数据体然后采用同样的方式将3D汉宁窗融合为一个数据体最终的一次波估计结果表示为:其中,/表示逐个元素的相除操作。d Determine whether all the data d in all data windows in the original data gather have been processed; if not, return to step c; if all have been processed, first use the 3D Hanning window to weight the primary wave estimated in each 3D data window , and merged into a data body Then use the same method to fuse the 3D Hanning window into a data volume The final primary wave estimation result is expressed as: Among them, / represents an element-by-element division operation.
此处,同样的方式是指把相同时间、空间和道集位置处的数据进行相加。Here, the same way means adding data at the same time, space and gather location.
下面利用2D实际数据验证本发明方法的有效性:Utilize 2D actual data below to verify the validity of the inventive method:
图2a为原始数据的共偏移距道集图。图2b为预测多次波的共偏移距道集图。图3a为基于最小二乘算法的一次波估计结果的共偏移距道集图。图3b为基于迭代重加权最小二乘算法的一次波估计结果的共偏移距道集图。图3c为基于交替分裂Bregman迭代算法的一次波估计结果的共偏移距道集图。图4a为基于最小二乘算法所去除多次波的共偏移距道集图。图4b为基于迭代重加权最小二乘算法所去除多次波的共偏移距道集图。图4c为基于交替分裂Bregman迭代算法所去除多次波的共偏移距道集图。图3a、图3b和图3c中得到相近的一次波估计结果,计算时间分别为8.88秒、37.10秒和9.63秒。相比于迭代重加权最小二乘算法,本发明中的交替分裂Bregman迭代算法在保持一次波估计精度的同时,能有效地提高计算效率。另外,图5a为原始数据的放大显示结果图,对应于图2a中的黑色方框。图5b为预测多次波的放大显示结果图。图5c为基于最小二乘算法所估计一次波的放大显示结果图。图5d为基于迭代重加权最小二乘算法所估计一次波的放大显示结果图。图5e为基于交替分裂Bregman迭代算法所估计一次波的放大显示结果图。其中,图5a至图5e中的白色箭头表明,相对于传统的最小二乘算法,本发明中的交替分裂Bregman迭代算法在一次波估计结果中能更好地去除残余多次波。其中,图2a至2b、图3a至3c、图4a至4c及图5a至5e中横坐标TraceNumber表示道号,纵坐标Time表示时间,单位为毫秒(ms)。Figure 2a is the co-offset gather map of the original data. Figure 2b is the co-offset gather map of the predicted multiples. Fig. 3a is the co-offset gather diagram of the primary wave estimation results based on the least squares algorithm. Figure 3b is the co-offset gather map of the primary wave estimation results based on the iterative reweighted least squares algorithm. Fig. 3c is the co-offset gather diagram of the primary wave estimation results based on the alternate splitting Bregman iterative algorithm. Fig. 4a is a common-offset gather diagram of multiples removed based on the least squares algorithm. Fig. 4b is a graph of common offset gathers with multiples removed based on the iterative reweighted least squares algorithm. Fig. 4c is the image of the common-offset gather of multiples removed based on the alternate splitting Bregman iterative algorithm. Similar primary wave estimation results are obtained in Fig. 3a, Fig. 3b and Fig. 3c, and the calculation time is 8.88 seconds, 37.10 seconds and 9.63 seconds respectively. Compared with the iterative reweighted least squares algorithm, the alternating split Bregman iterative algorithm in the present invention can effectively improve the calculation efficiency while maintaining the primary wave estimation accuracy. In addition, Fig. 5a is an enlarged display result diagram of the original data, which corresponds to the black box in Fig. 2a. Fig. 5b is an enlarged display result diagram of predicted multiple waves. Fig. 5c is an enlarged display result diagram of the primary wave estimated based on the least squares algorithm. Fig. 5d is an enlarged display result diagram of the primary wave estimated based on the iterative reweighted least squares algorithm. Fig. 5e is an enlarged display result diagram of the primary wave estimated based on the alternate splitting Bregman iterative algorithm. Wherein, the white arrows in Fig. 5a to Fig. 5e show that, compared with the traditional least squares algorithm, the alternating split Bregman iterative algorithm in the present invention can better remove residual multiples in the primary wave estimation results. 2a to 2b, 3a to 3c, 4a to 4c, and 5a to 5e, the abscissa TraceNumber represents the track number, and the ordinate Time represents time in milliseconds (ms).
当然,以上说明仅仅为本发明的较佳实施例,本发明并不限于列举上述实施例,应当说明的是,任何熟悉本领域的技术人员在本说明书的教导下,所做出的所有等同替代、明显变形形式,均落在本说明书的实质范围之内,理应受到本发明的保护。Of course, the above descriptions are only preferred embodiments of the present invention, and the present invention is not limited to the above-mentioned embodiments. It should be noted that all equivalent substitutions made by any person skilled in the art under the teaching of this specification , obvious deformation forms, all fall within the essential scope of this specification, and should be protected by the present invention.
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