卡尔曼滤波在重力场数据处理中的应用
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摘要
重力场资料处理是重力勘探的重要组成部分,随着科学技术的不断发展和数据采集精度的不断提高,高精度的重力异常数据处理新方法、新技术的研究显得更为重要。
本论文以递推滤波算法为理论基础,以地球物理重力场数据处理中的滤波方法、技术研究为主要目标,对卡尔曼滤波方法在重力场数据处理中的应用进行了研究与开发。
通过对传统的矩形窗、三角窗、汉宁窗以及切比雪夫窗函数技术指标的定量比较,对窗函数的空间域及频率域特性进行了分析;对匹配滤波的参数以及波数响应特性做了初步的说明;对基于维纳原理的维纳滤波和本文的重点卡尔曼滤波进行了研究,通过设计随机信号模型对两者的滤波效果进行比较;并且对卡尔曼滤波在重力位场数据处理中的应用做出了具体的分析和研究。
在实际应用中,选择牙克石(位于海拉尔盆地上)——林甸(位于松辽盆地上)高精度剖面布格重力异常数据,实现了上述方法在实际资料处理中的应用,并且运用重力归一化总梯度法对该剖面进行断裂构造划分,取得了较好的效果。由于笔者水平有限,在研究的过程中,可能存在着一些缺点和不足,敬请指正。
The gravity field data processing is an important part in the gravity prospecting, along with science technique of continuously development and data collect accuracy continuously to raise,the study of method and technology for high- precision data processing of gravity anomalies seem to very important.
Gravity anomaly without data processing can be seen as different depths underground,different scale,different physical parameters of the geological bodies stacking up at the ground effect,and the weight does not change over time with the smooth characteristics.Whether through a filtering method is more reasonable,in accordance with this stack depth anomaly(or wavelength) to open the whole decomposition,thereby to determine a more accurate or underground geological structure of the distribution and morphology.Therefore,the choice of what kind of filtering method is a very important job.This article is based on this theory,combined with Kalman filtering technology to Bouguer gravity anomaly data for processing. Through a variety of theoretical models of the spreadsheet shows that the better,more adaptable,free from interference with useful information and the relevance of information and the impact of the same phase.
For the observed potential field anomaly profile,after some necessary preprocessing,we can consider that it is underground at different depths,different scale,different physical parameters of the geological bodies in the ground on the superposition effect,and the weight has not changed over time smooth features, whether through a more reasonable filtering method,this superposition of anomalies in accordance with the depth(or wavelength) decomposition generally open,thus more accurate to judge the underground geological structure or the distribution and morphology.Therefore,the selection of what kind of filtering method is a very important job.This article is on this theoretical foundation,combined with Kalman filtering technology on the gravitational potential field measurement data for processing.Through a variety of theoretical models of the spreadsheet shows that the effect of better adapted,from the useful information and interference information of relevance and impact of the same phase.
Kalman filter since its inception in early 60s,one after another in many areas, been widely used.Although the Kalman filter with the Wiener filtering criteria are minimum variance filter,but they are required by the known conditions,the calculation method and the scope of application,such as not the same.At present,the separation of the regional market with the local field in the "Wiener filtering",Wiener filter in the signal and interference are not relevant under the conditions of a special case,the so-called separation of the regional market with the local field of "matched filtering",Wiener filter is essentially at the same phase signal and interference under the conditions of a special case.About Kalman filter in the application of geophysical applications,currently limited to seismic data processing.In this paper,using Kalman filter for potential field data processing,and discussed the separation of gravity anomalies in the application problem.
Regional market with the local field separation of the regional gravity field data are an important aspect of treatment.At the actual data interpretation also has important significance.Judging from the spectral analysis,regional market and the local field frequency components are different.Regional market to low-frequency components of the main local market dominated by high frequency components. Extracted using different wave number components of the field to complete the separation field.
1.Window function
Place at the actual conduct of field separation treatment are often required to observe the time limit for the signal at a certain time interval,only select a period of time required to analyze the signal.In this way,take a finite number of data,signal data is about to cut off the process,it means that the signal window function add to the operation.This operation later,usually occurs from the normal weight spectrum spread spectrum open to the situation,namely the so-called "spectral leakage." When carried out Discrete Fourier Transform,the time domain of the cut-off is necessary, therefore,the leakage effect is also a Discrete Fourier Transform(DFT) inherent in the need for suppression.In order to carry out suppression of spectral leakage can be inhibited through the window function weighted equivalent DFT filter sidelobe amplitude characteristics,or the weighted window function so that the limited length of the input signal cycle after the extension at the border to minimize the extent of discontinuous Ways of implementation.In addition,power spectrum estimation of the weighted window function also encountered problem.This shows that the weighted window function in power field separation technology to the important status of treatment.
Digital signal processing field of the window function used in the main are: rectangular window function,the triangular window function,Hanning window function,Chebyshev window function.
2.Matched Filtering
Matched filter response to the wave number reflects the regional market extract matched filter is a low-pass filter.Local field and extract the matched filter is a high-pass filter.But it downward continuation and derivation of the wave number has an important response is the difference between the wave number matched filter response to one of its asymptotic lines,it can only play the role of extracting high frequency components will not be enlarged a result of concussion.However,in order to better focus on effective information,in practical work with matched filter extracts the local market when they should be compatible with low-pass filter to suppress high-frequency interference.
3.Wiener filtering and Kalman filtering
Wiener filtering and Kalman filtering are based on minimum mean square error as the criterion of the linear estimator.Kalman filtering and Wiener filtering the difference is:(1) Kalman filtering and Wiener filtering to address the best method of filtering is not the same.Wiener filter is used in frequency domain and transfer function methods,Kalman are using time-domain and state variable methods.(2) Wiener filtering requirements of the process of auto-correlation function and cross-correlation function of simple knowledge,and Kalman filter requires time domain signal status variables and a detailed knowledge of the process.(3) Wiener filter for a smooth,while the Kalman filter is not required.
4.Kalman Filter-based sampling data Spline Interpolation
Spline interpolation of the basic approach is to use a series of discrete points give the coordinates,using cubic spline function of adjacent contact points,the adjacent spline function at convergence not only has the same function value,but also has the same tangent and curvature,which is very smooth.There is a whole interpolation function of these sub-cubic spline connected.
Cubic spline interpolation algorithms are derived equations have unknown,the corresponding equation is only months,it must only determine its solution must also provide two boundary conditions.Boundary conditions usually have the following:(1) second derivative conditions;(2) assumed that the sequence of data points for the cycle sequence;(3) slope conditions;(4) the conditions of virtual nodes;(5) "non-node" conditions;(6) Lagrange - cubic spline interpolation conditions.At the actual interpolation,the above methods there are less than certain.The first three conditions for a narrower scope of application,and in reality often can not meet its conditions,the conditions(4) only depends on the value of subjective judgments,the conditions(5) and(6) did not be able to take full advantage of known data points of information,when a relatively small number of data points on the interpolation accuracy of a greater impact on this use of Kalman filtering method known recursive data type values to estimate the follow-up data,and thus the volume of solution of the unknown method.Kalman filter in real terms are used recursive filtering methods, using linear unbiased minimum variance criteria in order to obtain the optimal estimation process,it can be applied to multi-input,multiple output of non-stationary random process.Through a given measurement of the number of column values to get the estimated state vector,estimated by the prediction,prediction error covariance matrix,the best gain,the filter is estimated that filtering error covariance matrix and the composition of the best initial value.
Measurement data obtained after the first data on its pre-processing to a certain extent,reduce the data noise,remove the outlier points.Then at the end of the right to select the number of data points for fitting.At fitting process,generally taking many second-order fitting,fitting because the order of First,excessive,volatile curve,there will be ups and downs of unnecessary so that the lower accuracy;two are at the time only by Kalman prediction to fit within the second-order recursive data.
By the nature of Kalman filter,we can see that it can effectively reduce the impact of noise.In addition,at sufficiently long time after iteration,the impact of incorrect initial value will gradually disappear,the best filter will converge to the status,therefore,in reality,when many of enough data points after filtering,Kalman filtering,after The value will be close to true value.
5.Kalman filter at yakeshi - Lindian profile application
Yakeshi - Lindian geophysical profiles across the Inner Mongolia Autonomous Region,after Heilongjiang Province,near to the North West.Northwest began in Yakeshi City of Inner Mongolia,and then to the southeast all the way through the avoidance of crossing Ukrainian slave ears.boqueron map Zalantun,Longjiang, Fulaerji,Qiqihar,such as cities and towns until the end of Heilongjiang Lindian total length of 540km.From the Bouguer gravity anomaly profile shows that low-value Daxinganling region against the backdrop of large negative anomalies,and both sides of the Hailar Basin and Songliao Basin is a small negative anomalies.
First of all,the use of Kalman filter for denoising of abnormal treatment,then the profile of the Bouguer anomaly separation by yakeshi - Lindian profile regional market and local market.As can be seen isolated from the regional anomaly field in the local field of residual small,isolated completely in line with the Bouguer gravity anomaly shown by the regional anomaly characteristics,and its apparent characteristics of the basin basement structure:local anomaly field noise is basically was removed,reflecting the ups and downs of local basins and surface density of non-uniform characteristics of local structures in the area are carried out to explain the basis for fine.
本论文以递推滤波算法为理论基础,以地球物理重力场数据处理中的滤波方法、技术研究为主要目标,对卡尔曼滤波方法在重力场数据处理中的应用进行了研究与开发。
通过对传统的矩形窗、三角窗、汉宁窗以及切比雪夫窗函数技术指标的定量比较,对窗函数的空间域及频率域特性进行了分析;对匹配滤波的参数以及波数响应特性做了初步的说明;对基于维纳原理的维纳滤波和本文的重点卡尔曼滤波进行了研究,通过设计随机信号模型对两者的滤波效果进行比较;并且对卡尔曼滤波在重力位场数据处理中的应用做出了具体的分析和研究。
在实际应用中,选择牙克石(位于海拉尔盆地上)——林甸(位于松辽盆地上)高精度剖面布格重力异常数据,实现了上述方法在实际资料处理中的应用,并且运用重力归一化总梯度法对该剖面进行断裂构造划分,取得了较好的效果。由于笔者水平有限,在研究的过程中,可能存在着一些缺点和不足,敬请指正。
The gravity field data processing is an important part in the gravity prospecting, along with science technique of continuously development and data collect accuracy continuously to raise,the study of method and technology for high- precision data processing of gravity anomalies seem to very important.
Gravity anomaly without data processing can be seen as different depths underground,different scale,different physical parameters of the geological bodies stacking up at the ground effect,and the weight does not change over time with the smooth characteristics.Whether through a filtering method is more reasonable,in accordance with this stack depth anomaly(or wavelength) to open the whole decomposition,thereby to determine a more accurate or underground geological structure of the distribution and morphology.Therefore,the choice of what kind of filtering method is a very important job.This article is based on this theory,combined with Kalman filtering technology to Bouguer gravity anomaly data for processing. Through a variety of theoretical models of the spreadsheet shows that the better,more adaptable,free from interference with useful information and the relevance of information and the impact of the same phase.
For the observed potential field anomaly profile,after some necessary preprocessing,we can consider that it is underground at different depths,different scale,different physical parameters of the geological bodies in the ground on the superposition effect,and the weight has not changed over time smooth features, whether through a more reasonable filtering method,this superposition of anomalies in accordance with the depth(or wavelength) decomposition generally open,thus more accurate to judge the underground geological structure or the distribution and morphology.Therefore,the selection of what kind of filtering method is a very important job.This article is on this theoretical foundation,combined with Kalman filtering technology on the gravitational potential field measurement data for processing.Through a variety of theoretical models of the spreadsheet shows that the effect of better adapted,from the useful information and interference information of relevance and impact of the same phase.
Kalman filter since its inception in early 60s,one after another in many areas, been widely used.Although the Kalman filter with the Wiener filtering criteria are minimum variance filter,but they are required by the known conditions,the calculation method and the scope of application,such as not the same.At present,the separation of the regional market with the local field in the "Wiener filtering",Wiener filter in the signal and interference are not relevant under the conditions of a special case,the so-called separation of the regional market with the local field of "matched filtering",Wiener filter is essentially at the same phase signal and interference under the conditions of a special case.About Kalman filter in the application of geophysical applications,currently limited to seismic data processing.In this paper,using Kalman filter for potential field data processing,and discussed the separation of gravity anomalies in the application problem.
Regional market with the local field separation of the regional gravity field data are an important aspect of treatment.At the actual data interpretation also has important significance.Judging from the spectral analysis,regional market and the local field frequency components are different.Regional market to low-frequency components of the main local market dominated by high frequency components. Extracted using different wave number components of the field to complete the separation field.
1.Window function
Place at the actual conduct of field separation treatment are often required to observe the time limit for the signal at a certain time interval,only select a period of time required to analyze the signal.In this way,take a finite number of data,signal data is about to cut off the process,it means that the signal window function add to the operation.This operation later,usually occurs from the normal weight spectrum spread spectrum open to the situation,namely the so-called "spectral leakage." When carried out Discrete Fourier Transform,the time domain of the cut-off is necessary, therefore,the leakage effect is also a Discrete Fourier Transform(DFT) inherent in the need for suppression.In order to carry out suppression of spectral leakage can be inhibited through the window function weighted equivalent DFT filter sidelobe amplitude characteristics,or the weighted window function so that the limited length of the input signal cycle after the extension at the border to minimize the extent of discontinuous Ways of implementation.In addition,power spectrum estimation of the weighted window function also encountered problem.This shows that the weighted window function in power field separation technology to the important status of treatment.
Digital signal processing field of the window function used in the main are: rectangular window function,the triangular window function,Hanning window function,Chebyshev window function.
2.Matched Filtering
Matched filter response to the wave number reflects the regional market extract matched filter is a low-pass filter.Local field and extract the matched filter is a high-pass filter.But it downward continuation and derivation of the wave number has an important response is the difference between the wave number matched filter response to one of its asymptotic lines,it can only play the role of extracting high frequency components will not be enlarged a result of concussion.However,in order to better focus on effective information,in practical work with matched filter extracts the local market when they should be compatible with low-pass filter to suppress high-frequency interference.
3.Wiener filtering and Kalman filtering
Wiener filtering and Kalman filtering are based on minimum mean square error as the criterion of the linear estimator.Kalman filtering and Wiener filtering the difference is:(1) Kalman filtering and Wiener filtering to address the best method of filtering is not the same.Wiener filter is used in frequency domain and transfer function methods,Kalman are using time-domain and state variable methods.(2) Wiener filtering requirements of the process of auto-correlation function and cross-correlation function of simple knowledge,and Kalman filter requires time domain signal status variables and a detailed knowledge of the process.(3) Wiener filter for a smooth,while the Kalman filter is not required.
4.Kalman Filter-based sampling data Spline Interpolation
Spline interpolation of the basic approach is to use a series of discrete points give the coordinates,using cubic spline function of adjacent contact points,the adjacent spline function at convergence not only has the same function value,but also has the same tangent and curvature,which is very smooth.There is a whole interpolation function of these sub-cubic spline connected.
Cubic spline interpolation algorithms are derived equations have unknown,the corresponding equation is only months,it must only determine its solution must also provide two boundary conditions.Boundary conditions usually have the following:(1) second derivative conditions;(2) assumed that the sequence of data points for the cycle sequence;(3) slope conditions;(4) the conditions of virtual nodes;(5) "non-node" conditions;(6) Lagrange - cubic spline interpolation conditions.At the actual interpolation,the above methods there are less than certain.The first three conditions for a narrower scope of application,and in reality often can not meet its conditions,the conditions(4) only depends on the value of subjective judgments,the conditions(5) and(6) did not be able to take full advantage of known data points of information,when a relatively small number of data points on the interpolation accuracy of a greater impact on this use of Kalman filtering method known recursive data type values to estimate the follow-up data,and thus the volume of solution of the unknown method.Kalman filter in real terms are used recursive filtering methods, using linear unbiased minimum variance criteria in order to obtain the optimal estimation process,it can be applied to multi-input,multiple output of non-stationary random process.Through a given measurement of the number of column values to get the estimated state vector,estimated by the prediction,prediction error covariance matrix,the best gain,the filter is estimated that filtering error covariance matrix and the composition of the best initial value.
Measurement data obtained after the first data on its pre-processing to a certain extent,reduce the data noise,remove the outlier points.Then at the end of the right to select the number of data points for fitting.At fitting process,generally taking many second-order fitting,fitting because the order of First,excessive,volatile curve,there will be ups and downs of unnecessary so that the lower accuracy;two are at the time only by Kalman prediction to fit within the second-order recursive data.
By the nature of Kalman filter,we can see that it can effectively reduce the impact of noise.In addition,at sufficiently long time after iteration,the impact of incorrect initial value will gradually disappear,the best filter will converge to the status,therefore,in reality,when many of enough data points after filtering,Kalman filtering,after The value will be close to true value.
5.Kalman filter at yakeshi - Lindian profile application
Yakeshi - Lindian geophysical profiles across the Inner Mongolia Autonomous Region,after Heilongjiang Province,near to the North West.Northwest began in Yakeshi City of Inner Mongolia,and then to the southeast all the way through the avoidance of crossing Ukrainian slave ears.boqueron map Zalantun,Longjiang, Fulaerji,Qiqihar,such as cities and towns until the end of Heilongjiang Lindian total length of 540km.From the Bouguer gravity anomaly profile shows that low-value Daxinganling region against the backdrop of large negative anomalies,and both sides of the Hailar Basin and Songliao Basin is a small negative anomalies.
First of all,the use of Kalman filter for denoising of abnormal treatment,then the profile of the Bouguer anomaly separation by yakeshi - Lindian profile regional market and local market.As can be seen isolated from the regional anomaly field in the local field of residual small,isolated completely in line with the Bouguer gravity anomaly shown by the regional anomaly characteristics,and its apparent characteristics of the basin basement structure:local anomaly field noise is basically was removed,reflecting the ups and downs of local basins and surface density of non-uniform characteristics of local structures in the area are carried out to explain the basis for fine.
引文
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[2]董焕成.重磁勘探教程[M].地质出版社,1993.
[3]罗孝宽,郭绍雍.应用地球物理教程-重力 磁法[M].北京:地质出版社.1991.
[4]王谦身,安玉林,张赤军等.重力学[M].北京:地震出版社.2003,258-263.
[5]穆石敏,申宁华,孙运生.区域地球物理数据处理方法及其应用[M].吉林科学技术出版社,1990.
[6]徐伯勋,白旭滨,于常青.信号处理及应用.地质出版社,1997.
[7]张贤达等.现代信号处理[M].北京:清华大学出版社,2003.
[8]O.库尔哈尼克.地球物理数字滤波引论[M].地质出版社,1993.
[9]丁玉美,阔永红,高新波.数字信号处理.西安电子科技大学出版社,2002.
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