大地测量联合反演的模式及算法研究
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摘要
大地测量反演问题是大地测量学科深入地学研究领域的核心问题之一,是利用地球表面观测到的形变资料推测地球内部介质物理状态的空间变化及演化的一个分支,它与地震学、地球物理学等学科的结合,在研究地球动力学和地球物理的深部结构细节、地球内部动力过程和物性特征等方面不仅具有理论意义,而且具有实用价值,已受到国内外学者的高度重视。特别是由大地测量所得的地壳形变与地震之间存在着某种形式的必然联系,利用震间和震前的形变测量,了解孕震过程,研究孕震模式,进而预测预报地震的发生,是大地测量反演的一个主要内容。位错理论就是研究震源机制的一个常用模式。
论文系统地讨论了大地测量反演的位错理论,研究了基于位错模式的多类数据的联合反演问题,进行了多种常用反演算法的比较分析,着重研究了区间算法,采用区间模拟退火法,进行了近震定位试验,并利用重力和GPS数据联合反演了川西地区的断层参数。
论文的具体研究工作和主要创新点包括以下几个部分:
1.位错模型的研究
论文系统总结了由于断层运动产生的位移、应变、应斜、重力的变化,以及地壳内部形变,并改正了文献中原有位错模型的偏导数中的不正确部分,为最小二乘等以求导为手段的反演研究做出了贡献,完善了位错理论。
2.联合反演模式的研究
多类数据的联合反演是本文研究的核心内容之一。广泛进行的地壳运动和变形的监测,可获得丰富的高质量的地表形变信息数据,包括GPS、水准测量、重力测量以及合成孔径雷达干涉测量(InSAR)的监测数据。实际上,地壳运动和地形变监测数据是地球内部动力过程地表力学响应的输出信号,这种响应是由地下介质的物理特性激发的。虽然各种响应互不相同,但由这些响应推断的地下介质是相同的。因此,联合反演是大地测量数据进行地球物理解释的理想工具。
论文提出采用附有相对权比确定的多类数据的联合反演。在位错模式下,通过模拟的GPS、水准和重力数据,研究了附有相对权比确定的采用GPS和水准、GPS和重力、水准和重力以及这三类数据共同参与的三维位错模式的联合反演问题。在反演区域或局部水平速度场方面,给出了兼顾权比确定的大地测量、地震和地质(第四纪断层滑动速率)三种数据的联合反演模式。
3.反演算法的研究
联合反演算法的研究是本文的另一个核心内容。反演最终归结为求目标函数的最小值,从数学角度上看是一个优化问题,传统的方法如最小二乘法和附有先验信息的贝叶斯法等,需要计算模型的偏导数,但通常来说,大地测量和地球物理模型是强烈非线性的,参数的偏导数非常复杂,甚至一些参数的偏导数很难得到。因此,近年来,无需计算模型偏导数的优化方法得到了广泛的运用。
在反演算法优缺点方面,论文比较了蒙特卡罗法、遗传算法、模拟退火法、随机耗费法和
Geodetic inversion is geodetic core that studies geoscience and also a branch that speculates on spatial change and evolution of physical state of interior medium in earth by deformation data measured. It is significant in theory and valuable in application to combine geodetic inversion with seismology and geophysics to study on geodynamics, deep-seated structural details of earth, the dynamical process of interior earth and material characteristics. Geodetic inversion is regarded by homely and abroad highly. Especially, crust deformation is natural related with earthquake. So it is a key task of geodetic inversion to research on the process and mode of warning signs of an earthquake, even to forecast an earthquake with interseismic and preseismic deformation measurement. Dislocation is a usual mode to study warning signs of an earthquake.The dislocation theory is researched systemically in the dissertation. The joint inversions with kinds of data based on dislocation are researched. Some usual algorithms are analyzed contrastively. Interval algorithm is discussed mainly. The interval Simulated Annealing algorithm is used to locate a local earthquake and jointly invert fault parameters with GPS and gravimetry in the west of Sichuan.The main research contents and new calculation methods in the dissertation are following:1. Research on dislocation modelThe changes of displacement, strain, tilt, gravity and crustal internal deformation due to dislocation are summarized systemically in the dissertation. Wrong Partial derivatives formulae of dislocation model in some papers are corrected in the dissertation. It is a contribution to researchers who use some methods based on partial derivatives of parameters, such as, the Least-Squared method. The correction perfect the dislocation theory2. Research on Joint Inversion modeJoint inversion with kinds of data is one of the keys of the dissertation. Some top-quality deformation data, such as GPS, leveling, gravimetry and InSar, are obtained by monitoring crustal movement. In fact, those data are output signals of responding to geodynamic process of the interior of earth. The responds to movements are different, but the medium is the same. So, joint inversion is a potential tool to analyze geophysical data.A kind of joint inversion that will invert the weight in the object function is proposed in the dissertation. Based on dislocation mode, the kind of joint inversion with simulated GPS, leveling and gravimetry data is used by twos or whole to invert the parameters of three-dimension fault model. In addition, this kind of joint inversion is also used to invert regional or local horizontal velocity with geodetic data, seismic data and geologic data, such as the Quaternary fault slip.3. Research on Inversion Algorithms
Researches on joint inversion algorithms are another key of the dissertation. Inversion aims to get the minimum of the object function. This is an optimal question in mathematics. The classical methods, such as the Least-Squared method and Bayesian method with a prior information of parameter, need partial derivatives of parameters. In general, geodetic or geophysical model is very nonlinear, the derivatives are very complicated and even it is difficult to express them in formulae. So, recent years, some methods without partial derivatives are used widely.Some algorithms, such as Monte Carlo, genetic algorithm, Simulated Annealing algorithm, random cost method and interval algorithm, are compared in the dissertation. Thereinto, Monte Carlo, genetic algorithm, Simulated Annealing algorithm and random cost method are based on stochastic search. They can sometimes jump over local optimum and converge to global one, but they can't be successful every time because of their inherent stochastic nature. They have the same chance to converge to local and global optimum. So they can't be called whole global optimizations, but a global optimization oriented. Especially, interval algorithm is regarded as a whole global optimization in the dissertation. It is superior to other optimization methods in reliability and appraisal of results. And it is a method to find all global minimizers of a constrained nonlinear function with several variables. It is impossible to converge to a local minimizer for interval algorithm. It is concluded that interval algorithm is a reliable and efficient global optimization method.These methods are compared by inverting fault parameters with simulated gravimetry data base on dislocation mode. Several tests are made with every method. To the stochastic method, the different tests bring different results. If the true value of parameter is unknown, it can not be concluded which answer should be selected as inversion result. Simulated annealing method is better among the all stochastic methods. Interval algorithm can always converge to an interval including global optimum and the upper of approaching error is computed easily.To accelerate the speed of computation of interval algorithm, it is combined with simulated annealing method for the first time. And the new method is called interval simulated annealing method in the dissertation. The combination accelerates the computation speed and makes algorithm reliable and exact. This is a hybrid of stochastic search and exhaustive search.An improvement of interval Newton method is given in the dissertation. It corrects the unreliable part of prototype algorithm and makes the method more reliable and stable. Some examples show the application of it in solving nonlinear equations and global optimization.4. Research on Location of Near EarthquakeSeismic location is to decide the location of hypocenter and the time of earthquake occurrence. It is a basic question of seismology. The location result can disclose some important information about earthquake activities and the earthquake circumstance, thus, the earthquake mechanism and cause of occurrence will be known more. With the more development of digital observation technology, the more accurate location of hypocenter is needed. This is helpful to study hypocenter
the crustal structure and the crustal velocity model.The methods and principles of seismic location with IA-SA and classical Geiger method are introduced in case of homogeneous crust. The focus parameters of Shacheng earthquake in 1976 are inverted by the two methods respectively. The result of IA-SA is superior to the one of Geiger method according to some quantitative compares.5. Research on Geodetic Inversion of the Faults of the West of Sichuan Province Sichuan locates the southeastern of Qinghai-Tibet Plateau. There were many earthquakes historically. The intensity of seismic activities is the fifth in our country. Sichuan province is an important part of South-North Seismic belt. Xianshuihe fault locates the western Sichuan province. It is famous home and abroad and characteristic on intensive structural activities. In addition, Litang-Dewu fault locates the southwestern of Xianshuihe fault. They are researched in detail in the dissertation.Multipurpose researches were done in Xianshuihe fault broadly. According to its character of activity, Xianshuihe fault is divided into northwestern segment, Qianning-Kangding segment, Zheduotang segment and Moxi segment. The data used in the dissertation include relative gravimetry between 1996 and 2001 and GPS velocities between 1991 and 2000.Firstly, the two kinds of data is inverted individually by SA and IA-SA so as to compare their results.There are two projects to invert GPS. The one inverted all parameters of four segments if Xianshuihe Fault. Through the map of velocities, there are obvious differences on some points. Considering the big velocity of some points on southwestern of Xianshuihe fault, the second project is brought forward to invert Litang-Dewu fault synchronously. 7 parameters of every fault segment will be inverted, that is, the location of fault and strike are given some fixed values. According to value of object function, the results of IA-SA is superior to the ones SA. Therefore, the results of IA-SA are regarded as the inversion results with GPS data. The velocity measured is consistent with the one inverted.According to the maps of annual gravity changes isolines between 1996 and 2001, Xianshuihe fault is the boundary of plus isolines and negative isolines. This says the intensive activities of both sides of fault. So it is necessary to consider the action of fault activity to gravity changes. The inversion with gravimetry data resembles the second project of GPS inversion, that is, there are 7 parameters of every fault segment inverted. Still, the results of IA-SA is superior to the ones SA.At the end of the dissertation, a joint inversion with GPS and gravimetry data is done. Two projects are also given with the relatively weight ratio fixed to 0.5 or inverted. The all ten parameters of every fault are inverted by IA-SA during the two projects. The relatively weight ratio of gravimetry inverted is 0.314. The value of object function with the relatively weight ratio inverted is small than the one of another project. The results show that the project with weight ratio inverted is better and match the different kinds of data more rational.
It can be summarized that Xianshuihe fault is mainly a left lateral fault. The northwestern segment has the most intensive activity with a strike slip 13mm/a. The strike slip velocity in middle segment is 4.9~6.9mm/a. But the strike slip velocity in southeastern, the Moxi segment, arrives at 8.28mm/a. Three dislocation components of Litang-Dewu fault is close to each other, and it has the maximum tensile components, 5.12mm/a, among all 5 fault segments.
论文系统地讨论了大地测量反演的位错理论,研究了基于位错模式的多类数据的联合反演问题,进行了多种常用反演算法的比较分析,着重研究了区间算法,采用区间模拟退火法,进行了近震定位试验,并利用重力和GPS数据联合反演了川西地区的断层参数。
论文的具体研究工作和主要创新点包括以下几个部分:
1.位错模型的研究
论文系统总结了由于断层运动产生的位移、应变、应斜、重力的变化,以及地壳内部形变,并改正了文献中原有位错模型的偏导数中的不正确部分,为最小二乘等以求导为手段的反演研究做出了贡献,完善了位错理论。
2.联合反演模式的研究
多类数据的联合反演是本文研究的核心内容之一。广泛进行的地壳运动和变形的监测,可获得丰富的高质量的地表形变信息数据,包括GPS、水准测量、重力测量以及合成孔径雷达干涉测量(InSAR)的监测数据。实际上,地壳运动和地形变监测数据是地球内部动力过程地表力学响应的输出信号,这种响应是由地下介质的物理特性激发的。虽然各种响应互不相同,但由这些响应推断的地下介质是相同的。因此,联合反演是大地测量数据进行地球物理解释的理想工具。
论文提出采用附有相对权比确定的多类数据的联合反演。在位错模式下,通过模拟的GPS、水准和重力数据,研究了附有相对权比确定的采用GPS和水准、GPS和重力、水准和重力以及这三类数据共同参与的三维位错模式的联合反演问题。在反演区域或局部水平速度场方面,给出了兼顾权比确定的大地测量、地震和地质(第四纪断层滑动速率)三种数据的联合反演模式。
3.反演算法的研究
联合反演算法的研究是本文的另一个核心内容。反演最终归结为求目标函数的最小值,从数学角度上看是一个优化问题,传统的方法如最小二乘法和附有先验信息的贝叶斯法等,需要计算模型的偏导数,但通常来说,大地测量和地球物理模型是强烈非线性的,参数的偏导数非常复杂,甚至一些参数的偏导数很难得到。因此,近年来,无需计算模型偏导数的优化方法得到了广泛的运用。
在反演算法优缺点方面,论文比较了蒙特卡罗法、遗传算法、模拟退火法、随机耗费法和
Geodetic inversion is geodetic core that studies geoscience and also a branch that speculates on spatial change and evolution of physical state of interior medium in earth by deformation data measured. It is significant in theory and valuable in application to combine geodetic inversion with seismology and geophysics to study on geodynamics, deep-seated structural details of earth, the dynamical process of interior earth and material characteristics. Geodetic inversion is regarded by homely and abroad highly. Especially, crust deformation is natural related with earthquake. So it is a key task of geodetic inversion to research on the process and mode of warning signs of an earthquake, even to forecast an earthquake with interseismic and preseismic deformation measurement. Dislocation is a usual mode to study warning signs of an earthquake.The dislocation theory is researched systemically in the dissertation. The joint inversions with kinds of data based on dislocation are researched. Some usual algorithms are analyzed contrastively. Interval algorithm is discussed mainly. The interval Simulated Annealing algorithm is used to locate a local earthquake and jointly invert fault parameters with GPS and gravimetry in the west of Sichuan.The main research contents and new calculation methods in the dissertation are following:1. Research on dislocation modelThe changes of displacement, strain, tilt, gravity and crustal internal deformation due to dislocation are summarized systemically in the dissertation. Wrong Partial derivatives formulae of dislocation model in some papers are corrected in the dissertation. It is a contribution to researchers who use some methods based on partial derivatives of parameters, such as, the Least-Squared method. The correction perfect the dislocation theory2. Research on Joint Inversion modeJoint inversion with kinds of data is one of the keys of the dissertation. Some top-quality deformation data, such as GPS, leveling, gravimetry and InSar, are obtained by monitoring crustal movement. In fact, those data are output signals of responding to geodynamic process of the interior of earth. The responds to movements are different, but the medium is the same. So, joint inversion is a potential tool to analyze geophysical data.A kind of joint inversion that will invert the weight in the object function is proposed in the dissertation. Based on dislocation mode, the kind of joint inversion with simulated GPS, leveling and gravimetry data is used by twos or whole to invert the parameters of three-dimension fault model. In addition, this kind of joint inversion is also used to invert regional or local horizontal velocity with geodetic data, seismic data and geologic data, such as the Quaternary fault slip.3. Research on Inversion Algorithms
Researches on joint inversion algorithms are another key of the dissertation. Inversion aims to get the minimum of the object function. This is an optimal question in mathematics. The classical methods, such as the Least-Squared method and Bayesian method with a prior information of parameter, need partial derivatives of parameters. In general, geodetic or geophysical model is very nonlinear, the derivatives are very complicated and even it is difficult to express them in formulae. So, recent years, some methods without partial derivatives are used widely.Some algorithms, such as Monte Carlo, genetic algorithm, Simulated Annealing algorithm, random cost method and interval algorithm, are compared in the dissertation. Thereinto, Monte Carlo, genetic algorithm, Simulated Annealing algorithm and random cost method are based on stochastic search. They can sometimes jump over local optimum and converge to global one, but they can't be successful every time because of their inherent stochastic nature. They have the same chance to converge to local and global optimum. So they can't be called whole global optimizations, but a global optimization oriented. Especially, interval algorithm is regarded as a whole global optimization in the dissertation. It is superior to other optimization methods in reliability and appraisal of results. And it is a method to find all global minimizers of a constrained nonlinear function with several variables. It is impossible to converge to a local minimizer for interval algorithm. It is concluded that interval algorithm is a reliable and efficient global optimization method.These methods are compared by inverting fault parameters with simulated gravimetry data base on dislocation mode. Several tests are made with every method. To the stochastic method, the different tests bring different results. If the true value of parameter is unknown, it can not be concluded which answer should be selected as inversion result. Simulated annealing method is better among the all stochastic methods. Interval algorithm can always converge to an interval including global optimum and the upper of approaching error is computed easily.To accelerate the speed of computation of interval algorithm, it is combined with simulated annealing method for the first time. And the new method is called interval simulated annealing method in the dissertation. The combination accelerates the computation speed and makes algorithm reliable and exact. This is a hybrid of stochastic search and exhaustive search.An improvement of interval Newton method is given in the dissertation. It corrects the unreliable part of prototype algorithm and makes the method more reliable and stable. Some examples show the application of it in solving nonlinear equations and global optimization.4. Research on Location of Near EarthquakeSeismic location is to decide the location of hypocenter and the time of earthquake occurrence. It is a basic question of seismology. The location result can disclose some important information about earthquake activities and the earthquake circumstance, thus, the earthquake mechanism and cause of occurrence will be known more. With the more development of digital observation technology, the more accurate location of hypocenter is needed. This is helpful to study hypocenter
the crustal structure and the crustal velocity model.The methods and principles of seismic location with IA-SA and classical Geiger method are introduced in case of homogeneous crust. The focus parameters of Shacheng earthquake in 1976 are inverted by the two methods respectively. The result of IA-SA is superior to the one of Geiger method according to some quantitative compares.5. Research on Geodetic Inversion of the Faults of the West of Sichuan Province Sichuan locates the southeastern of Qinghai-Tibet Plateau. There were many earthquakes historically. The intensity of seismic activities is the fifth in our country. Sichuan province is an important part of South-North Seismic belt. Xianshuihe fault locates the western Sichuan province. It is famous home and abroad and characteristic on intensive structural activities. In addition, Litang-Dewu fault locates the southwestern of Xianshuihe fault. They are researched in detail in the dissertation.Multipurpose researches were done in Xianshuihe fault broadly. According to its character of activity, Xianshuihe fault is divided into northwestern segment, Qianning-Kangding segment, Zheduotang segment and Moxi segment. The data used in the dissertation include relative gravimetry between 1996 and 2001 and GPS velocities between 1991 and 2000.Firstly, the two kinds of data is inverted individually by SA and IA-SA so as to compare their results.There are two projects to invert GPS. The one inverted all parameters of four segments if Xianshuihe Fault. Through the map of velocities, there are obvious differences on some points. Considering the big velocity of some points on southwestern of Xianshuihe fault, the second project is brought forward to invert Litang-Dewu fault synchronously. 7 parameters of every fault segment will be inverted, that is, the location of fault and strike are given some fixed values. According to value of object function, the results of IA-SA is superior to the ones SA. Therefore, the results of IA-SA are regarded as the inversion results with GPS data. The velocity measured is consistent with the one inverted.According to the maps of annual gravity changes isolines between 1996 and 2001, Xianshuihe fault is the boundary of plus isolines and negative isolines. This says the intensive activities of both sides of fault. So it is necessary to consider the action of fault activity to gravity changes. The inversion with gravimetry data resembles the second project of GPS inversion, that is, there are 7 parameters of every fault segment inverted. Still, the results of IA-SA is superior to the ones SA.At the end of the dissertation, a joint inversion with GPS and gravimetry data is done. Two projects are also given with the relatively weight ratio fixed to 0.5 or inverted. The all ten parameters of every fault are inverted by IA-SA during the two projects. The relatively weight ratio of gravimetry inverted is 0.314. The value of object function with the relatively weight ratio inverted is small than the one of another project. The results show that the project with weight ratio inverted is better and match the different kinds of data more rational.
It can be summarized that Xianshuihe fault is mainly a left lateral fault. The northwestern segment has the most intensive activity with a strike slip 13mm/a. The strike slip velocity in middle segment is 4.9~6.9mm/a. But the strike slip velocity in southeastern, the Moxi segment, arrives at 8.28mm/a. Three dislocation components of Litang-Dewu fault is close to each other, and it has the maximum tensile components, 5.12mm/a, among all 5 fault segments.
引文
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