多阶模式瑞利波频散特征与反演研究
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摘要
面波勘探是浅层横波速度结构探测的一项重要无损检测工具,它包括野外数据采集、面波频散数据提取和横波速度反演三个步骤。反演横波速度是面波勘探的最终目的,也是三个步骤中最重要的一步。它包含两部分内容：第一是正演计算,即假定速度模型计算理论频散曲线；第二是最优化算法,即通过迭代寻找与野外数据拟合最好的理论速度模型。三个步骤中每一步处理的精度如何都将影响到最终的反演精度。另外,针对目前面波反演多数是只用基阶模式的频散曲线进行反演,有的甚至仍沿用最初的半波长近似法、拐点法、渐近线法等,这些方法简单、粗糙、主观性强,用到的仅是横波速度Vs与瑞利波速度VR的近似计算关系,并非真正意义上的反演,所以解释结果误差大。而面波频散往往存在多个模式,高阶模式的瑞利波有时携带了关于介质更多的信息,特别是在低速层存在时,高频段能量几乎是高阶模式居于主导地位。因此在反演中应同时考虑基阶模式和高阶模式的频散曲线。本文从多阶模式频散曲线的正演计算及特征分析、瑞利波场有限差分数值模拟、多阶模式频散数据的反演算法及提高反演非唯一性的措施、从野外实际数据中提取多阶模式频散曲线的方法等几个方面进行了深入的探讨、分析和研究。本文的研究是在国家863计划的资助下完成的,是“十五”863计划前沿探索课题(A类)“反射地震面波提取与浅层结构探测技术”(2005AA615010)的延续,属该课题的后续研究。通过本文的研究取得如下研究成果和结论：
1、实现了Thomson—Haskells算法,并在此基础上对频散函数进行了改进,使其适于海洋模型频散曲线的计算,得到了存在上覆液体表层情况下的多阶模式面波频散曲线。实现了瑞利波场的高阶交错网格有限差分数值模拟,并将模拟单炮记录提取的频散曲线与用频散函数计算的理论频散曲线相对照,探讨分析了瑞利波各模式的实际激发情况。
2、对存在上覆液体层时的两层、三层以及低速夹层的固体层状介质海洋模型做了波场模拟和频散曲线的计算,分析了当上覆液体表层的厚度变化时多阶模式面波频散曲线特征,并用波场模拟结果对其进行验证。通过与没有液体表层时的完全固体介质模型相对比,研究了存在上覆液体表层时多阶模式面波频散曲线独特的形态特征,进一步引伸出在滩浅海进行地震勘探中应注意的问题。
3、在多阶模式频散曲线反演方面,对反演参数进行了简化,通过细化分层将反演参数减少为只有一个横波速度变量,验证了细化分层方法用于频散曲线反演的可行性和有效性。与同时反演横波速度和层厚度的常规反演方法相比,细化分层方法避免了反演过程中改变分层数和层厚度等参数,大大简化了反演计算过程。这种方法既满足了反演分辨率的要求,又能使反演结果更接近真实情况。
4、由于LM(Levenberg-Marquardt)反演方法对初始模型的依赖性较大,选择一个合理的初始模型在反演计算中起着至关重要的作用。本文将1/3(或1/2)波长深度处的横波速度Vs近似看做与瑞利波相速度VR相等,利用基阶模式的瑞利波速度(VR)—频率(f)数据对,通过公式z=Lr/3和LR=VR/f来构造初始模型p0。某一深度处的横波速度可通过三次样条插值获得。按该方法计算的初始值p0基本上在模型的真实值ptrue附近,从而避免了初始值选取的盲目性,大大节约了反演迭代时间,保证了反演程序的快速性和稳定性。
5、实现了用LM方法和GA(Genetic Algorithm)方法进行基阶模式和多阶模式的反演,通过理论模型验证,得出GA方法的反演效果优于LM方法,但GA方法的缺点是反演耗时太长。鉴于GA方法的这一不足,本文提出了适于高阶模式反演的ULM(updated Levenberg-Marquardt)反演方案,其反演精度与GA方法相当,但反演耗时远低于GA方法。因此,在实际应用中ULM方法既保证了较高的反演精度,又不至于耗时太长,是一种较为理想的反演方法。
6、在野外数据频散数据提取方面实现了用f-k法、f-p法和相移法提取频散曲线,并对三种方法的提取效果进行了对比分析。对目前的频散曲线提取法方法进行了改进,结合f-p法和相移法的优点提出了f-p、相移叠加法,该方法兼顾了f-p法和相移法的优点,既补充了基阶模式低频段的信息,又保证了高阶模式得到有效分辨。
7、通过对野外实际数据的处理和二维横波速度剖面的反演并与半波长近似法反演结果进行对比分析。半波长近似法反演只利用了1阶模式的数据,且进行了半波长近似,势必会影响反演精度。另外,由于反演分层需要处理人员有丰富的经验知识,处理结果易受人为因素的影响。而本文的研究由于采用了细化分层,反演过程无需人为控制分层,减少了人为因素的影响,同时可以实现多阶模式频散数据的反演,在一定程度上提高了反演精度。
总之,本文通过将模拟单炮记录提取的频散曲线与用频散函数计算的理论频散曲线相对照的方法,探讨分析了瑞利波的频散特征及各模式的实际激发情况,深化了人们对于面波频散特征的认识,并且对面波地震勘探、无损检测等方面的实际应用具有重要的理论价值和实际意义。同时,为在滩浅海及湖泊等表层为液体覆盖层的地区进行面波地震勘探和研究提供了一定的研究思路和理论依据。
论文实现了多阶模式频散数据的提取和反演,并对反演参数进行了细化分层,丰富了面波反演研究的内容,使得在实际应用中真正实现多阶模式频散数据的反演成为可能,弥补了目前仅仅用基阶模式进行面波反演这一不足,提高了反演精度。并编制了相应的处理程序,实际数据处理分析表明反演程序具有一定的经济效益和实用价值。本文的研究属国家863课题“反射地震面波提取与浅层结构探测技术”研究成果的一部分,是该课题所开发软件“反射地震多道瞬态面波分析与正反演软件(SW863 V1.0)”的正演和反演部分。该软件目前已获得国家软件著作权登记(登记号：2008SR09155)。
Surface wave exploration is an important tool to detect the shallow velocity structure of S waves non-destructively, which consists of three main steps:acquisition of surface wave in the field, extraction of dispersion data and, and inversion. To invert S waves velocity is the ultimate objective of surface wave exploration, which is the most important step among the three main steps. The inversion process includes two main algorithms. One is forward modeling, in which the model profile is assumed, and the theoretical dispersion data are derived. The other is optimization algorithm. The second algorithm is an iterative numerical process to search for the theoretical model profile that produces dispersion data that most closely match the field data. The process precision of each step will affect the final inversion accuracy. On the other hand, only the fundamental mode dispersion data are used in most surface wave inversions at present. Even some old methods such as halfwavelength approximation method, inflection point method, asymptote approximation method and so on, are also used now. These simplely and roughly methods include certain subjectivities to be used. They only use the approximate relation between the S-wave velocity and the Rayleigh velocity in inversion, which are not ture inversion indeed and leade to large errors in the inversion results. However, there are several modes in the surface dispersion data. Higher mode dispersion data often possess more information about the media. Especially, when a low velocity interlayer exists in the media, higher mode dispersion data occupy the dominant energies of high frequency segments. So, fundamental mode and higher mode dispersion data should be considered in the inversion. In this dissertation, three aspects contents are studied deeply. The first is the forward modeling of multiple-mode dispersion curves and their characteristics as well as the Rayleigh wave field modeling by staggered-grid finite-difference method. The second is the inversion of multiple-mode dispersion data and some measures to improve the uniqueness of inversion. The third is the methods to extract multiple-mode dispersion curves from field data. This study was supported by the National 863 Foundation Project of China (2005AA615010), and was the follow-up study of the project of'Surface Wave Extraction of Reflection Seismics and Shallow Structure Detecting Technique'. This PhD dissertation obtains such achievements and conclusions as follows:
1. The conventional Thomson-Haskell fast compution method is achieved successfully. It is also revised to be suitable for ocean models. The multiple-mode dispersion curves of ocean models are calculated and analyzed. And simultaneously, high-order staggered-grid finite-difference scheme is used to calculate the Rayleigh wave field. The dispersion characteristics of Rayleigh waves and how their multiple-mode can be excitated in practice are studied by comparing the theoretical dispersion curves from dispersion function with those extracted from synthetical record.
2. Dispersion curves are calculated numberically respectively for tow-layers, three-layers and low velocity interlayer models, which are covered with a liquid layer. And their corresponding wave field are simulated at the same time. The characteristics of multiple-mode dispersion curves for models with different thickness of the overlying liquid layer are analysed thoroughly. The results got from dispersion function are also verificated by wave field simulating. The geometric characteristics of the multi-mode dispersion curves are compared to those of that without a liquid surface. And then, some problems which should be taken into consideration when seismic exploration is applied in off-shore areas were pointed out.
3. In the inversion of multiple-mode dispersion curves, a subdividing layering method to invert the dispersion curves of surface wave is put forward. After subdivision, there remains just only the shear velocity to be inverted in the inversion process. The inversion results obtained from subdividing layering method approach closely to the actual model, which shows that the subdividing layering method is feasible and effective in dispersion curves inversion. Comparing with the conventional inversion method in which the shear velocity and the layer thickness are inverted simultaneously, the subdividing layering method avoids changing the layer numbers and the thickness of each layer, which simplifies the inversion process greatly. This method can not only satisfy the requirement of inversion resolution, but also make the inversion result close to the actual situation.
4. Because the inversion result of Levenberg-Marquardt method depend on initial model greatly, it is very important to select a rational in the inversion. The S-wave velocity Vs in the depth of 1/3 (or 1/2) times of the Rayleigh wavelength is considered to be equal to the phase velocity VR. An initial model p0 is constructed using the Rayleigh wave velocity (VR) and frequency (f) data pairs from fundamental mode by the formulae of z=LR/3 and LR=vR/f. Cubic spline interpolation is used to calculate S-wave velocity Vs at specified depth. An initial model p0 calculated by this method is close to the true model ptrue, which avoid selecting initial model blindly, save iteration time greatly, and ensure the inversion process running fastly and steadily.
5. Levenberg-Marquardt (LM) method and Genetic Algorithm (GA) are used in fundamental and multiple-mode inversion. Theoretical model testing proved that GA obtained a better result than LM. But GA is much expensively in time consumption. Considering this disadvantage of GA, this dissertation put forward an updated scheme of Levenberg-Marquardt method (ULM), whose accuracy is comparatively with GA. But the time consumption of ULM is far bellow GA. In practical application, ULM can not only ensure high accuracy for inversion, but also cost small time. So, ULM is an ideal inversion method.
6. In the aspect of extraction of multiple-mode dispersion curves from field data, f-k method,f-p methods and phase-shift method are used. The extraction result of these three methods are studied and analyzed. This PhD dissertation update the present extracting method of dispersion curves by combining the advantage of f-p method with that of phase-shift method together, and then get a f-p & phase shift-stacking method. This method possesses both the advantage of f-p method and phase shift method, which not only renew the information of fundamental mode, but also remain higher modes to have a good resolution.
7. The field actual data are processed to obtain dispersion data which are used to invert 2D S-wave profile. And the results are compared with those obtained by half-wavelenth approximation methods in which just one mode of dispersion data is used in the inversion. At the same time, half-wavelength approximation is also used in the inversion. These will certainly affect the accuracy of inversion. On the other hand, the procedure of layering and inversion request abundant experience for the processer. That is to say, the inversion results of half-wavelenth approximation methods are easy to be affected by personal factors. However, this study adopts the subdividing layering method, which need not user to control the inversion. At the same tme, the program can also invert multiple-mode dispersion data. So, it improves the accuracy of inversion in certain degree.
In a word, this PhD dissertation study the dispersion characteristics of Rayleigh waves and how their multiple-mode can be excitated in practice by comparing the theoretical dispersion curves from dispersion function with those extracted from synthetical record. The study results deepen people's understanding on dispersion characteristics of surface waves. They also have important theoretical and practical value in the aspects of surface wave exploration and non-destructive testing. At the same time, this study may provide some thought and theoretical bases for surface wave exploration in liquid-covered areas.
The dissertation accomplished the extraction and inversion of multiple-mode dispersion curves, and simplified the inversion parameters into one variable by subdividing layering method. All this studies not only enrich the inversion study of surface wave, but also make it possible to use multiple-mode dispersion data to invert the S-wave velocity in practice.it make up the deficiency of present inversion which only use fundamental dispersion curves, and improve the accuracy of inversion. Corresponding processing programs have been written in this study. The actual data processing results shows that the programs are in possession of great economic benefits and useful value. This study is one part of the National 863 Foundation project of'Surface Wave Extraction of Reflection Seismics and Shallow Structure Detecting Technique'. One production of the project is the software of'Reflection Seismics Multi Channel Analysis of Surface Waves and Forward Modeling and Inversion(SW863 V1.0)', where the forward modeling and inversion parts are the main work of this dissertation. At present, this software has obtain the software copyright registration of China(registration number:2008SR09155).
1、实现了Thomson—Haskells算法,并在此基础上对频散函数进行了改进,使其适于海洋模型频散曲线的计算,得到了存在上覆液体表层情况下的多阶模式面波频散曲线。实现了瑞利波场的高阶交错网格有限差分数值模拟,并将模拟单炮记录提取的频散曲线与用频散函数计算的理论频散曲线相对照,探讨分析了瑞利波各模式的实际激发情况。
2、对存在上覆液体层时的两层、三层以及低速夹层的固体层状介质海洋模型做了波场模拟和频散曲线的计算,分析了当上覆液体表层的厚度变化时多阶模式面波频散曲线特征,并用波场模拟结果对其进行验证。通过与没有液体表层时的完全固体介质模型相对比,研究了存在上覆液体表层时多阶模式面波频散曲线独特的形态特征,进一步引伸出在滩浅海进行地震勘探中应注意的问题。
3、在多阶模式频散曲线反演方面,对反演参数进行了简化,通过细化分层将反演参数减少为只有一个横波速度变量,验证了细化分层方法用于频散曲线反演的可行性和有效性。与同时反演横波速度和层厚度的常规反演方法相比,细化分层方法避免了反演过程中改变分层数和层厚度等参数,大大简化了反演计算过程。这种方法既满足了反演分辨率的要求,又能使反演结果更接近真实情况。
4、由于LM(Levenberg-Marquardt)反演方法对初始模型的依赖性较大,选择一个合理的初始模型在反演计算中起着至关重要的作用。本文将1/3(或1/2)波长深度处的横波速度Vs近似看做与瑞利波相速度VR相等,利用基阶模式的瑞利波速度(VR)—频率(f)数据对,通过公式z=Lr/3和LR=VR/f来构造初始模型p0。某一深度处的横波速度可通过三次样条插值获得。按该方法计算的初始值p0基本上在模型的真实值ptrue附近,从而避免了初始值选取的盲目性,大大节约了反演迭代时间,保证了反演程序的快速性和稳定性。
5、实现了用LM方法和GA(Genetic Algorithm)方法进行基阶模式和多阶模式的反演,通过理论模型验证,得出GA方法的反演效果优于LM方法,但GA方法的缺点是反演耗时太长。鉴于GA方法的这一不足,本文提出了适于高阶模式反演的ULM(updated Levenberg-Marquardt)反演方案,其反演精度与GA方法相当,但反演耗时远低于GA方法。因此,在实际应用中ULM方法既保证了较高的反演精度,又不至于耗时太长,是一种较为理想的反演方法。
6、在野外数据频散数据提取方面实现了用f-k法、f-p法和相移法提取频散曲线,并对三种方法的提取效果进行了对比分析。对目前的频散曲线提取法方法进行了改进,结合f-p法和相移法的优点提出了f-p、相移叠加法,该方法兼顾了f-p法和相移法的优点,既补充了基阶模式低频段的信息,又保证了高阶模式得到有效分辨。
7、通过对野外实际数据的处理和二维横波速度剖面的反演并与半波长近似法反演结果进行对比分析。半波长近似法反演只利用了1阶模式的数据,且进行了半波长近似,势必会影响反演精度。另外,由于反演分层需要处理人员有丰富的经验知识,处理结果易受人为因素的影响。而本文的研究由于采用了细化分层,反演过程无需人为控制分层,减少了人为因素的影响,同时可以实现多阶模式频散数据的反演,在一定程度上提高了反演精度。
总之,本文通过将模拟单炮记录提取的频散曲线与用频散函数计算的理论频散曲线相对照的方法,探讨分析了瑞利波的频散特征及各模式的实际激发情况,深化了人们对于面波频散特征的认识,并且对面波地震勘探、无损检测等方面的实际应用具有重要的理论价值和实际意义。同时,为在滩浅海及湖泊等表层为液体覆盖层的地区进行面波地震勘探和研究提供了一定的研究思路和理论依据。
论文实现了多阶模式频散数据的提取和反演,并对反演参数进行了细化分层,丰富了面波反演研究的内容,使得在实际应用中真正实现多阶模式频散数据的反演成为可能,弥补了目前仅仅用基阶模式进行面波反演这一不足,提高了反演精度。并编制了相应的处理程序,实际数据处理分析表明反演程序具有一定的经济效益和实用价值。本文的研究属国家863课题“反射地震面波提取与浅层结构探测技术”研究成果的一部分,是该课题所开发软件“反射地震多道瞬态面波分析与正反演软件(SW863 V1.0)”的正演和反演部分。该软件目前已获得国家软件著作权登记(登记号：2008SR09155)。
Surface wave exploration is an important tool to detect the shallow velocity structure of S waves non-destructively, which consists of three main steps:acquisition of surface wave in the field, extraction of dispersion data and, and inversion. To invert S waves velocity is the ultimate objective of surface wave exploration, which is the most important step among the three main steps. The inversion process includes two main algorithms. One is forward modeling, in which the model profile is assumed, and the theoretical dispersion data are derived. The other is optimization algorithm. The second algorithm is an iterative numerical process to search for the theoretical model profile that produces dispersion data that most closely match the field data. The process precision of each step will affect the final inversion accuracy. On the other hand, only the fundamental mode dispersion data are used in most surface wave inversions at present. Even some old methods such as halfwavelength approximation method, inflection point method, asymptote approximation method and so on, are also used now. These simplely and roughly methods include certain subjectivities to be used. They only use the approximate relation between the S-wave velocity and the Rayleigh velocity in inversion, which are not ture inversion indeed and leade to large errors in the inversion results. However, there are several modes in the surface dispersion data. Higher mode dispersion data often possess more information about the media. Especially, when a low velocity interlayer exists in the media, higher mode dispersion data occupy the dominant energies of high frequency segments. So, fundamental mode and higher mode dispersion data should be considered in the inversion. In this dissertation, three aspects contents are studied deeply. The first is the forward modeling of multiple-mode dispersion curves and their characteristics as well as the Rayleigh wave field modeling by staggered-grid finite-difference method. The second is the inversion of multiple-mode dispersion data and some measures to improve the uniqueness of inversion. The third is the methods to extract multiple-mode dispersion curves from field data. This study was supported by the National 863 Foundation Project of China (2005AA615010), and was the follow-up study of the project of'Surface Wave Extraction of Reflection Seismics and Shallow Structure Detecting Technique'. This PhD dissertation obtains such achievements and conclusions as follows:
1. The conventional Thomson-Haskell fast compution method is achieved successfully. It is also revised to be suitable for ocean models. The multiple-mode dispersion curves of ocean models are calculated and analyzed. And simultaneously, high-order staggered-grid finite-difference scheme is used to calculate the Rayleigh wave field. The dispersion characteristics of Rayleigh waves and how their multiple-mode can be excitated in practice are studied by comparing the theoretical dispersion curves from dispersion function with those extracted from synthetical record.
2. Dispersion curves are calculated numberically respectively for tow-layers, three-layers and low velocity interlayer models, which are covered with a liquid layer. And their corresponding wave field are simulated at the same time. The characteristics of multiple-mode dispersion curves for models with different thickness of the overlying liquid layer are analysed thoroughly. The results got from dispersion function are also verificated by wave field simulating. The geometric characteristics of the multi-mode dispersion curves are compared to those of that without a liquid surface. And then, some problems which should be taken into consideration when seismic exploration is applied in off-shore areas were pointed out.
3. In the inversion of multiple-mode dispersion curves, a subdividing layering method to invert the dispersion curves of surface wave is put forward. After subdivision, there remains just only the shear velocity to be inverted in the inversion process. The inversion results obtained from subdividing layering method approach closely to the actual model, which shows that the subdividing layering method is feasible and effective in dispersion curves inversion. Comparing with the conventional inversion method in which the shear velocity and the layer thickness are inverted simultaneously, the subdividing layering method avoids changing the layer numbers and the thickness of each layer, which simplifies the inversion process greatly. This method can not only satisfy the requirement of inversion resolution, but also make the inversion result close to the actual situation.
4. Because the inversion result of Levenberg-Marquardt method depend on initial model greatly, it is very important to select a rational in the inversion. The S-wave velocity Vs in the depth of 1/3 (or 1/2) times of the Rayleigh wavelength is considered to be equal to the phase velocity VR. An initial model p0 is constructed using the Rayleigh wave velocity (VR) and frequency (f) data pairs from fundamental mode by the formulae of z=LR/3 and LR=vR/f. Cubic spline interpolation is used to calculate S-wave velocity Vs at specified depth. An initial model p0 calculated by this method is close to the true model ptrue, which avoid selecting initial model blindly, save iteration time greatly, and ensure the inversion process running fastly and steadily.
5. Levenberg-Marquardt (LM) method and Genetic Algorithm (GA) are used in fundamental and multiple-mode inversion. Theoretical model testing proved that GA obtained a better result than LM. But GA is much expensively in time consumption. Considering this disadvantage of GA, this dissertation put forward an updated scheme of Levenberg-Marquardt method (ULM), whose accuracy is comparatively with GA. But the time consumption of ULM is far bellow GA. In practical application, ULM can not only ensure high accuracy for inversion, but also cost small time. So, ULM is an ideal inversion method.
6. In the aspect of extraction of multiple-mode dispersion curves from field data, f-k method,f-p methods and phase-shift method are used. The extraction result of these three methods are studied and analyzed. This PhD dissertation update the present extracting method of dispersion curves by combining the advantage of f-p method with that of phase-shift method together, and then get a f-p & phase shift-stacking method. This method possesses both the advantage of f-p method and phase shift method, which not only renew the information of fundamental mode, but also remain higher modes to have a good resolution.
7. The field actual data are processed to obtain dispersion data which are used to invert 2D S-wave profile. And the results are compared with those obtained by half-wavelenth approximation methods in which just one mode of dispersion data is used in the inversion. At the same time, half-wavelength approximation is also used in the inversion. These will certainly affect the accuracy of inversion. On the other hand, the procedure of layering and inversion request abundant experience for the processer. That is to say, the inversion results of half-wavelenth approximation methods are easy to be affected by personal factors. However, this study adopts the subdividing layering method, which need not user to control the inversion. At the same tme, the program can also invert multiple-mode dispersion data. So, it improves the accuracy of inversion in certain degree.
In a word, this PhD dissertation study the dispersion characteristics of Rayleigh waves and how their multiple-mode can be excitated in practice by comparing the theoretical dispersion curves from dispersion function with those extracted from synthetical record. The study results deepen people's understanding on dispersion characteristics of surface waves. They also have important theoretical and practical value in the aspects of surface wave exploration and non-destructive testing. At the same time, this study may provide some thought and theoretical bases for surface wave exploration in liquid-covered areas.
The dissertation accomplished the extraction and inversion of multiple-mode dispersion curves, and simplified the inversion parameters into one variable by subdividing layering method. All this studies not only enrich the inversion study of surface wave, but also make it possible to use multiple-mode dispersion data to invert the S-wave velocity in practice.it make up the deficiency of present inversion which only use fundamental dispersion curves, and improve the accuracy of inversion. Corresponding processing programs have been written in this study. The actual data processing results shows that the programs are in possession of great economic benefits and useful value. This study is one part of the National 863 Foundation project of'Surface Wave Extraction of Reflection Seismics and Shallow Structure Detecting Technique'. One production of the project is the software of'Reflection Seismics Multi Channel Analysis of Surface Waves and Forward Modeling and Inversion(SW863 V1.0)', where the forward modeling and inversion parts are the main work of this dissertation. At present, this software has obtain the software copyright registration of China(registration number:2008SR09155).
引文
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