水平界面任意空间取向TI同类反射非双曲时距研究
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摘要
水平界面任意空间取向TI同类反射非双曲时距研究
各向同性介质中水平界面CMP(Common Middle Point)集同类反射波近、远偏移距反射时距严格为双曲时距。TI(Transverse Isotropy)各向异性介质中近偏移距反射时距为双曲时距，而远偏移距反射时距为非双曲时距。关于VTI(TI with a Vertical symmetry axis)、HTI(TI with a Horizontal symmetry axis)、TTI(TI with a Titled symmetry axis confined to incident plane)以及弱各向异性等特殊介质条件的研究有大量的成果。姚陈(2005)给出了任意强弱、任意空间取向TI(Transverse Isotropy with an Arbitrary spatial orientation，ATI)介质中NMO速度的扩展研究；在此基础上，本文扩展研究任意强弱、ATI介质中非双曲时距，包括理论研究和正演模拟，以及TI介质参数反演两部分的研究。
理论和正演部分包括对非双曲动校正方程的修正；以及基于任意空间取向TI坐标系到测线坐标系的变换方法，推导给出水平界面ATI介质中同类反射波(非转换波)关于平方走时[t~2(x~2)]的泰勒级数展开式中的四次时差项系数(A_4)的精确解析表达式。
在对非双曲动校正方程进行修正时，基于我们给出的精确A_4系数解析解和NMO速度解析解，给出了ATI介质中远偏移距非双曲动校正方程中分母系数(A~*)公式，使得非双曲动校正方程能更好地拟合反射时距。由此，我们扩大了非双曲动校正方程的适用范围，从而实现了ATI介质中远偏移距非双曲时距的动校叠加。
我们给出的A_4精确解析表达式有利于各向异性解释，反演介质各向异性参数，以及提高成像质量。此A_4精确解析表达式，对TI的各向异性强弱及空间取向没有限制，将已有研究结果作为其中的特例统一起来，包括了VTI、HTI、TTI和弱各向异性近似等特殊情况。
我们给出的精确解与弱各向异性近似解的比较研究表明：随着各向异性参数ε和δ的增大，近似解失去了精确性、存在较大误差。精确解与近似解的差异不仅表现在A_4值的大小及符号(正负)，而且表现在A_4随方位的变化特征。
通过与各向异性射线追踪算法给出的精确时距结果对比得出：我们导出的A_4精确解析解可以用来解析研究任意强弱ATI介质中随方位变化的非双曲时距，修正后的非双曲动校正方程能精确地描述任意强弱ATI中随测线方位变化的走时曲线，可以用来替代耗时、多偏移距、多方位的射线追踪方法正演模拟ATI介质中远偏移距反射走时。
在反演部分中，我们论述了将遗传算法(GA)应用于各向异性参数反演的实现过程。特别论述了利用多方位二维反射P波长偏移距非双曲走时资料，结合其他资料(如检测炮、钻井或测井)所提供的垂直界面反射速度，来反演获取TI介质参数的可行性及唯一性。对于VTI介质，P波反射由V_(p0)、ε和δ三个参数来描述，在其它资料给出垂直速度(V_(p0))的前提条件下，ε和δ两个参数可由近偏移距NMO速度和远偏移距四次时差系数(A_4)两个条件来约束反演，那么反演解是唯一的。相比VTI介质，ATI介质中增加了对称轴倾角(θ_c)与方位(φ_c)两个参数，问题的复杂性可以通过方位变化的非双曲时距来解决。因此，我们提出了基于三条测线剖面的NMO速度和四次时差项系数进行ATI介质参数反演的新思路，利用三条测线剖面的三个近偏移距NMO速度和一个远偏移距A_4系数四个条件来约束反演ε、δ、θ_c和φ_c四个参数。最后，由遗传算法实现了TI介质的各向异性和空间取向参数反演，反演的精度和稳定性较高。
In isotropic media, the reflection traveltime-offset of pure (non-converted) modes from a horizontal interface in CMP (Common Middle Point) gathers can be strictly described by a hyperbolic curve for both near and far-offset. While in TI (Transverse Isotropy) media, such reflection traveltime-offset is a hyperbolic curve for near-offset, but a nonhyperbolic curve for far-offset. For VTI, HTI, TTI and weak anisotropy approximation, there are many researches. Yao (2005) presents the exact analytic solution of the NMO velocity for the ATI (TI with an Arbitrary spatial orientation) media. In this thesis, we attempt to extend the study of the nonhyperbolic reflection traveltime-offset for the far-offset to the ATI media with arbitrary anisotropy strength. Our research is divided into two parts: theoretic forward modeling and TI parameter inversion.
In the part of forward modeling, we adjust the nonhyperbolic moveout equation and present an exact analytic expression for the quartic moveout coefficient (A_4) of the Taylor series expansion of the squared traveltime [ t~2 (x~2) ] for the ATI media through the coordinates transformation.
For the adjusted nonhyperbolic moveout equation, based on our exact analytic solution of A_4, and NMO velocity, a formula of the denominator coefficient (A*) in the nonhyperbolic moveout equation for the far-offset in the ATI media is presented, which makes the nonhyperbolic moveout equation fit the reflection traveltime exactly. Therefore, our work extends the application of the nonhyperbolic moveout equation to the ATI media and makes the nonhyperbolic moveout correction and stack of the far-offset in the ATI media.
Our analytic solution of A_4 facilitates anisotropy interpretation, the analyses of the influence factors, the inversion of the anisotropy parameters and improving the imaging quality. The solution of A_4 has no limitation to the anisotropy strength and the TI orientation. It unifies all the special cases in existing researches, such as VTI, HTI, TTI, and weak anisotropy approximation.
A comparison between our exact solution and the approximate solution of A_4 for weak anisotropy shows that the approximate solution for weak anisotropy loses its exactness and has notable errors with the increasing anisotropic parametersεandδ. The exact and approximate solutions are different in the magnitude and signs (positive and negative) of A_4 as well as the variations with azimuths.
Compared with the exact traveltime-offset of the ray-tracing algorithm, our exact analytic solution of A_4 can be used for calculating the nonhyperbolic traveltime-offset with different azimuth in the ATI media. The adjusted nonhyperbolic moveout equation can precisely describe the traveltime curves with the different azimuth in the ATI media with arbitrary anisotropy strength, and can also replace the timeconsuming, multioffset, multiazimuth ray tracing method to do the forward modelling of the reflection traveltime for the far-offset in the ATI media.
In the second part of our study, we discuss the performance of the parameter inversion of anisotropy and TI orientation by means of the genetic algorithm. For the P-wave reflection, the NMO velocity and A_4 in the ATI media can be described by five parameters (V_(p0),ε,δ,θ_c, andφ_c) .In comparison with the VTI media, there are new two parameters (θ_c,φ_c) for the orientation of the symmetric axis in the ATI media. The new two parameters can be obtained through the nonhyperbolic traveltime-offset with different azimuth. Like the case of the VTI, only the nonhyperbolic traveltime data of the P-wave are not sufficient to retrieve the three parameters V_(p0),εandδ, suggesting that the inversion can be performed by using multiazimuth nonhyperbolic (long-spread) P-wave reflection traveltime data, and vertical velocity from check shot and drill or log well data. We discuss the feasibility of the inversion condition and the uniqueness of the inversion result. In our inversion with three profiles, we use three different near-offset NMO velocities and one far-offset A_4 in conjunction with vertical velocity or interface depth from the other data. Then, the inversion is performed for anisotropy parameters and the TI orientation with the genetic algorithm. The numerical tests demonstrate that the precision and stability of our inversion is satisfactory.
各向同性介质中水平界面CMP(Common Middle Point)集同类反射波近、远偏移距反射时距严格为双曲时距。TI(Transverse Isotropy)各向异性介质中近偏移距反射时距为双曲时距，而远偏移距反射时距为非双曲时距。关于VTI(TI with a Vertical symmetry axis)、HTI(TI with a Horizontal symmetry axis)、TTI(TI with a Titled symmetry axis confined to incident plane)以及弱各向异性等特殊介质条件的研究有大量的成果。姚陈(2005)给出了任意强弱、任意空间取向TI(Transverse Isotropy with an Arbitrary spatial orientation，ATI)介质中NMO速度的扩展研究；在此基础上，本文扩展研究任意强弱、ATI介质中非双曲时距，包括理论研究和正演模拟，以及TI介质参数反演两部分的研究。
理论和正演部分包括对非双曲动校正方程的修正；以及基于任意空间取向TI坐标系到测线坐标系的变换方法，推导给出水平界面ATI介质中同类反射波(非转换波)关于平方走时[t~2(x~2)]的泰勒级数展开式中的四次时差项系数(A_4)的精确解析表达式。
在对非双曲动校正方程进行修正时，基于我们给出的精确A_4系数解析解和NMO速度解析解，给出了ATI介质中远偏移距非双曲动校正方程中分母系数(A~*)公式，使得非双曲动校正方程能更好地拟合反射时距。由此，我们扩大了非双曲动校正方程的适用范围，从而实现了ATI介质中远偏移距非双曲时距的动校叠加。
我们给出的A_4精确解析表达式有利于各向异性解释，反演介质各向异性参数，以及提高成像质量。此A_4精确解析表达式，对TI的各向异性强弱及空间取向没有限制，将已有研究结果作为其中的特例统一起来，包括了VTI、HTI、TTI和弱各向异性近似等特殊情况。
我们给出的精确解与弱各向异性近似解的比较研究表明：随着各向异性参数ε和δ的增大，近似解失去了精确性、存在较大误差。精确解与近似解的差异不仅表现在A_4值的大小及符号(正负)，而且表现在A_4随方位的变化特征。
通过与各向异性射线追踪算法给出的精确时距结果对比得出：我们导出的A_4精确解析解可以用来解析研究任意强弱ATI介质中随方位变化的非双曲时距，修正后的非双曲动校正方程能精确地描述任意强弱ATI中随测线方位变化的走时曲线，可以用来替代耗时、多偏移距、多方位的射线追踪方法正演模拟ATI介质中远偏移距反射走时。
在反演部分中，我们论述了将遗传算法(GA)应用于各向异性参数反演的实现过程。特别论述了利用多方位二维反射P波长偏移距非双曲走时资料，结合其他资料(如检测炮、钻井或测井)所提供的垂直界面反射速度，来反演获取TI介质参数的可行性及唯一性。对于VTI介质，P波反射由V_(p0)、ε和δ三个参数来描述，在其它资料给出垂直速度(V_(p0))的前提条件下，ε和δ两个参数可由近偏移距NMO速度和远偏移距四次时差系数(A_4)两个条件来约束反演，那么反演解是唯一的。相比VTI介质，ATI介质中增加了对称轴倾角(θ_c)与方位(φ_c)两个参数，问题的复杂性可以通过方位变化的非双曲时距来解决。因此，我们提出了基于三条测线剖面的NMO速度和四次时差项系数进行ATI介质参数反演的新思路，利用三条测线剖面的三个近偏移距NMO速度和一个远偏移距A_4系数四个条件来约束反演ε、δ、θ_c和φ_c四个参数。最后，由遗传算法实现了TI介质的各向异性和空间取向参数反演，反演的精度和稳定性较高。
In isotropic media, the reflection traveltime-offset of pure (non-converted) modes from a horizontal interface in CMP (Common Middle Point) gathers can be strictly described by a hyperbolic curve for both near and far-offset. While in TI (Transverse Isotropy) media, such reflection traveltime-offset is a hyperbolic curve for near-offset, but a nonhyperbolic curve for far-offset. For VTI, HTI, TTI and weak anisotropy approximation, there are many researches. Yao (2005) presents the exact analytic solution of the NMO velocity for the ATI (TI with an Arbitrary spatial orientation) media. In this thesis, we attempt to extend the study of the nonhyperbolic reflection traveltime-offset for the far-offset to the ATI media with arbitrary anisotropy strength. Our research is divided into two parts: theoretic forward modeling and TI parameter inversion.
In the part of forward modeling, we adjust the nonhyperbolic moveout equation and present an exact analytic expression for the quartic moveout coefficient (A_4) of the Taylor series expansion of the squared traveltime [ t~2 (x~2) ] for the ATI media through the coordinates transformation.
For the adjusted nonhyperbolic moveout equation, based on our exact analytic solution of A_4, and NMO velocity, a formula of the denominator coefficient (A*) in the nonhyperbolic moveout equation for the far-offset in the ATI media is presented, which makes the nonhyperbolic moveout equation fit the reflection traveltime exactly. Therefore, our work extends the application of the nonhyperbolic moveout equation to the ATI media and makes the nonhyperbolic moveout correction and stack of the far-offset in the ATI media.
Our analytic solution of A_4 facilitates anisotropy interpretation, the analyses of the influence factors, the inversion of the anisotropy parameters and improving the imaging quality. The solution of A_4 has no limitation to the anisotropy strength and the TI orientation. It unifies all the special cases in existing researches, such as VTI, HTI, TTI, and weak anisotropy approximation.
A comparison between our exact solution and the approximate solution of A_4 for weak anisotropy shows that the approximate solution for weak anisotropy loses its exactness and has notable errors with the increasing anisotropic parametersεandδ. The exact and approximate solutions are different in the magnitude and signs (positive and negative) of A_4 as well as the variations with azimuths.
Compared with the exact traveltime-offset of the ray-tracing algorithm, our exact analytic solution of A_4 can be used for calculating the nonhyperbolic traveltime-offset with different azimuth in the ATI media. The adjusted nonhyperbolic moveout equation can precisely describe the traveltime curves with the different azimuth in the ATI media with arbitrary anisotropy strength, and can also replace the timeconsuming, multioffset, multiazimuth ray tracing method to do the forward modelling of the reflection traveltime for the far-offset in the ATI media.
In the second part of our study, we discuss the performance of the parameter inversion of anisotropy and TI orientation by means of the genetic algorithm. For the P-wave reflection, the NMO velocity and A_4 in the ATI media can be described by five parameters (V_(p0),ε,δ,θ_c, andφ_c) .In comparison with the VTI media, there are new two parameters (θ_c,φ_c) for the orientation of the symmetric axis in the ATI media. The new two parameters can be obtained through the nonhyperbolic traveltime-offset with different azimuth. Like the case of the VTI, only the nonhyperbolic traveltime data of the P-wave are not sufficient to retrieve the three parameters V_(p0),εandδ, suggesting that the inversion can be performed by using multiazimuth nonhyperbolic (long-spread) P-wave reflection traveltime data, and vertical velocity from check shot and drill or log well data. We discuss the feasibility of the inversion condition and the uniqueness of the inversion result. In our inversion with three profiles, we use three different near-offset NMO velocities and one far-offset A_4 in conjunction with vertical velocity or interface depth from the other data. Then, the inversion is performed for anisotropy parameters and the TI orientation with the genetic algorithm. The numerical tests demonstrate that the precision and stability of our inversion is satisfactory.
引文
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