多井源距VSP速度分析及逆时偏移
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摘要
垂直地震剖面(VSP)独特的优点使其在能源和矿产资源的勘探以及开发中起着不可忽视的作用。在考虑速度各向异性的情况下,如何从多炮VSP数据本身求出合适的速度模型然后对地下地质构造进行成像,这仍然是一个具有挑战性的工作。本文研究在具有倾斜对称轴的TI(TTI)介质情况下多井源距VSP数据的速度分析以及逆时偏移,在内容上涉及到TTI介质准P波方程的有限差分解法、初至波和反射波射线追踪、走时速度参数反演和逆时偏移等方面。
首先回顾TTI介质弹性波传播的基本理论,对前人给出的TTI介质准P波方程,用直接求解线性方程组的方法推导了任意阶导数任意偶数阶精度有限差分系数的计算公式,由此建立了该准P波方程的时间二阶、空间任意偶数阶精度有限差分格式,实现了TTI介质VSP准P波方程有限差分数值模拟。并利用平面波在各向异性介质与各向同性介质中的等效性,推导了该有限差分格式的稳定性条件和频散公式。在这个有限差分解法的基础上,采用零延时互相关成像条件实现了二维TTI介质多井源距VSP数据的准P波方程逆时偏移。
把前人给出的VTI介质初至波走时插值算法扩展到TTI介质的情况。根据该算法以及Fermat原理,通过在反射界面上搜索最小走时的方法,实现了二维TTI介质反射波的走时计算以及射线追踪。
根据二维TTI介质的群速度表达式,建立了多井源距VSP初至波和反射波走时的表达式,由此推导出了TTI介质地震波走时对各速度参数(即对称轴方向的准P波速度a。、TTI介质对称轴倾角φ以及Thomsen参数ε和δ)偏导数的计算公式,并利用Gauss-Newton反演方法实现了TTI介质速度参数反演。
最后提出一种联合TTI介质速度参数反演和逆时偏移的多井源距VSP迭代速度分析方法。从初始速度模型出发,固定速度界面,利用VSP走时反演各地层的速度参数；然后由反演结果进行偏移成像,根据成像道集估计出新的地层界面位置；由此更新的速度模型再次进行走时反演和偏移处理,从而形成迭代算法。该方法的应用效果由一套模型数据和一套实测数据来说明。
Vertical seismic profiling (VSP) has been playing a significant role in both the exploring and developing of energy and mineral resources for its advantages. Though widely discussed, it's still a challenge to build a suitable velocity model and use the model to image underground structures in a satisfied way from multi-shot VSP data alone in the presence of anisotropy. Therefore, this thesis tries to study the velocity analysis and reverse-time migration of multi-offset VSP data under the hypothesis of tilted transversely isotropic (TTI) media approximation of the rock velocity, in which some aspects of seismic knowledge, such as the finite difference (FD) solution of quasi-P wave equation, ray tracing for first arrivals and reflections, treveltime inversion for velocity parameters, and reverse-time migration, are included.
First briefly reviews some basic theories relevant to propagation of elastic waves in TTI media. Based on FD coefficients for any order derivatives with any even order accuracy computed from a linear system solver, the FD approximation of the quasi-P wave equation with accuracy of two-order in temporal and any even order in spatial domain is built to model synthetic VSP data. Subsequently, by making use of the equivalence of plane waves between TTI and isotropic media, the stability condition and dispersion relation of the FD approximation are presented. And a VSP reverse-time migration scheme based on the FD approximation of quasi-P wave equation and with zero-lag correlation imaging condition is given.
An existing interpolation algorithm for first arrival traveltime computation in VTI media is extended to the case of TTI media. According to the first arrival traveltime calculation algorithm and the Fermat principle, the traveltime computing and ray tracing algorithms for reflections in TTI media by a search for minimum traveltime along reflection interfaces are presented.
From the group velocity expression for TTI media, this thesis sets up the traveltime expressions for first arrivals and reflections, as well as the partial-derivative formulas of treveltime with respect to velocity parameters (velocity of quasi-P wave in symmetry direction, dip of symmetric axis and two Thomsen parameters) for multi-offset VSP, and uses Gauss-Newton method to implement velocity parameters inversion for TTI media.
In combination with traveltime inversion and reflection data migration, the thesis presents an iterative velocity analysis approach. From the initial model, the approach fixes positions of velocity interfaces and uses VSP traveltimes to invert velocity parameters, then implements reverse-time migration by using the inverted results. From the migration results, new interfaces are estimated and a new traveltime inversion is conducted to form an iterative algorithm. At last, the effect of the algorithm is demonstrated by both a set of synthetic and a set of field multi-offset VSP data.
首先回顾TTI介质弹性波传播的基本理论,对前人给出的TTI介质准P波方程,用直接求解线性方程组的方法推导了任意阶导数任意偶数阶精度有限差分系数的计算公式,由此建立了该准P波方程的时间二阶、空间任意偶数阶精度有限差分格式,实现了TTI介质VSP准P波方程有限差分数值模拟。并利用平面波在各向异性介质与各向同性介质中的等效性,推导了该有限差分格式的稳定性条件和频散公式。在这个有限差分解法的基础上,采用零延时互相关成像条件实现了二维TTI介质多井源距VSP数据的准P波方程逆时偏移。
把前人给出的VTI介质初至波走时插值算法扩展到TTI介质的情况。根据该算法以及Fermat原理,通过在反射界面上搜索最小走时的方法,实现了二维TTI介质反射波的走时计算以及射线追踪。
根据二维TTI介质的群速度表达式,建立了多井源距VSP初至波和反射波走时的表达式,由此推导出了TTI介质地震波走时对各速度参数(即对称轴方向的准P波速度a。、TTI介质对称轴倾角φ以及Thomsen参数ε和δ)偏导数的计算公式,并利用Gauss-Newton反演方法实现了TTI介质速度参数反演。
最后提出一种联合TTI介质速度参数反演和逆时偏移的多井源距VSP迭代速度分析方法。从初始速度模型出发,固定速度界面,利用VSP走时反演各地层的速度参数；然后由反演结果进行偏移成像,根据成像道集估计出新的地层界面位置；由此更新的速度模型再次进行走时反演和偏移处理,从而形成迭代算法。该方法的应用效果由一套模型数据和一套实测数据来说明。
Vertical seismic profiling (VSP) has been playing a significant role in both the exploring and developing of energy and mineral resources for its advantages. Though widely discussed, it's still a challenge to build a suitable velocity model and use the model to image underground structures in a satisfied way from multi-shot VSP data alone in the presence of anisotropy. Therefore, this thesis tries to study the velocity analysis and reverse-time migration of multi-offset VSP data under the hypothesis of tilted transversely isotropic (TTI) media approximation of the rock velocity, in which some aspects of seismic knowledge, such as the finite difference (FD) solution of quasi-P wave equation, ray tracing for first arrivals and reflections, treveltime inversion for velocity parameters, and reverse-time migration, are included.
First briefly reviews some basic theories relevant to propagation of elastic waves in TTI media. Based on FD coefficients for any order derivatives with any even order accuracy computed from a linear system solver, the FD approximation of the quasi-P wave equation with accuracy of two-order in temporal and any even order in spatial domain is built to model synthetic VSP data. Subsequently, by making use of the equivalence of plane waves between TTI and isotropic media, the stability condition and dispersion relation of the FD approximation are presented. And a VSP reverse-time migration scheme based on the FD approximation of quasi-P wave equation and with zero-lag correlation imaging condition is given.
An existing interpolation algorithm for first arrival traveltime computation in VTI media is extended to the case of TTI media. According to the first arrival traveltime calculation algorithm and the Fermat principle, the traveltime computing and ray tracing algorithms for reflections in TTI media by a search for minimum traveltime along reflection interfaces are presented.
From the group velocity expression for TTI media, this thesis sets up the traveltime expressions for first arrivals and reflections, as well as the partial-derivative formulas of treveltime with respect to velocity parameters (velocity of quasi-P wave in symmetry direction, dip of symmetric axis and two Thomsen parameters) for multi-offset VSP, and uses Gauss-Newton method to implement velocity parameters inversion for TTI media.
In combination with traveltime inversion and reflection data migration, the thesis presents an iterative velocity analysis approach. From the initial model, the approach fixes positions of velocity interfaces and uses VSP traveltimes to invert velocity parameters, then implements reverse-time migration by using the inverted results. From the migration results, new interfaces are estimated and a new traveltime inversion is conducted to form an iterative algorithm. At last, the effect of the algorithm is demonstrated by both a set of synthetic and a set of field multi-offset VSP data.
引文
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