横向非均匀介质中接收函数的数值模拟与偏移成像研究
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摘要
用横向非均匀介质模拟并解释接收函数，是地球内部结构研究的一个潜在的发展方向。
本文对接收函数的反褶积方法和线性化反演进行了改进，发展了时间域的接收函数多道信号估计和小波变换反演方法。在此基础上，重点研究和发展了横向非均匀介质中，基于波动方程的数值模拟与偏移成像方法，首次将多重网格算法引入到弹性波方程的数值模拟和接收函数的偏移成像，还发展了一种延迟边界方法，以消除人为边界反射的影响。数值检验表明，本文所提出的横向非均匀介质接收函数的数值模拟与偏移成像可用于地球内部介质横向不均匀性的研究。
接收函数的提取和反演是接收函数研究的核心问题。基于多道信号估计理论，本文提出了一种接收函数的多道反褶积方法，从一组远震事件中直接提取共同的因子—接收函数，有效地提高了接收函数的精度和分辨率。为克服广义线性反演对初始模型的依赖性，并保持其快速收敛的特点，本文首次将小波变换引入到接收函数波形反演，将接收函数分解到不同的分辨尺度上，分别进行广义线性反演，并将低分辨率的反演结果作为高分辨率反演的初始模型，渐近地获取宽频带接收函数的模型，克服了非线性问题线性化带来的非唯一性。
在水平分层介质接收函数的波形反演研究的基础上，本文系统阐述了非均匀介质中弹性波传播数值模拟常用的三种有限差分方法：显式差分、隐式差分和交错网格法，首次将多重网格算法应用于弹性波方程的数值模拟问题，克服了交错网格法和显式差分法稳定性差，以及隐式差分法计算效率低的缺点，大大提高了弹性波数值模拟的精度、稳定性和计算效率。
为了消除波动方程数值模拟中普遍存在的虚假边界反射问题，基于波在传播方向上的相位延迟和振幅衰减特性，本文提出了一种延迟边界方法，有效地消除了人为边界的假反射，提高了波场数值模拟的效率。
以下覆半无限空间近垂直入射平面P波，作为弹性波数值模拟的特例，来模拟接收函数，从而为横向非均匀介质中接收函数的反演和偏移成像问题奠定了研究基础。
本文还在接收函数射线反投影叠加成像的基础上，提出了一种基于波动方程的接收函数叠前偏移成像方法，将同一事件接收函数中的转换波和直达P波震相以各自的速度向深度方向逆时延拓成像，并通过不同慢度接收函数的叠加，得到最终的偏移成像结果。典型的介质模型数值分析表明，与射线方法相比，接收函数的波动方程叠前偏移能对横向非均匀介质准确成像，不仅有较高的分辨率，而且对多次波有较明显的压制作用。
对本文所提出的接收函数叠前偏移方法作进一步的发展，可以用于实际的远震体波波形数据，在揭示地壳上地幔结构的横向非均匀性研究中，具有颇为广阔的应用前景。
The modeling and interpretation of receiver function for lateral inhomogeneous media is a potential study field for the physics of the Earth interior.
In this paper, deconvolution and linearized inversion of receiver function are improved; multi-channel deconvolution and wavelet inversion are developed for receiver function. The elastic wave motion equation is applied in the simulation and migration of receiver function in lateral inhomogeneous media, multi-grid algorithm is introduced in numerical modeling of elastic wave motion equation, and phase-delay boundary condition is also provided to absorb boundary reflection. Numerical test shows that the method presented in this paper can be applied in the lateral inhomogeneity study of the Earth Interior.
Deconvolution and inversion of receiver function is a basic problem for receiver function study. Multi-channel deconvolution, based on multi-channel signal analysis, is presented to recover receiver function from three-component teleseismic P waveforms clustered within certain backazimuth and epicenter distance, to increase the resolution of receiver function. Wavelet inversion is also introduced to broadband receiver function, to solve for nonuniqueness cased by linear approximation of nonlinear problem, and broadband receiver function is decomposed into multi-resolution versions, and the inversion result for the low-resolution version is iteratively taken as the initial model for the high-resolution, and gradually obtain the inversion model for broadband receiver function.
Three finite-difference methods, i.e., stagger grid, implicit and explicit algorithms, are analyzed in detail. Multi-grid algorithm is firstly introduced in elastic wave simulation, to solve for the stability problem inherent in stagger grid and implicit algorithm, also for the efficiency problem inherent in explicit algorithm, and the precision, stability and efficiency for simulation of elastic wave arc increased by multi-grid method.
Phase-delay method is provided to effectively absorb boundary reflection and increase efficiency for wave motion simulation, based on phase delay and amplitude decaying features along wave propagation.
Receiver function is simulated for inhomogeneous media, as a special case for elastic wave modeling with nearly vertical incidence plane P wave as initial condition, and provide the base for inversion and migration of receiver function in inhomogeneous media.
Prestack migration method, based on wave motion equation, is also developed for receiver function, and compared with ray method. Both P-to-S conversion wave and direct P phase contained in receiver function are migrated and imaged by reverse-time migration for data gather including all receiver functions recorded in all
seismological stations for one event, and imaging profile is finally obtained by stacking for all events. Numerical migration for typical models show that, in contrast to ray method, prestack wave motion migration can correctly image inhomogeneous media, and suppress multiple reflection wave effectively.
Prestack migration method presented in this paper should be developed to apply in observational teleseismic P waveform data, to study the inhomogeneity of crust and upper mantle.
本文对接收函数的反褶积方法和线性化反演进行了改进，发展了时间域的接收函数多道信号估计和小波变换反演方法。在此基础上，重点研究和发展了横向非均匀介质中，基于波动方程的数值模拟与偏移成像方法，首次将多重网格算法引入到弹性波方程的数值模拟和接收函数的偏移成像，还发展了一种延迟边界方法，以消除人为边界反射的影响。数值检验表明，本文所提出的横向非均匀介质接收函数的数值模拟与偏移成像可用于地球内部介质横向不均匀性的研究。
接收函数的提取和反演是接收函数研究的核心问题。基于多道信号估计理论，本文提出了一种接收函数的多道反褶积方法，从一组远震事件中直接提取共同的因子—接收函数，有效地提高了接收函数的精度和分辨率。为克服广义线性反演对初始模型的依赖性，并保持其快速收敛的特点，本文首次将小波变换引入到接收函数波形反演，将接收函数分解到不同的分辨尺度上，分别进行广义线性反演，并将低分辨率的反演结果作为高分辨率反演的初始模型，渐近地获取宽频带接收函数的模型，克服了非线性问题线性化带来的非唯一性。
在水平分层介质接收函数的波形反演研究的基础上，本文系统阐述了非均匀介质中弹性波传播数值模拟常用的三种有限差分方法：显式差分、隐式差分和交错网格法，首次将多重网格算法应用于弹性波方程的数值模拟问题，克服了交错网格法和显式差分法稳定性差，以及隐式差分法计算效率低的缺点，大大提高了弹性波数值模拟的精度、稳定性和计算效率。
为了消除波动方程数值模拟中普遍存在的虚假边界反射问题，基于波在传播方向上的相位延迟和振幅衰减特性，本文提出了一种延迟边界方法，有效地消除了人为边界的假反射，提高了波场数值模拟的效率。
以下覆半无限空间近垂直入射平面P波，作为弹性波数值模拟的特例，来模拟接收函数，从而为横向非均匀介质中接收函数的反演和偏移成像问题奠定了研究基础。
本文还在接收函数射线反投影叠加成像的基础上，提出了一种基于波动方程的接收函数叠前偏移成像方法，将同一事件接收函数中的转换波和直达P波震相以各自的速度向深度方向逆时延拓成像，并通过不同慢度接收函数的叠加，得到最终的偏移成像结果。典型的介质模型数值分析表明，与射线方法相比，接收函数的波动方程叠前偏移能对横向非均匀介质准确成像，不仅有较高的分辨率，而且对多次波有较明显的压制作用。
对本文所提出的接收函数叠前偏移方法作进一步的发展，可以用于实际的远震体波波形数据，在揭示地壳上地幔结构的横向非均匀性研究中，具有颇为广阔的应用前景。
The modeling and interpretation of receiver function for lateral inhomogeneous media is a potential study field for the physics of the Earth interior.
In this paper, deconvolution and linearized inversion of receiver function are improved; multi-channel deconvolution and wavelet inversion are developed for receiver function. The elastic wave motion equation is applied in the simulation and migration of receiver function in lateral inhomogeneous media, multi-grid algorithm is introduced in numerical modeling of elastic wave motion equation, and phase-delay boundary condition is also provided to absorb boundary reflection. Numerical test shows that the method presented in this paper can be applied in the lateral inhomogeneity study of the Earth Interior.
Deconvolution and inversion of receiver function is a basic problem for receiver function study. Multi-channel deconvolution, based on multi-channel signal analysis, is presented to recover receiver function from three-component teleseismic P waveforms clustered within certain backazimuth and epicenter distance, to increase the resolution of receiver function. Wavelet inversion is also introduced to broadband receiver function, to solve for nonuniqueness cased by linear approximation of nonlinear problem, and broadband receiver function is decomposed into multi-resolution versions, and the inversion result for the low-resolution version is iteratively taken as the initial model for the high-resolution, and gradually obtain the inversion model for broadband receiver function.
Three finite-difference methods, i.e., stagger grid, implicit and explicit algorithms, are analyzed in detail. Multi-grid algorithm is firstly introduced in elastic wave simulation, to solve for the stability problem inherent in stagger grid and implicit algorithm, also for the efficiency problem inherent in explicit algorithm, and the precision, stability and efficiency for simulation of elastic wave arc increased by multi-grid method.
Phase-delay method is provided to effectively absorb boundary reflection and increase efficiency for wave motion simulation, based on phase delay and amplitude decaying features along wave propagation.
Receiver function is simulated for inhomogeneous media, as a special case for elastic wave modeling with nearly vertical incidence plane P wave as initial condition, and provide the base for inversion and migration of receiver function in inhomogeneous media.
Prestack migration method, based on wave motion equation, is also developed for receiver function, and compared with ray method. Both P-to-S conversion wave and direct P phase contained in receiver function are migrated and imaged by reverse-time migration for data gather including all receiver functions recorded in all
seismological stations for one event, and imaging profile is finally obtained by stacking for all events. Numerical migration for typical models show that, in contrast to ray method, prestack wave motion migration can correctly image inhomogeneous media, and suppress multiple reflection wave effectively.
Prestack migration method presented in this paper should be developed to apply in observational teleseismic P waveform data, to study the inhomogeneity of crust and upper mantle.
引文
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