Cosine-modulated window function-based staggered-grid finite-difference forward modeling

The numerical dispersion and computational cost are high for conventional Taylor series expansion staggered-grid finite-difference forward modeling owing to the high frequency of the wavelets and the large grid intervals. In this study, the cosine-modulated binomial window function (CMBWF)-based staggered-grid finite-difference method is proposed. Two new parameters, the modulated time and modulated range are used in the new window function and by adjusting these two parameters we obtain different characteristics of the main and side lobes of the amplitude response. Numerical dispersion analysis and elastic wavefield forward modeling suggests that the CMBWF method is more precise and less computationally costly than the conventional Taylor series expansion staggered-grid finitedifference method.     

基于Chebyshev自褶积组合窗的有限差分算子优化方法

有限差分法广泛应用于地震波数值模拟、成像和波形反演中,差分数值解的精度直接影响着地震成像和反演的效果.因为有限差分算子可以通过截断伪谱法的空间褶积序列得到,而截断窗函数的属性影响有限差分算子逼近微分算子的精度.具体地讲,窗函数的幅值响应的主瓣和旁瓣决定了有限差分算子逼近的精度,主瓣越窄,旁瓣衰减越大,则有限差分算子逼近微分算子的精度越高,更好地压制数值频散.基于此认识,本文提出了一种基于Chebyshev自褶积组合窗截断逼近的有限差分算子优化方法.Chebyshev自褶积组合窗的主瓣较窄,且旁瓣衰减大,其可通过只调节三个参数,更直观和可视化地控制主瓣和旁瓣的形状,改变有限差分算子逼近微分算子的精度;该窗函数截断逼近的有限差分算子不仅有较大的谱覆盖范围,而且精度误差波动较小,这表明低阶的差分算子可以达到高阶算子的精度,且逼近误差更稳定;从经济上来讲,将有效地减少模拟计算花费,提高计算效率.     

一种时空域优化的高精度交错网格差分算子与正演模拟

如何有效压制数值频散是有限差分正演模拟研究中的关键问题之一.近年来,许多学者对二阶声波方程的差分算子开展了大量的优化工作,在压制频散方面取得不错的效果.一阶压强-速度方程广泛用于研究地震波在地下变密度模型中传播规律,目前针对一阶方程的优化工作大多只是在空间差分算子上展开.本文在前人研究的基础上,推导出一阶声波方程中压强场与偏振速度场之间的解析关系,据此在传统交错网格基础上给出一种高精度的显式时间递推格式,该递推格式将时间差分与空间差分算子结合在一起,并采用共轭梯度法得到精确时间递推匹配系数,实现时空差分算子的同时优化.在编程实现算法的基础上,通过频散分析与三个典型模型测试表明：本文方法能够较为有效地压制时间频散与空间频散,提高数值计算精度;同时对复杂模型也有很好适用性.     

基于时间高精度-空间隐式矩形交错网格有限差分的弹性波数值模拟

针对弹性波数值模拟, 现有的时间高阶有限差分方法主要基于显式差分和正方形网格单元建立的, 因此容易引起较强数值频散且缺乏灵活性.基于上述问题, 本文通过结合十字形和菱形模板设计了一种改进的矩形组合差分模板, 在此基础上发展了隐式交错网格差分方法求解弹性波方程.该方案采用改进差分模板和二阶离散格式共同近似时间导数, 采用隐式差分格式求解空间导数.进一步给出了泰勒级数展开和最小二乘优化两种算法求取的高阶差分系数.联合应用高阶差分方案和波场分离技术产生高精度的弹性波场.将本文方法与几种现有差分方法进行了对比, 包括: 显式和隐式时间二阶差分法, 显式时间高阶差分法.数值分析和模型算例表明, 本文方法比其他方法具有更高的精度和灵活性.

     

Numerical simulation of seismic wavefields in TTI media using the rotated staggered-grid compact finite-difference scheme

Numerical simulation in transverse isotropic media with tilted symmetry axis(TTI) using the standard staggered-grid finite-difference scheme(SSG)results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme(RSG) is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme(CSG) is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme(RSGC). The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.     

一种全局优化的隐式交错网格有限差分算法及其在弹性波数值模拟中的应用

在数值模拟中,隐式有限差分具有较高的精度和稳定性.然而,传统隐式有限差分算法大多由于需要求解大型矩阵方程而存在计算效率偏低的局限性.本文针对一阶速度-应力弹性波方程,构建了一种优化隐式交错网格有限差分格式,然后将改进格式由时间-空间域转换为时间-波数域,利用二范数原理建立目标函数,再利用模拟退火法求取优化系数.通过对均匀模型以及复杂介质模型进行一阶速度-应力弹性波方程数值模拟所得单炮记录、波场快照分析表明:这种优化隐式交错网格差分算法与传统的几种显式和隐式交错网格有限差分算法相比不但降低了计算量,而且能有效的压制网格频散,使弹性波数值模拟的精度得到有效的提高.     

高阶交错网格有限差分法纵横波波场分离数值模拟

本文给出了一种等价的弹性波动方程,以解决完全弹性波场中不能完全分离耦合的纵横波波场问题.对该弹性波动方程进行公式换算,推导出新型等价一阶双曲型方程,应用高阶交错网格有限差分法求解该方程,并给出了相应的最佳匹配层(PML)吸收边界条件,对均匀介质模型、复杂Marmousi模型和实际地质模型进行波场分离数值试验,准确得到了混合波场、完全分离的纯纵横波波场.数值结果表明,本文方法具有比传统方法更好的数值模拟精度和边界吸收效果,同时分析分离后的纵横波纯波场,可观察到较为丰富的能量转换信息,并发现纯纵波场中的非均匀平面波现象,该波为S波以临界角入射情况下的反射SP波,这对认识复杂弹性波的传播规律及弹性波理论具有重要意义.     

A staggered-grid high-order finite-difference modeling for elastic wave field in arbitrary tilt anisotropic media

Introduction The real Earth usually presents anisotropy. Therefore, it is of theoretical and practical sig- nificance for many fields as oil and gas, seismic exploration and production, earthquake prediction, detection of deep structure and so on to study on seismic wave theory, numerical simulation method and its applications in the anisotropic media (Crampin, 1981, 1984; Crampin et al, 1986; Hudson et al, 1996; Liu et al, 1997; Thomsen, 1986, 1995; TENG et al, 1992; HE and ZHANG, 1996)…     

拟空间域弹性波方程交错网格有限差分逆时偏移

弹性波逆时偏移是一种高精度的复杂构造地震成像方法.然而,在传统的基于矩形网格离散化的逆时偏移中,介质界面通常会产生畸变.另外,因使用双程波动方程进行波场延拓,其产生的反射波会在成像过程中产生偏移假象.为解决这些问题,本文提出了一种拟空间域弹性波方程高阶交错网格有限差分格式,并给出了差分格式的稳定性条件,进而实现了高精度的拟空间域弹性波方程有限差分逆时偏移.模型实验表明,若在计算拟空间域采样间隔时引入速度界面信息,则拟空间域弹性波方程高阶交错网格有限差分逆时偏移能够避免常规弹性波方程逆时偏移中弯曲界面形态畸变问题;此外基于该方法进行波场延拓时可有效压制弯曲界面的假散射现象,并能有效压制层间反射波,因此可以减少剖面上的偏移假象,从而显著提高成像的质量.

     

时间-空间高阶精度矩形交错网格隐式有限差分声波正演模拟

有限差分方法因其操作简单、计算消耗低而成为地震勘探领域中最为常用的数值模拟方法之一, 然而用离散的显式差分算子数值逼近地震波动方程中的连续导数容易导致数值频散, 并且基于正方形网格离散形式的有限差分方法对不同地质模型的适应性较低.针对一阶变密度声波方程的数值模拟, 本文发展了一种适用于矩形网格离散形式的时间高阶空间隐式有限差分格式, 可以有效压制时间和空间频散, 同时灵活的网格剖分增强了其应用的广泛性.基于本文矩形交错网格时间高阶空间隐式有限差分格式的时空域频散关系和变量替换的思想, 首先采用泰勒级数展开方法求解不同方向的非轴上时间差分系数及轴上空间差分系数, 使本文差分格式可以获得任意偶数阶时间和空间精度.为了进一步提高本文差分格式在更大波数区域的空间模拟精度, 我们采用线性优化方法来求取新的轴上空间差分系数用于一阶变密度声波方程的波场迭代求解中.频散、稳定性分析及数值模拟算例表明: 相比于传统十字形空间域隐式有限差分格式, 本文矩形交错网格时间高阶空间隐式有限差分格式在精度、稳定性和效率方面均具有优势.

     

Seismic modeling with an optimal staggered-grid finite-difference scheme based on combining Taylor-series expansion and minimax approximation

Staggered-grid finite-difference (SGFD) schemes have been used widely in seismic modeling. The spatial difference coefficients of the SGFD scheme are generally determined by a Taylor-series expansion (TE) method or optimization methods. However, high accuracy is hardly guaranteed both at small and large wavenumbers by using these conventional methods. We propose a new optimal SGFD scheme based on combining TE and minimax approximation (MA) for high accuracy modeling. The optimal spatial SGFD coefficients are calculated by applying a combination of TE and MA to the dispersion relation, where the implementation of the MA method is based on a Remez algorithm. We adopt the optimal SGFD coefficients to solve first-order spatial derivatives of the elastic wave equations and then perform numerical modeling. Dispersion analyses and seismic modeling show the advantage of the proposed optimal method. The optimal SGFD scheme has greater accuracy than the TE-based SGFD scheme for the same spatial difference operator length. In addition, the optimal SGFD scheme can also adopt a shorter operator length to achieve the high accuracy reducing the computational cost.     

Acoustic VTI modeling and pre-stack reverse-time migration based on the time–space domain staggered-grid finite-difference method

Reverse-time migration (RTM) is based on seismic numerical modeling algorithms, and the accuracy and efficiency of RTM strongly depend on the algorithm used for numerical solution of wave equations. Finite-difference (FD) methods have been widely used to solve the wave equation in seismic numerical modeling and RTM. In this paper, we derive a series of time–space domain staggered-grid FD coefficients for acoustic vertical transversely isotropic (VTI) equations, and adopt these difference coefficients to solve the equations, then analyze the numerical dispersion and stability, and compare the time–space domain staggered-grid FD method with the conventional method. The numerical analysis results demonstrate that the time–space domain staggered-grid FD method has greater accuracy and better stability than the conventional method under the same discretizations. Moreover, we implement the pre-stack acoustic VTI RTM by the conventional and time–space domain high-order staggered-grid FD methods, respectively. The migration results reveal that the time–space domain staggered-grid FD method can provide clearer and more accurate image with little influence on computational efficiency, and the new FD method can adopt a larger time step to reduce the computation time and preserve the imaging accuracy as well in RTM. Meanwhile, when considering the anisotropy in RTM for the VTI model, the imaging quality of the acoustic VTI RTM is better than that of the acoustic isotropic RTM.     

二维频率空间域25点优化系数差分格式弹性波数值模拟(英文)

频率空间域地震波数值模拟具有独特的优势:可以同时模拟多源的波传播、每个频率之间独立并行地计算、计算频带选择灵活、不存在累计误差、容易模拟粘弹性介质中地震波传播.但是该方法的最大瓶颈是对于计算机内存的巨大需求.我们使用压缩存储系数矩阵的方法,极大地减少了计算机内存的需求量.同时为了减少短筹分算子的数值频散,引用了频率空间域25点弹性波波动方程的差分格式,并使用了最小二乘意义下求出的优化差分系数.为了克服边界反射,采用了最佳匹配层吸收边界条件.数值模拟试验证明:用压缩存储系数矩阵及优化差分系数的频率空间域25点差分格式进行弹性波正演模拟,可以减少数值频散,提高计算精度.使用较大的网格间距,降低计算机内存需求,并保持较高的计算效率.该正演方法为后续弹性波偏移和弹性参数反演提供较好的基础.     

CSAMT三维交错采样有限差分数值模拟

系统分析大地电磁三维交错采样有限差分算法的基础上,根据可控源音频大地电磁场特征,采用将总场分解为一次场和二次场计算,一次场利用快速汉克尔变换,二次场利用数值模拟的思路.从CSAMT满足的麦克斯韦方程组积分形式出发,利用交错采样有限差分算法推导了电场和磁场的离散关系式,提出了简洁的边界条件和合理的剖分方案,所实现的CSA...     

基于交错网格有限差分法的断面波叠前时间偏移成像影响因素正演分析

断层和断裂带的有效识别是地震资料解释中的重要环节,断层在地震信号响应中以断面波的形式体现,因此断面波成像的质量关系到断层的精细识别与刻画.本文利用精度较高的交错网格有限差分正演模拟方法对断面波成像的影响因素进行了正演研究,主要正演分析的参数包括采集因素中的电缆长度和采集方向,地质因素中的断层倾角、断距、反射系数,以及处理因素中的偏移方法等几个方面.通过正演论证得出：采用合理的采集参数能够提高断面波的照明度;有效结合地质因素能够提高断面波的解释精度;利用合理的偏移方法能够使断层归位更加准确,断面波有效成像.基于以上结论,对于断面波的精确识别与刻画,应综合采集因素,处理因素及地质因素,只有这样才能提高断层的解释精度,有效减小解释误差.     

交错网格中基于波数域插值的波场分离方法研究（英文）

应用多分量地震资料进行成像时通常需要先做波场分离,然后再对分离的波型进行成像。其中,波场分离可以在空间域或波数域实现。然而,由于用交错网格有限差分进行弹性波场数值模拟时,用来进行波数域波场分离的质点振动速度分量定义在不同网格节点上,本文提出了利用波数域插值方法来估算同一网格节点所需质点振动速度值;进而给出了先进行波数域插值后进行波场分离的波数域保幅波场分离方案。数值实验结果表明波数域插值方法具有较高的插值精度且保幅波场分离方法具有较好的保幅性,将本文方法进一步应用于弹性波逆时偏移可以获得保幅性较好的成像结果且对存在一定程度速度误差情况具有较好的适应性。     

傅里叶有限差分法三维波动方程正演模拟

傅里叶有限差分(FFD)法兼有相位屏法和隐式有限差分法二者的优势,能够处理复杂地质构造中的波传播问题,但在三维情形下,算子的双向分裂会引起明显的方位各向异性误差.本文用Fourier变换计算双向分裂过程中的高阶交叉项,消除了方位各向异性误差.该方法充分利用了FFD法在双域实现的算法结构,明显减少了由于引入误差校正所带来的计算量.将该方法应用于修改后的三维French模型的地震正演问题,并将得到的叠后记录、单炮记录同全波有限差分法的模拟结果进行对比,结果证实了该方法对一次反射波具有较高的模拟精度,在内存需求和计算效率方面则具有更大的优势.     

Acoustic finite-difference modeling beyond conventi-onal Courant-Friedrichs-Lewy stability limit: App-roach based on variable-length temporal and spatial operators

Conventional finite-difference (FD) methods cannot model acoustic wave propagation beyond Courant-Friedrichs-Lewy (CFL) numbers 0.707 and 0.577 for two-dimensional (2D) and three-dimensional (3D) equal spacing cases, respectively, thereby limiting time step selection. Based on the definition of temporal and spatial FD operators, we propose a variable-length temporal and spatial operator strategy to model wave propagation beyond those CFL numbers while preserving accuracy. First, to simulate wave propagation beyond the conventional CFL stability limit, the lengths of the temporal operators are modified to exceed the lengths of the spatial operators for high-velocity zones. Second, to preserve the modeling accuracy, the velocity-dependent lengths of the temporal and spatial operators are adaptively varied. The maximum CFL numbers for the proposed method can reach 1.25 and 1.0 in high velocity contrast 2D and 3D simulation examples, respec-tively. We demonstrate the effectiveness of our method by modeling wave propagation in simple and complex media.     

Inversion-based deblending using migration operators

In this paper, we compare the denoising- and inversion-based deblending methods using Stolt migration operators. We use Stolt operator as a kernel to efficiently compute apex-shifted hyperbolic Radon transform. Sparsity promoting transforms, such as Radon transform, can focus seismic data into a sparse model to separate signals, remove noise or interpolate missing traces. Therefore, Radon transforms are a suitable tool for either the denoising- or the inversion-based deblending methods. The denoising-based deblending treats blending interferences as random noise by sorting the data into new gathers, such as common receiver gather. In these gathers, blending interferences exhibit random structures due to the randomization of the source firing times. Alternatively, the inversion-based deblending treats blending interferences as a signal, and the transform models this signal by incorporating the blending operator to formulate an inversion problem. We compare both methods using a robust inversion algorithm with sparse regularization. Results of synthetic and field data examples show that the inversion-based deblending can produce more accurate signal separation for highly blended data.