刘洪1,2,3,4,,
1. 中国科学院地质与地球物理研究所, 北京 100029
2. 中国科学院地球科学研究院, 北京 100029
3. 中国科学院油气资源研究院重点实验室, 北京 100029
4. 中国科学院大学, 北京 100049
基金项目: 国家重点研发计划（2018YFF01013503），国家自然科学基金项目（41630319），国家重点研发计划深地专项项目（2016YFC0601101）和港东二区油藏渗流地球物理提高采收率研究联合资助
详细信息
作者简介: 黄继伟, 男, 1989年生, 在读博士研究生, 主要从事油储地球物理研究.E-mail:huangjw@mail.iggcas.ac.cn
通讯作者: 刘洪, 男, 1959年生, 研究员, 主要从事地震波成像和油储地球物理研究.E-mail:liuhong@mail.iggcas.ac.cn
中图分类号: P631收稿日期:2019-07-11
修回日期:2020-06-20
上线日期:2020-08-05
New k-space scheme for modeling elastic wave propagation in heterogeneous media
HUANG JiWei1,2,3,4,,LIU Hong1,2,3,4,,
1. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
2. Institute of Earth Science, Chinese Academy of Sciences, Beijing 100029, China
3. Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
4. University of Chinese Academy of Sciences, Beijing 100049, China
More Information
Corresponding author: LIU Hong,E-mail:liuhong@mail.iggcas.ac.cn
MSC: P631--> Received Date: 11 July 2019
Revised Date: 20 June 2020
Available Online: 05 August 2020
摘要
摘要:传统的伪谱（PS）方法，采用傅里叶变换（FT）计算空间导数具有很高的精度，每个波长仅需要两个采样点，而时间导数采用有限差分（FD）近似因而精度较低.当采用大时间步长时，由于时空精度不平衡，PS法存在不稳定性问题.原始的k-space方法可以有效地克服这些问题但是却无法适用于非均匀介质.为了提高原始k-space方法模拟非均匀介质波动方程的精度，我们提出了一种新的k-space算子族.它是用非均匀介质的变速度代替原k-space算子中的常数补偿速度构造得到，引入低秩近似可以高效求解.我们将构造的新的k-space算子应用于耦合的二阶位移波动方程，而不是交错网格一阶速度应力波动方程，使模拟弹性波的计算存储量减少.我们从数学上证明了基于二阶波动方程的k-space方法与基于一阶波动方程的k-space方法是等价的.数值模拟实验表明，与传统的PS、交错网格PS和原始的k-space方法相比，我们的新方法可以在时间和空间步长较大的均匀和非均匀介质中，为弹性波的传播提供更精确的数值解.在保持稳定性和精度的同时，采用较大的时空采样间隔，可以大大降低数值模拟的计算成本.
关键词: k-space算子/
低秩近似/
弹性波传播/
非均匀介质
Abstract:The traditional Pseudo-Spectral (PS) method achieve an accurate spatial approximation with only two points required per wavelength, whereas it has low accuracy in temporal approximation because using FD approximation. This unbalanced scheme of the PS method has temporal dispersion and instability problems when a large time step is used. The original k-space method can effectively overcome these problems; however, it is not suitable for seismic modeling in heterogeneous media and requires a large memory. To solve this problem, we have developed a new family of k-space operators which are constructed by replacing the constant compensation velocity in the original k-space operators with the variable velocity of heterogeneous media. A low-rank approximation is introduced to obtain solutions at a high efficiency. To deal with the large memory requirement, the constructed k-space operators are applied to the second-order displacement wave equations instead of the first-order velocity-stress wave equations on the staggered grid, which reduces the computational memory. We mathematically demonstrate that this k-space scheme based on the second-order wave equations is equivalent to the original one based on the first-order wave equations. Numerical modeling experiments show that this new scheme can provide analytical and more accurate solutions for acoustic and elastic wave propagation in homogeneous and heterogeneous media with large time and space steps compared with the traditional PS, staggered grid PS and k-space methods. By using larger temporal sampling intervals while maintaining the stability and accuracy, this scheme can greatly reduce the computational cost for long-time modeling.
Key words:k-space operator/
Low-rank approximation/
Wave propagation/
Heterogeneous media
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