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物探与化探  2019, Vol. 43 Issue (1): 110-117    DOI: 10.11720/wtyht.2019.2562
     方法研究·信息处理·仪器研制 本期目录 | 过刊浏览 | 高级检索 |
基于高斯束理论的有限频核函数计算
王守进1, 敬朋贵2, 蔡杰雄1
1. 中国石油化工股份有限公司 石油物探技术研究院,江苏 南京 025111
2. 中国石油化工股份有限公司勘探分公司,四川 成都 610041
The finite frequency kernel function calculation based on Gassian beam theory
Shou-Jin WANG1, Peng-Gui Jing2, Jie-Xiong CAI1
1. Academy of Petroleum Geophysical Exploration Technology,SINOPEC,Nanjing 025111,China
2. Branch of Geological Exploration,SINOPEC,Chengdu 610041,China
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摘要 

相对于常规射线层析速度建模,基于波动理论的层析速度建模考虑了波的带限特性,反演分辨率更高。波动理论层析的核心在于波路径(有限频核函数)的计算。文中详细介绍了一种基于高斯束算子计算有限频核函数的方法,分析了初始束宽度和高斯束出射角度间隔对计算精度的影响;并针对高斯束近源处误差较大的缺陷,提出了改进的束参数以提高近源精度;详细分析了初始束宽度和角度间隔对改进高斯束方法的影响及改进高斯束的聚焦特性;数值算例验证了该方法在缓变介质中计算有限频核函数的可行性,计算效率较高且可处理回折波的核函数。

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王守进
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关键词 有限频核函数高斯束初始束宽度束参数    
Abstract

In comparison with the routine ray tomographic velocity model construction,the tomographic velocity model construction based on undulation theory considers the belt limitation property of the wave,and hence it has higher inversion resolution.The core of the undulation theory tomography lies in the calculation of the wave route (finite frequency kernel function).This paper introduces in detail a method for calculation of finite frequency kernel function based on Gassian beam operator,analyzes the effect of the initial width and the emergence angle interval of the Gassian beam on the calculation precision.To overcome the defect of the relatively large error at the near-source place of the Gassian beam,the authors put forward improved beam parameters so as to raise the near-source precision.This paper also analyzes in detail the effect of initial beam width and angle interval on the improved Gassian beam and the focussing characteristics of the improved Gassian beam.Digital calculation example has verified the feasibility of this method in calculation of finite frequency kernel function.Its calculation efficiency is relatively high and it can process kernel function of the inflection wave.

Key wordsfinite frequency    kernel function    Gassian beam    initial beam width    beam parameters
收稿日期: 2017-12-14      出版日期: 2019-02-20
:  P631.4  
基金资助:国家科技重大专项(2017ZX05036)
作者简介: 王守进(1991-),男,硕士,现就职于中石化石油物探技术研究院,工程师,从事地震偏移成像及速度反演工作。Email:wangshj. swty@sinopec.com
引用本文:   
王守进, 敬朋贵, 蔡杰雄. 基于高斯束理论的有限频核函数计算[J]. 物探与化探, 2019, 43(1): 110-117.
Shou-Jin WANG, Peng-Gui Jing, Jie-Xiong CAI. The finite frequency kernel function calculation based on Gassian beam theory. Geophysical and Geochemical Exploration, 2019, 43(1): 110-117.
链接本文:  
https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2019.2562      或      https://www.wutanyuhuatan.com/CN/Y2019/V43/I1/110
Fig.1  不同初始束宽度和角度间隔对格林函数精度的影响
a—不同初始束宽度对格林函数精度的影响;b—不同角度间隔对格林函数精度的影响
Fig.2  20 Hz单频格林函数的高斯束解、解析解及其误差比较
a—20 Hz单频格林函数的解析解;b—20 Hz单频格林函数高斯束解;c—解析解和高斯束叠加解的差值;d—水平切线误差对比
Fig.3  不同束宽度和出射角度间隔对改进高斯束精度的影响
a—改进高斯束不同初始束宽度对计算格林函数结果的影响;b—改进高斯束不同出射角度间隔对计算格林函数的影响
Fig.4  常规高斯束与改进高斯束单条高斯束结果对比
a—常规束参数高斯束;b—改进束参数高斯束;c—改进束参数与常规高斯束的对比
Fig. 5  高低速相间分布的层状速度模型
Fig.6  单条高斯束经过层状速度模型时束宽度变化
a—常规高斯束;b—改进高斯束
Fig.7  0~50 Hz频率范围的高斯权重系数
Fig.8  解析解与高斯束计算的20 Hz单频核函数及误差
a—20 Hz核函数解析解;b—高斯束计算的核函数;c—解析解与高斯束解的整体差值;d—中间竖直切线差值
Fig.9  解析解和高斯束解带限核函数及误差对比
a—5~25 Hz带限核函数的解析解;b—5~25 Hz带限核函数的高斯束解;c—中间位置横向切线结果对比
Fig.10  常梯度模型下的带限核函数及纵向切线结果
a—常梯度速度模型带限核函数;b—中间位置纵向切线结果
Fig. 11  丁山某工区速度模型及高斯束方法计算得到层析带限核函数
a—丁山某工区深度域初始速度模型;b—从反射点出发到达炮检点的带限核函数
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