﻿ 利用反投影方法计算陆地有限水体气枪震源激发过程
 地球物理学报  2018, Vol. 61 Issue (3): 1000-1012 PDF

1. 中国地震局地球物理研究所 中国地震局地震观测与地球物理成像重点实验室, 北京 100081;
2. 南京大学 地球科学与工程学院, 南京 210023

Calculating the propagation of airgun source in a limited water body using the back-projection method
HU JiuPeng1, WANG WeiTao1, WANG BaoShan1, CHEN Yong2, JIANG ShengMiao1
1. Institute of Geophysics, China Earthquake Administration(Seismic Observation and Geophysical Imaging Laboratory), Beijing 100081, China;
2. School of Earth Sciences and Engineering, Nanjing University, Nanjing 210023, China
Abstract: The large volume airgun source can be applied to probing geophysical structure and changes on regional scales. But so far it still lacks of a solid theoretical model to characterize the propagation features of the land air-gun signal due to the complexity of the water-solid boundary. The research on air-gun in a limited land water body can further understanding of the physical mechanism of the airgun and the principle of different earthquake phases distribution. As a method to image earthquake rupture, back-projection can provide qualified results with a few kinetic parameters. We present a modified back-projection method to simulate the energy distribution of the air-gun source located in a land limited water body. We decompose the excitation of airgun into five simplified physical processes, and establish numerical models for each process to calculate its theoretical wave field, which is used as input data of the new method. Numerical calculations show that this new method is able to capture the evolution of the wave field and characterize the distribution of the source energy. We also find that enough reasonably arranged hydrophones can help achieve better results. This method provides a new approach to quickly evaluate the effectiveness of land airgun and to further understanding of the airgun features.
Key words: Back-projection    Airgun source    Limited water body
0 引言

1 方法和原理 1.1 改进的反投影方法

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 (2)

1.2 实验方法及谱元法简介

2 数据和结果

2.1 模型1，半无限空间均匀水体中反投影方法的验证

 图 1 均匀半空间水体模型 长160 m，高100 m的半空间水体模型，三角形代表接收台站，五角星代表震源，浅灰色为水体. Fig. 1 Homogeneous half-space water body model Half-space water body model of 160 meters long and 100 meters high. Triangles represent the receivers, star indicates the airgun source and the grey part denotes the water body.

 图 2 均匀半空间模型接收台站模拟数据 (a)纵坐标为归一化振幅; (b)纵坐标为道数.由于模型简单，模拟得到的波形形态简单. Fig. 2 Simulation data of receiving station in homogeneous half-space model Horizontal axes represent time in seconds; (a) and (b) vertical axes are normalized amplitude and trace numbers, respectively. Due to the simpleness of the model, the waveforms obtained by simulation are not complex.

 图 3 反投影法得到的震源处的理论波形 (a)应用直接叠加方法计算; (b)应用4次方根叠加法计算.可以看出两种叠加方法在0.1 s之前对应较好，在0.25 s之后，4次方根叠加法极大的提高了微弱信号的振幅.在约0.08 s和0.09 s处波形变化剧烈，压力数据从负变为正. Fig. 3 The theoretical waveform of the source obtained by the back-projection method (a) and (b) are derived by direct stacking method and 4th root stacking method, respectively. The results of two methods match well before 0.1 second, while the 4th root stacking method enhances the amplitude of the weak signal after 0.25 second. Both results see dramatic changes between 0.08~0.09 second with the pressure value turn from negative to positive.

 图 4 反投影方法与数值模拟方法的波场对照 (a)震源激发后0.08 s的压力场形态; (b)震源激发后0.09 s的压力场形态; (c, d)数值模拟结果得到的原始压力场形态，图c对应0.08 s，图d对应0.09 s.图中压力数据均经过自归一化.五角星处为震源位置.图(a, b)中均可看到因水面影响而导致的压力场形态变化，并且其形态分别与图(c, d)差别不大. Fig. 4 The wave field calculated by back-projection method compared to the results of numerical simulation (a) Wave field at 0.08 second; (b) Wave field at 0.09 second; (c) and (d) original pressure field calculated by numerical simulation at 0.08 second and 0.09 second, respectively. All the data are self-normalized. Horizontal and vertical axes are both model scale in meters. The star denotes the airgun source. The pressure field varies due to the water surface in both (a) and (b), which are very similar to those in (c) and (d), respectively.
2.2 模型2，半无限空间均匀水体中双震源的反投影方法的验证

 图 5 半无限空间均匀水体中双震源模型 长160 m，高100 m的半空间水体模型，其中三角形代表接收台站，五角星代表震源，两震源时间间隔0.05 s，浅灰色为水体. Fig. 5 Bi-source model for homogeneous half-space water body Half-space water body model of 160 meters long and 100 meters high. Triangles represent the receivers, stars indicate the two airgun sources with 0.05 second gap and the grey part denotes the water body.
 图 6 模型1与模型2模拟波形的对比 实线为模型1中谱元法模拟波形，虚线为模型2中谱元法模拟波形.对比发现，加入第二个震源后，波形前半部分一致，后部分信号得到延长. Fig. 6 Waveform comparison between Model 1 and Model 2 Simulated waveform by spectral element method is represented as solid line in Model 1 and dash line in Model 2. The comparison indicates after adding the second source, the former half of the waveform is consistent while the latter half is stretched.

 图 7 单震源波场分布与双震源波场分布对比 图中压力数据均经过自归一化.五角星处为震源位置，时刻均为震源激发后0.11 s. (a)模型1单震源模型中反投影法计算得到的波场压力形态; (b)模型2双震源模型中反投影法计算得到的波场压力形态.可以看出图b中第二个震源的起震. Fig. 7 Comparison of single source and bi-source wave field distribution Pressure data is self-normalized. Horizontal and vertical axes are both model scale in meters. The star denotes the airgun source. Both figures captured at 0.11 seconds. (a) Waveform is calculated by back-projection method for single source model (Model 1); (b) Waveform calculated by back-projection method for bi-source model (Model 2). The initiation of second source can be seen in (b).
2.3 模型3，半无限空间均匀水体中气泡震荡情况的反投影方法的验证

 图 8 半无限空间均匀水体中气泡震荡模型 模型长160 m，高100 m的半空间水体模型，其中三角形代表接收台站，五角星代表震源，浅灰色为水体，白色为空气气泡.围绕空气气泡很近的一圈密集的点源模拟气泡的膨胀运动. Fig. 8 Bubble oscillation model in homogeneous half-space water body Half-space water body model of 160 meters long and 100 meters high. Triangles represent the receivers and stars indicate the airgun sources. The grey part denotes the water body and the white part denotes the bubble. The dense point sources surrounding the bubble are used to simulate bubble expansion.

 图 9 气泡震荡模型中反投影法计算得到的波场形态 (a)震源激发后0.08 s的压力场形态; (b)震源激发后0.09 s的压力场形态.图中压力数据均经过自归一化.X轴与Y轴分别为模型尺寸，单位为m，白色圆形代表气泡.图a和图b中均可看到因水面影响而导致的压力场形态变化. Fig. 9 The wave field calculated by back-projection method with bubble oscillation model (a) Wave field at 0.08 second; (b) Wave field at 0.09 second. All the data are self-normalized. Horizontal and vertical axes are both model scale in meters. The white parts denote the bubble. The pressure field varies due to the water surface in both (a) and (b).
2.4 模型4，不同观测仪器配置条件下的反投影方法的对比

 图 10 不同的水听器配置方案 图中为6个不同水听器配置方案对应的6个半无限空间水体模型.模型长160 m，高100 m的半空间水体模型，其中三角形代表接收台站，五角星代表震源，浅灰色为水体.(a，d) 6个水听器; (b，e) 12个水听器; (c，f) 24个水听器.其中图a, b, c中的模型水听器均匀分布，而图d, e, f中对应的模型水听器随机分布，但依然左右对称. Fig. 10 Different hydrophone configurations Each figure corresponds to one hydrophone configuration. Each model is 160 meters long and 100 meters high. Triangles represent the receivers and stars indicate the airgun sources. The grey part denotes the water body. (a) and (d) 6 hydrophones; (b) and (e)12 hydrophones; (c) and (f) 24 hydrophones. (a), (b) and (c) uniform distributed hydrophones; (d), (e) and (f) randomly but vertically symmetrical distributed hydrophones.

 图 11 不同水听器配置方案对应反投影方法计算结果 图中压力数据均经过自归一化.五角星处为震源位置.(A)为0.08 s时刻波场压力形态，(B)为0.09 s波场压力形态.每幅图中的编号与图 10对应.对比发现，对于均匀分布的水听器配置方案，数目为12时就可以达到较好的效果.而对于非均匀排列的水听器配置方案，则需要更多的数目. Fig. 11 Results of back-projection method for different hydrophone configurations All pressure data are self-normalized. Horizontal and vertical axes are both model scale in meters. Stars indicate the airgun sources. The left figure is captured at 0.08 second, while the right figure at 0.09 second. The figure sequence is the same as Fig. 10. Comparison shows that 12 hydrophones are enough for the uniformly distributed configuration. However, more hydrophones are needed for randomly distributed configuration.

2.5 模型5，陆地水体实验中气枪震源激发实验的反投影方法的验证

 图 12 陆地有限小水体模型 模型长160 m，高100 m的半空间水体模型，其中三角形代表接收台站，五角星代表震源，浅灰色为水体，深灰色为固体介质. Fig. 12 Land limited water body model Half-space water body model of 160 meters long and 100 meters high. Triangles represent the receivers, star indicates the airgun source, the light grey part denotes the water body and the dark grey denotes solid medium.

 图 13 陆地有限小水体模型接收台站模拟数据 横纵坐标为归一化振幅.相比模型1，可见由于固液界面的反射作用，波形变得复杂. Fig. 13 Simulation data of receiving station in land limited water body model Horizontal axis represents time in seconds; the vertical axis is normalized amplitude. Compared to Model 1, the waveform is more complicated due to the reflection at the solid-liquid boundary.
 图 14 陆地水体模型中反投影法计算得到的压力场分布 图中压力数据均经过自归一化.五角星处为震源位置，其中背景中的浅灰色为固体介质.图(a, b, c, d)分别为模型5中反投影法计算得到的震源激发后0.06 s，0.08 s，0.11 s和0.13 s后的波场压力形态，其特征反映了水体固液界面形状对波场的影响.图(b)和(d)中锯齿状的边界为网格划分时网格单元边界. Fig. 14 The distribution of pressure field calculated by back-projection method with land water body model All pressure data are self-normalized. Horizontal and vertical axes are both model scale in meters. Stars indicate the airgun sources and the light grey represents solid medium. (a)—(d) are the wave field calculated by back-projection method at 0.06, 0.08, 0.11 and 0.13 second respectively, which reflect the influence of the solid-liquid boundary to waveform.

3 分析和讨论

4 结论

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