Study on the radiation and reception of the wave field in a single-well imaging system with an eccentric source
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摘要:
通过最速下降积分法获得了充液井孔中偏心点声源激发的井外波场的远场渐近解；利用互易性获得井外存在反射体时井内偏心接收的波场渐近解，渐近解结果与有限差分的结果吻合；分析了声源频率、偏心距离以及方位角对波场辐射与接收的影响.计算发现：声源频率是影响井外波场的主导因素，声源频率较低时，偏心点声源激发的远场波场与偏心距离无关，可以将偏心点声源视为中心声源；声源频率较高时，偏心点声源激发的远场波场与中心声源之间存在不可忽略的差异，且频率越高、偏心距离越大，差异越大.计算还发现：采用偏心声源与偏心接收时，辐射波场与接收波场的幅度都具有方位角依赖性.最后我们给出利用反射波幅度变化来消除反射体方位角180°不确定性的算例.
Abstract:The far-field asymptotic solutions to the wave field excited by an eccentric point source in a fluid-filled borehole are derived by the steepest descent integration method. When there is a reflector outside the borehole, the asymptotic solution to the reflected wave field received by eccentric receivers in the borehole is obtained using reciprocity. The asymptotic results are in good agreement with those from the finite difference method. The effects of frequency and eccentric distance on the wave field are analyzed. Simulations show that frequency is the dominant factor affecting the wave field outside the borehole. When the frequency is low, the far-field wave field excited by the eccentric source is independent of eccentric distance, and the eccentric source can be regarded as a central source. When the frequency is high, the difference between the far-field wave field excited by the eccentric point source and the central source cannot be neglected. The higher the frequency and the greater the eccentric distance, the greater the difference is. Simulations also show that the amplitude of the radiated wave field and the received wave field are both azimuth-dependent when using the eccentric source and eccentric receivers. Finally, an example is given to show the elimination of the 180° uncertainty of azimuth angle of the reflector by using the variation of reflected wave amplitude.
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Key words:
- Eccentric source /
- Asymptotic solution /
- Single-well imaging /
- Azimuth
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图 2
低频声源辐射的井外远处P波的前4阶分量
Figure 2.
The first four components of far-filed P wave waveforms outside the borehole with low-frequency source
图 3
中频声源辐射的井外远场P波波场的前4阶分量
Figure 3.
First four order components of far-filed P wave waveforms outside the borehole with moderate-frequency source
图 4
中频声源辐射的井外远场S波波场的前4阶分量
Figure 4.
First four order components of far-filed S wave waveforms outside the borehole with moderate-frequency source
图 5
低频时偏心源与居中源激发的井外波场比较
Figure 5.
Comparison between wave fields outside borehole generated by eccentric source and central source with low frequency
图 6
中频时偏心源与居中源激发的井外波场比较
Figure 6.
Comparison between wave fields outside borehole generated by eccentric source and central source with moderate frequency
图 7
高频时偏心源与居中源激发的井外波场比较
Figure 7.
Comparison between wave fields outside borehole generated by eccentric source and central source with high frequency
图 8
快速地层中不同方位角下的接收器接收到的波场和归一化波场辐射图
Figure 8.
Waveforms received by receivers with different azimuths in the fast formation and normalized radiation patterns
图 9
快速地层中不同方位角下的接收器接收到的波场和归一化波场辐射图
Figure 9.
Waveforms received by receivers with different azimuths in the fast formation and normalized radiation patterns
图 10
慢速地层中不同方位角下的接收器接收到的波场和归一化波场辐射波
Figure 10.
Waveforms received by receivers with different azimuths in the slow formation and normalized radiation patterns
图 11
含偏心声源和偏心接收器的声波远探测模型图
Figure 11.
Single-well imaging model with eccentric source and eccentric receivers
图 12
声源与接收器都位于井轴时的远探测示意图
Figure 12.
Sketch of remote detection with source and receivers located at the borehole axis
图 13
井轴处接收到的声压全波波形
Figure 13.
Full waveforms of the acoustic pressure at the borehole axis
图 14
反射波渐近解与数值解的对比
Figure 14.
Comparison between asymptotic solutions and numerical solutions to reflected waves
图 15
不同方位角反射体时井内接收器接收到反射波波形
Figure 15.
Reflected waveforms from the reflectors with different azimuths
图 17
方位角相差180°时井内接收器接收到反射全波
Figure 17.
Reflected waveforms with azimuth difference between the reflectors as 180°
图 18
声源与接收器时发生偏心时接收到的归一化反射波指向图
Figure 18.
Normalized reception patterns of reflected waves when source and receiver are eccentric
表 1
井外流体和地层参数
Table 1.
Parameters of borehole fluid and formations
密度/(kg·m-3) 纵波速度/(m·s-1) 横波速度/(m·s-1) 流体 1000 1500 - 快速地层1 2000 3000 1800 快速地层2 2600 4000 2300 慢速地层 2000 2200 1200 
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