# 精密可控震源非线性扫描信号优化设计

2. 中国北京 100036 中国地震局地震预测研究所  本文收到日期：2016-07-27 基金项目：中国地震局地震预测研究所基本科研业务费专项（项目编号：2014IES0202，2015IES0307，2015IES010303）  作者简介：崔仁胜 (1985-), 男, 助理研究员, 主要从事地震观测技术研究工作。E-mail:crs3s@126.com                          通信作者：周银兴, 工程师, 主要从事地震观测技术研究工作。E-mail:geozyx@sohu.com            摘要：基于精密可控震源发射信号特性，根据能量均衡原则和信噪比最大原则，设计不同频谱的非线性扫描信号。通过灵活设计角频率-时间关系来分配不同频率的能量，有效改善发射信号的频谱特征和相关子波形态。与线性扫描信号相比，损失部分发射能量，换取分辨能力的提高，对可控震源探测具有一定实际意义。关键词精密可控震源    扫描信号    能量均衡    信噪比最大    分辨能力    Optimal Design of nonlinear sweep signal of CASS Cui Rensheng1,2, Zhou Yinxing1,2, Chen Yang1,2, Lin Zhan1,2, Xue Bing1,2, Wang Hongti1,2    1. Key Laboratory of Earthquake Prediction, China Earthquake Administration, Beijing 100036, China;
2. Institute of Earthquake Science, China Earthquake Administration, Beijing 10036, ChinaAbstract: Taking the feature of the transmitting signal of the Controlled Accurately Seismic Source (CASS) into account, the different sweep signals with different spectrum could be designed based on the energy balance principle or maximum signal to noise ratio principle. The energy distribution of different frequency is determined by the frequency-time relationship, and the frequency-time relationship is designed with good flexibility base on two principles. The spectrum and correlation wavelet of the designed signal would be improved. Compared with linear sweep signal, the designed signal loses some energy, but improves the resolution. It is meaningful for vibroseis surveying.CASS    sweep signal    energy balance principle    maximum signal to noise ratio principle    resolution capability     0 引言

1 发射信号设计原则1.1 发射信号

 $F\left( t \right) = 2Mr\omega {\left( t \right)^2}\cos \left( {\varphi \left( t \right)} \right)$ (1)

 图 1 精密可控震源旋转示意Fig.1 Diagram of the rotation of CASS

 $s\left( t \right) = B\omega \left( t \right)\sin \left( {\int_0^t {\omega \left( t \right){\rm{d}}t} } \right)$ (2)

 $E = \int\limits_0^T {{s^2}\left( t \right){\rm{d}}t}$ (3)

1.2 能量均衡原则

 ${A^2}\Delta T \approx \Delta E$ (4)

ΔE为能量，发射信号各频率能量应近似等于ΔE，即ΔE为固定值，不随频率变化。结合式 (2)，因此发射信号各角频率持续时间与振幅的平方成反比，只考虑速度波形，发射信号振幅与角速度成正比，因此各频率持续时间与角频率的平方成反比。通过在较低角频率处分配较长的持续时间，在较高频率处分配较少的发射时间，实现信号振幅谱平坦，保证各频率能量均衡提高。

1.3 信噪比最大原则

 $P = \frac{{{{\left[ {\int {S\left( f \right)\cos \theta \left( f \right){\rm{d}}f} } \right]}^2}}}{{\left[ {\int {{S^2}\left( f \right) + {N^2}\left( f \right)} } \right]{\rm{d}}f}}$ (5)

 $P = \frac{{{P_0}}}{{1 + \frac{{\int {{N^2}\left( f \right){\rm{d}}f} }}{{\int {{S^2}\left( f \right){\rm{d}}f} }}}}$ (6)

 ${\rm{SN}}{{\rm{R}}^2} = \frac{{\int {{S^2}\left( f \right){\rm{d}}f} }}{{\int {{N^2}\left( f \right){\rm{d}}f} }}$ (7)

 $P = \frac{{{P_0}}}{{1 + \frac{1}{{{\rm{SN}}{{\rm{R}}^2}}}}}$ (8)

 图 2 扫描信号的相关子波Fig.2 Correlative wavelet of the sweep signal

2 可控震源发射信号设计

 图 3 发射信号设计流程Fig.3 Diagram of the signal designing

2.1 能量均衡原则下设计发射信号

 图 4 能量均衡拟合扫描信号角频率—时间曲线和理论发射信号Fig.4 The angular frequency-time relationship and the transmitting signal of the designed signal based on energy balance principle

 图 5 能量均衡拟合扫描信号的频谱和相关子波Fig.5 The spectrum and the correlative wavelet of the designed signal based on energy balance principle

2.2 信噪比最大原则下设计扫描信号

 图 6 信噪比最大拟合扫描信号角频率—时间曲线和理论发射信号Fig.6 The angular frequency-time relationship and the transmitting signal of the designed signal based on maximum signal to noise ratio principle

 图 7 信噪比最大拟合扫描信号的频谱和相关子波Fig.7 The spectrum and the correlative wavelet of the designed signal based on maximum signal to noise ratio principle

3 不同发射信号对比

 图 8 线性扫描信号角频率—时间曲线和理论发射信号Fig.8 The angular frequency-time relationship and the transmitting signal of the linear sweep signal

 图 9 线性扫描信号的频谱和相关子波Fig.9 The spectrum and the correlative wavelet of the linear sweep signal

 表 1 3种扫描信号对比Tab. 1 The comparison of 3 kinds of signals          信号相对发射能量相关子波主旁瓣比值线性扫描信号3.079 3×1052.159 8能量均衡拟合扫描信号2.368 9×1054.549 6信噪比最大拟合扫描信号2.304 4×1055.022 6 表 1  3种扫描信号对比  Tab.1 The comparison of 3 kinds of signals

 图 10 3种扫描信号角频率—时间关系对比Fig.10 The comparison of angular frequency-time relationship about 3 kinds of signals

4 结束语

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