摘要
在时间域中,谐波经过反射系数“系统”后不改变频率,符合线性时不变系统的条件,因此在时间域中可以用子波与反射系数序列褶积的方法计算时间域合成地震记录。由于在深度域中圆波数是介质速度的函数,深度域子波的波数随介质速度变化,因此地震子波在深度域中传播并不满足线性时不变系统的条件,不能直接用褶积的方法计算深度域合成地震记录。文中利用简单的理论模型,通过对深度域中的速度、深度参数进行适当的变换,使其在“新深度域”中符合线性时不变系统的条件,在保证层间旅行时不变的情况下,定义深度域地震子波的介质速度为标准速度,将其他各层的速度都以标准速度进行调整,并对层间厚度也做相应的调整。通过上述变换,可把时间域中的计算方法引用到深度域中,再通过反变换处理,将“新深度域”中的褶积结果反变换到原深度域中。文中还指出,如果不考虑深度域与时间域之间的重采样误差,常规时间域合成地震记录经时深转换到深度域后的结果应该与本文介绍的深度域合成地震记录结果一致。
In time domain, the harmonic wave does not change frequency when passing through the reflection coefficients “system”, coinciding with the condition of linear time-invariant system, so, the synthetic seismograph in time domain can be computed by convolution of wavelet with reflection coefficients sequence. Because the circular wavenumber is function of medium velocity in depth domain and the wavenumber of wavelet in depth domain changes with the velocity of medium, the propagation of seismic wavelet in depth domain does not meet the condition of linear time-invariant system and synthetic seismograph in depth domain can't be computed directly by convolution. Using simple theoretic model and by the aid of appropriate transform of velocity and depth parameters in depth domain, making them conform the linear time-invariant condition in “new depth domain”, the paper defines the medium velocity of seismic wavelet in depth domain as standard velocity in a condition of invariant interlayer travel times and adjusts the velocities in other separate layers according to the standard velocity, the thickness of layers is adjusted accordingly as well. The computational methods in time domain can be used in depth domain by the aid of above mentioned transform; the convolved results in “new depth domain” can be inversely transformed into original depth domain by the inverse transform processing. The paper also pointed out that the results transformed synthetic seismograph in time domain into depth domain by time-depth transform should be consistent with that introduced in the paper if the resampling errors between depth and time domains are neglected.
出处
《石油地球物理勘探》
EI
CSCD
北大核心
2006年第6期640-643,共4页
Oil Geophysical Prospecting
关键词
时间域
圆频率
深度域
圆波数
褶积
线性时不变系统
速度深度函数变换
time domain, circular frequency, depth domain, circular wavenumber, convolution, linear time-invariant system, transform of velocity and depth functions
