Abstract：In time domain,the harmonic wave does not change frequency when passing through the reflection coefficients “system”,coinciding with the condition of linear timeinvariant 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 timeinvariant 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 timeinvariant 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 timedepth transform should be consistent with that introduced in the paper if the resampling errors between depth and time domains are neglected.
林伯香, 胡中平, 薛诗桂. 利用变换深度域速度函数制作深度域合成地震记录[J]. 石油地球物理勘探, 2006, 41(6): 640-643.
Lin Bo-xiang, Hu Zhong-ping, Xue Shi-gui. Using velocity function in transformed depth domain to make synthetic seismograph in depth domain. OGP, 2006, 41(6): 640-643.
