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根据微分定理,对地震记录求n阶导数,相当于用一个滤波特性为(jω)n的滤波器对其进行滤波。该滤波器的振幅特性与圆频率ω的n次幂成正比。因此,人们试图采用导数法来补偿地震波在地层介质中传播的高频损失。然而,经过理论分析和模型正演表明,对原始地震记录分别求取一阶和二阶时间导数,只能提高剖面的视频率,并不能真正提高剖面的分辨率。同时还表明,对地震记录求导以后,虽然对高频成分有所提升,但与此同时又压制了低频成分。因此,当地震记录高频成分信噪比较低时,求导不但不能提高分辨率反而还会降低整个剖面的信噪比。
According to the differential theorem, finding the nth order derivative of the seismic record is equivalent to filtering it with a filter whose filter characteristic is (jω) n. The amplitude characteristic of the filter is proportional to the power n of the circular frequency ω. Therefore, people try to use the derivative method to compensate for the high frequency loss of seismic waves propagating in formation media. However, theoretical analysis and model forward show that the first and second order time derivative of the original seismogram can only increase the video frequency of the section, and can not really improve the resolution of the section. At the same time, it also shows that after the derivation of the seismogram, although the high-frequency component is improved, at the same time, the low-frequency component is suppressed. Therefore, when the signal-to-noise ratio of the high-frequency component of the seismic record is low, the derivation can not only improve the resolution but also reduce the signal-to-noise ratio of the entire profile.