求导能否提高地震记录的分辨率

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（ｊｗ）＾ｎ的滤波器对其进行滤波。该滤波器的振幅特性与圆频率ｗ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，只能提高剖面的视频率，并不能真正提高剖面的

Can derivation improve the resolution of seismogram?

Solving for the n-order derivative of seismogram in terms of differential theorem is equivalent to filtering it with the use of filter whose frequency characteristicis (j)n and whose amplitude characteristic is directly proportional to nth power of(circular frequency)- Therefore,geophysicists try to use derivation method t0 compensate the high-frequency contents which have been lost during seismic wave propagation- However,theoretical analysis and forward modeling show that solving forthe first-order tiine derivative and the second-order time derivative of raw seismograms respectively only raises the apparent frequency of seismic section,but fails toimprove its resolution. It is also shown that after the derivation of seismograms,high-frequency contents are ameliorated in some degree while low-frequency contents are damaged surely. Thus we can say that the derivation fails to improve resolution but lowers the signl/noise ratio of whole seismic section when the high frequency content has low signal/noise ratio