均匀介质中的F

1、均匀介质中的F        【中文摘要】F-K反偏移(频率波数域反偏移)是一种在频率波数域内实现从偏移场到观测场变换的反射地震成像方法。其严格理论到目前为止只对均匀介质成立,这意味着,在一般条件下只能近似地给出F-K反偏移的计算公式。鉴于这个事实,本文首先系统地先容了均匀介质中的F-K反偏移的基本理论,然后着重对实在现算法进行了讨论。具体涉及到的题目有角频率间隔的选取、插值方法的采用、奇异点处理和边沿效应处理等。此外,本文还讨论了F-K反偏移在数值模拟中的应用及F-K反偏移与Kirchhoff反偏移之间的异同。&

2、#39;);【Abstract】 The seismic imaging is the finally aim of the seismic exploration and also the kernel of reflect seismology . Nowadays, the seismic migration imaging is the most important seismic imaging, the migration which contain time migration and depth migration is that time domain is transfor

3、med to migrated section . At the same time there is an inverse process to migration that we call demigration. Under a demigration ,the migrated image is transformed from the depth domain( time domain )back to the time domain. Similar to migration, demigration also assumes a basic role in the complet

4、e imaging theory. Demigration is the inverse process to seismic migration, provided the macro-velocity model, the measurement configuration, and the ray code are kept the same, In other words, when changing macro-velocity measurement configuration and ray code, the demigration will have a lot of imp

5、lementation, for example configuration transform remigration ray-code transformation forward modeling and enhancing signal-to-noise. At present there are three methods for migration that are Kirchhoff migration F-K migration and finite difference migration. Similar to migration, demigration also hav

6、e different approaches for its implementation. F-K demigration is processed in the frequency-wavenumber domain. Using the same ideas of F-K migration in constant, layer and complex velocity media model, F-K demigration can also be completed. The reason of emphasizing the constant velocity F-K demigr

7、ation is that its exact solution could become a reference standard for other approximate solution and it is the base of the F-K demigration in complex velocity media. Migration image spectrum mapping to demigration section spectrum is the key of the constant velocity F-K demigration.Constant velocit

8、y F-K demigration implementation: through the migrated section to be two-dimensional Fourier transform migrated section spectrum, from the dispersion of the relationship between migrated section mapped to the observation section ,then time observation section to do anti-two-dimensional Fourier trans

9、form the time observation. Due to discrete calculation, the mapping relates to interpolation and the original single mapping relation appears two interpolation strategy. One strategy is that equal interval points interpolate unequal interval points, another strategy that unequal interval points inte

10、rpolate equal interval points is inverse to front strategy. To achieve the two interpolation, the strategy is feasible, but the strategy one involved subtraction, two similar number will affect the accuracy. In order to reserve the high frequency of the migration section ,the angular frequency inter

11、val of demigration section must assume=' . If small interval the high frequency components must be lost ,but when the migrated section some high frequency spectrum is zero, reduce angular frequency interval appropriate will not result in the loss frequency components. The object of interpolation

12、 is complex, so this is a complex interpolation in real domain, hence we put forward three methods which respective are real and image respective interpolation, module and phase respective interpolation, Frequency domain direct interpolation. By analyzing impulse demigration model, the precision of

13、real and image respective interpolation is restricted by the shake factor, so when removing it ,the precision have a great improvement, but there also have limitations. First, this method is relevant with reflective of the location, in other words must first know the specific location of the reflect

14、or. Second, when the reflection of the level the impact of shake factor can be completely removed, but the layers are tilted reflection, the impact can not be completely removed. As a result of phase is a discontinuity function, precision of module and phase respective interpolation is lower. Freque

15、ncy domain direct interpolation is a undistorted interpolation in theory. However we usually need truncation for calculation efficiency, this will introduce error. On the singularity point the function value will become infinitude for which the integral can be unstable, the approximate substitution

16、can solute the problem, in this * we adopt Tayler expandedness and pada expandedness.Demigrating the impulse migration image ,the demigration section is accord with ray theory on the travel time. Same as the migration there is period effect in the demigration, on account of Fourier transform. Add ze

17、ros used in this article and add attenuation trace are good methods for eliminating the period effect ,but double the length of the original data, horizontal and vertical direction need to fill zero, which caused a threefold increase in the amount of data, increase the amount of computation, this is

18、 also the current frequency - calculation of the wave number domain Bottlenecks. There are lots of applications with demigration. Forward modeling is one of them. Demiration and forward modeling is the biggest difference between the different starting point, the demigration from the migrated section to get observation section ,and forward modeling from the geological structure to observation section. Forward modeling by demigration ,first through geological structure to co