基于复杂地表波场延拓的静校正方法研究
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摘要
本论文研究的重点是F-K域静校正,和偏移等常规地震处理不一样,F-K域静校正并不是在同一平面上进行波场延拓改造的,所以在时频转换的时候往往容易忽略频率域和时间域的变量对应关系。而直接对地震记录进行时频转换是不科学的,因为在起伏地表条件下波数并不是与空间横向偏移距坐标对应,而是与包含着两个变量(横向变量和纵向变量)的地表对应。这样进行波场延拓静校正处理并不是沿着垂直方向延拓的,其方向是很难预知的。根据上述问题运用F-K域法进行静校正的关键步骤是如何正确处理好时频对应关系。
针对上述的问题,本文提出了变换坐标系波场延拓静校正,基本思想是根据地表函数建立变换坐标系,将检波器的空间位置投影到水平面上,并且新坐标系下转化波动方程以及推导频率域延拓公式,然后将地震记录延拓一定的深度,恢复这个深度区间内的全部真实波场,最后再转换到原空间直角坐标系中,选取合适水平基准面,取出该基准面记录,得到的记录即为完成静校正后的结果。通过对模型以及实际资料的分析,证明了该方法的有效性和可行性。
Nowadays it is widely recognized that complex surface problem is a difficulty in complex surface seismic exploration. In recent years, seismic exploration focuses more and more in the west. However, static correction in western region can be hardly achieved because of the complex surface and complexity of the structure conditions. Searching for petroleum is very imperative for which is indispensable as a national strategic material. The influence of complex surface to seismic records contains two most important factors: elevation and low-speed region impact. Usually the traditional static correction can be achieved very well under the surface consistency assumption in the simple structure underground work area if there are not dramatic ups and downs in the surface. The residual static correction can be adopted to select the higher signal to noise ratio reference trace. The inadequate volume of the first static correction caused by spherical proliferation and non-uniform of low-speed area can be eliminated very well by the relevant deconvolution algorithm. However, the spherical surface reflector up-going wave can no longer meet the premise of surface consistency assumption where there are dramatic ups and downs in the surface. So we cannot select higher signal to noise ratio reference trace in residual static correction, sometimes cannot even select one trace. As a result, signals of seismic records cannot be stacked in the same phase through residual static correction, while which affects the signal to noise ratio at the beginning of processing and also the follow-up work.
This thesis belongs to the research of seismic data processing and main point is FK statics correction. It meanly focus on how to improve the effect of static correction, how to consider those factors which affect the seismic data, such as ragged surface、low velocity zone、coordinates of receiver point and shot point and so on. The purpose of the steps are in order to make sure that the seismic data can be stacked with the same phase and eliminate the lack of statics correction which can help optimizing the following steps. Nowadays FK method have a lot of merits, it can be used in many seismic data processing, such as migration and filtering. What's more, many new methods such as wavelet transform, curvelet transform were developed based on FK method, so we can easily get it that FK method have many merits, the algorithm of it is very simple and speed is very fast, thus, it will have a very good effect if we can use it to reconstruct wave field for statics correction. As mentioned before, residual static correction can compensate the lack of field statics correction in some aclinic areas whose constructions are simple, but as the seismic exploration becoming higher accuracy and higher resolution, there are lots of areas whose surfaces are complex, we can not find a good reference trace for residual static correction, what's even more, traditional statics correction is not effective in such areas. FK migration proves that FK method is a good method with high accuracy and high resolution. Moshe Reshef, Stolt R H and some other scholars have used this method into FK migration and achieved a very good effect, so if we can use it into statics correction, I think it can achieve a good effect either. John R. Berryhill is the first man who have used this method into statics correction, however, it is different from FK migration, static correction is a processing which does not reconstruct wave field in the same level, so when translating a seismic data into frequency-wavenumber domain, people always neglect the relationship between wavenumber and space. If we translate a seismic data into frequency-wavenumber domain directly by using FFT transform, it is obvious wrong, to a certain extent, it equals traditional time-shift statics correction. In a other words, If we translate a seismic data into frequency-wavenumber domain directly by using FFT transform, we cannot find the right wavenumber to correspond to the space, and the wavenumber gotten by FFT is correspond to the transverse direction, it is obvious incorrect. So the key point of using FK statics correction is finding the relationship between wavenumber and space. And the most important problem is considering the factor of complex surface in frequency-wavenumber domain for seismic traces in complex area are not in the same level, so if we translate those into frequency-wavenumber domain directly by FFT, the information contained in frequency-wavenumber domain is not about a same level, the Helmholtz equation and wave field extrapolation formula cannot be used into this kind of data.
To solve the previous problems, this article focuses on time-frequency corresponding and the influence to seismic records caused by undulating surface in frequency domain, proposes the static correction method of wave field extension in frequency domain under coordinate system transformation. The main idea is to lay the detector projections on the same level through coordinate transformation according to elevation function which can be obtained by Lagrange interpolation, so that the seismic records of undulating surface in new coordinate system can be considered to be received at the same level. On this premise, the Fourier transform to seismic profile can be ensure that is done to the seismic records at level surface, so the number of waves calculated by discrete Fourier transform would correspond to the space coordinates. But the following problem is that all above are carried out in the new coordinate system. So we need to derive wave equation in the new coordinate system through coordinate transformation. After that, we also need to derive new extension equation. Then use the speed of the surface filling to extend all of the seismic records to a certain depth range whose interval can be calculated by the biggest elevation difference. We can fully recover the seismic wave field in a certain depth interval by extension, and obtain the seismic records on datum finally. So we take into account the factors of surface fluctuations while extension is carried out, thus every trace is extended upward to the level datum according to its true vertical velocity, which means that this method is superior to the traditional static correction which uses assumption velocity for the elevation correction. Secondly, we can ensure the corresponding between wave number and space distance through the Fourier transformation to seismic data, so as to follow-up processing. Secondly, through this method of seismic data on the Fourier transform can guarantee space wave number and the corresponding distance so as to follow-up treatment. According to the current basic situation, combine with the national 863 Project "metal mining multi-wave seismic processing and interpretation of new technologies, new methods of Lujiang - Magang Zongyang ore actual seismic data", this article has completed the following parts:
I have studied and analyzed the static correction processing of seismic data and related contents and questions. 1: Summarize several new static correction methods. 2: The main effect factors of static correction. 3: The basic principle of wave field extension. 4: The principle and difficulty of the extension static correction of wave equation.
I have derived the wave equation and equation formula in new coordinate system.
I have dealt with the sound forward records under undulating surface model by my own procedures, so that extension static correction algorithms of wave equation in frequency domain can be achieved.
Then procedures would be applied on actual seismic data in LuZong and completed data would be stacked. Find the feasibility and advantages of this method by modeling and actual data processing
针对上述的问题,本文提出了变换坐标系波场延拓静校正,基本思想是根据地表函数建立变换坐标系,将检波器的空间位置投影到水平面上,并且新坐标系下转化波动方程以及推导频率域延拓公式,然后将地震记录延拓一定的深度,恢复这个深度区间内的全部真实波场,最后再转换到原空间直角坐标系中,选取合适水平基准面,取出该基准面记录,得到的记录即为完成静校正后的结果。通过对模型以及实际资料的分析,证明了该方法的有效性和可行性。
Nowadays it is widely recognized that complex surface problem is a difficulty in complex surface seismic exploration. In recent years, seismic exploration focuses more and more in the west. However, static correction in western region can be hardly achieved because of the complex surface and complexity of the structure conditions. Searching for petroleum is very imperative for which is indispensable as a national strategic material. The influence of complex surface to seismic records contains two most important factors: elevation and low-speed region impact. Usually the traditional static correction can be achieved very well under the surface consistency assumption in the simple structure underground work area if there are not dramatic ups and downs in the surface. The residual static correction can be adopted to select the higher signal to noise ratio reference trace. The inadequate volume of the first static correction caused by spherical proliferation and non-uniform of low-speed area can be eliminated very well by the relevant deconvolution algorithm. However, the spherical surface reflector up-going wave can no longer meet the premise of surface consistency assumption where there are dramatic ups and downs in the surface. So we cannot select higher signal to noise ratio reference trace in residual static correction, sometimes cannot even select one trace. As a result, signals of seismic records cannot be stacked in the same phase through residual static correction, while which affects the signal to noise ratio at the beginning of processing and also the follow-up work.
This thesis belongs to the research of seismic data processing and main point is FK statics correction. It meanly focus on how to improve the effect of static correction, how to consider those factors which affect the seismic data, such as ragged surface、low velocity zone、coordinates of receiver point and shot point and so on. The purpose of the steps are in order to make sure that the seismic data can be stacked with the same phase and eliminate the lack of statics correction which can help optimizing the following steps. Nowadays FK method have a lot of merits, it can be used in many seismic data processing, such as migration and filtering. What's more, many new methods such as wavelet transform, curvelet transform were developed based on FK method, so we can easily get it that FK method have many merits, the algorithm of it is very simple and speed is very fast, thus, it will have a very good effect if we can use it to reconstruct wave field for statics correction. As mentioned before, residual static correction can compensate the lack of field statics correction in some aclinic areas whose constructions are simple, but as the seismic exploration becoming higher accuracy and higher resolution, there are lots of areas whose surfaces are complex, we can not find a good reference trace for residual static correction, what's even more, traditional statics correction is not effective in such areas. FK migration proves that FK method is a good method with high accuracy and high resolution. Moshe Reshef, Stolt R H and some other scholars have used this method into FK migration and achieved a very good effect, so if we can use it into statics correction, I think it can achieve a good effect either. John R. Berryhill is the first man who have used this method into statics correction, however, it is different from FK migration, static correction is a processing which does not reconstruct wave field in the same level, so when translating a seismic data into frequency-wavenumber domain, people always neglect the relationship between wavenumber and space. If we translate a seismic data into frequency-wavenumber domain directly by using FFT transform, it is obvious wrong, to a certain extent, it equals traditional time-shift statics correction. In a other words, If we translate a seismic data into frequency-wavenumber domain directly by using FFT transform, we cannot find the right wavenumber to correspond to the space, and the wavenumber gotten by FFT is correspond to the transverse direction, it is obvious incorrect. So the key point of using FK statics correction is finding the relationship between wavenumber and space. And the most important problem is considering the factor of complex surface in frequency-wavenumber domain for seismic traces in complex area are not in the same level, so if we translate those into frequency-wavenumber domain directly by FFT, the information contained in frequency-wavenumber domain is not about a same level, the Helmholtz equation and wave field extrapolation formula cannot be used into this kind of data.
To solve the previous problems, this article focuses on time-frequency corresponding and the influence to seismic records caused by undulating surface in frequency domain, proposes the static correction method of wave field extension in frequency domain under coordinate system transformation. The main idea is to lay the detector projections on the same level through coordinate transformation according to elevation function which can be obtained by Lagrange interpolation, so that the seismic records of undulating surface in new coordinate system can be considered to be received at the same level. On this premise, the Fourier transform to seismic profile can be ensure that is done to the seismic records at level surface, so the number of waves calculated by discrete Fourier transform would correspond to the space coordinates. But the following problem is that all above are carried out in the new coordinate system. So we need to derive wave equation in the new coordinate system through coordinate transformation. After that, we also need to derive new extension equation. Then use the speed of the surface filling to extend all of the seismic records to a certain depth range whose interval can be calculated by the biggest elevation difference. We can fully recover the seismic wave field in a certain depth interval by extension, and obtain the seismic records on datum finally. So we take into account the factors of surface fluctuations while extension is carried out, thus every trace is extended upward to the level datum according to its true vertical velocity, which means that this method is superior to the traditional static correction which uses assumption velocity for the elevation correction. Secondly, we can ensure the corresponding between wave number and space distance through the Fourier transformation to seismic data, so as to follow-up processing. Secondly, through this method of seismic data on the Fourier transform can guarantee space wave number and the corresponding distance so as to follow-up treatment. According to the current basic situation, combine with the national 863 Project "metal mining multi-wave seismic processing and interpretation of new technologies, new methods of Lujiang - Magang Zongyang ore actual seismic data", this article has completed the following parts:
I have studied and analyzed the static correction processing of seismic data and related contents and questions. 1: Summarize several new static correction methods. 2: The main effect factors of static correction. 3: The basic principle of wave field extension. 4: The principle and difficulty of the extension static correction of wave equation.
I have derived the wave equation and equation formula in new coordinate system.
I have dealt with the sound forward records under undulating surface model by my own procedures, so that extension static correction algorithms of wave equation in frequency domain can be achieved.
Then procedures would be applied on actual seismic data in LuZong and completed data would be stacked. Find the feasibility and advantages of this method by modeling and actual data processing
引文
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[2] He J, Liu Y, Geng J, The study and analysis of floating datum selection for rugged terrain[J], Applied geophysics, 2007, 4(2): 101-110;
[3] Li P, Qian R, Feng Z, Yang X, An intermediate reference datum static correctiontechnique and its applications[J].Applied geophysics, 2005, 2(2): 80-84.
[4]郭树祥，分频剩余静校正方法及应用效果分析[J]，石油地球物理勘探，2001，36（6）：735-739.
[5]耿建华，黄海贵，马在田，Kirchhoff积分波场延拓基准面静校正方法研究[J]，同济大学学报，1996，24（6）：665-669.
[6] J W Wiggins. Kirchhoff integral extrapolation and migration of nonplanardata[J].Geophysics, 1984, 49(8）：1239-1248.
[7]崔兴福，徐凌，陈立康.复杂近地表波动方程波场延拓静校正[J]石油勘探与开发，2006，33（1）：80-84.
[8]李卫忠，复杂地表地区近地表模型与静校正[J]，油气地质与采收率，2007，14（3）：73-76.
[9]方伍宝，李满树，孙爱萍，周腾，基于Born近似的波动方程静校正技术[J]，石油物探，2004，43（1）：26-29.
[10] R. Garotta. New approaches to long wavelength residual static corrections [C].SEG Expanded Abstracts, 1984: 678-689.
[11] William A. Schneider, Shih-Yen Kuo. Refraction modeling for static corrections[C]. SEG Expanded Abstracts, 1985: 295-299.
[12] Xu Chang, Yike Liu, Hui Wang, Fuzhong Li, Jing Chen 3-D tomographic staticcorrection [J].Geophysics, 2002, 67(4): 1275-1758.
[13] Robbert van Vossen, Jeannot Trampert, Full-waveform static corrections usingblind channel identification[J].Geophysics,2007,72(4): U55-U66.
[14] John R. Berryhill. Wave equation datuming[J].Geophysics.1979,44(8): 1329-1344.
[15]John R. Berryhill. Wave equation datuming before stack[J].Geophysics, 1984,49(11): 2064-2067.
[16]R H Stolt. Migration by Fourier Transform[J].Geophysics, 1978, 43(1): 23-48.
[17]Moshe Reshef. Depth migration from irregular surfaces with depth extrapolationmethods [J].Geophysics, 1991, 56(1): 119-112.
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