基于高阶统计量理论的地震层位自动拾取与油气检测技术研究
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摘要
随着油气勘探开发程度的深入,油气勘探难度也在不断加大。由于勘探条件的复杂,获得的地震资料的信噪比和分辨率往往都很低,从而严重影响了其处理与解释的效果。因此在弱信号条件下,提出检测信号的新方法,解决勘探目标显得尤为重要。高阶统计量理论作为一种描述随机信号特征的数学工具,目前在地震勘探领域已经有了初步的应用；本文在此理论的基础上论述的两类方法以抑制高斯噪声对地震层位拾取的影响和应用地震分频技术进行油气检测为目的。
作为油气检测的基础,地震层位自动拾取的工作显得越来越重要。为了提高层位拾取的工作效率,人们提出了许多地震层位自动拾取方法,如人工神经网络方法、模式识别方法、互相关方法等。上述方法中互相关方法稳定性最好,应用也最广泛。但是当地震资料中的噪声具有强相关性时,互相关方法会拾取噪声间的时间延迟值,致使层位拾取结果出现误差。本文充分利用地震层位横向波形相似性原理以及四阶累积量一维切片对高斯噪声免疫的特点,提出了基于四阶累积量一维切片的地震层位自动拾取方法,具体有如下创新点：
1、1993年Tugnait给出了基于四阶累积量一维切片的信号时间延迟估计公式,公式中采用的是可变长度的分析时窗。在地震勘探数据处理中,采用可变长度分析时窗计算时,存在受坏道影响大、计算结果失稳、时移量拾取不足等问题；因此为了避免上述问题,本论文采用稳健性更好的固定长度的分析时窗,并且根据实际需要对延迟时参数的位置作了相应的改变。
2、当地下介质是分层比较均匀的情况下,地震信号是一种近似于广义高斯分布的、偏度为零的具有对称分布的随机信号。对于对称分布的随机信号,其三阶累积量为零,因此三阶累积量已经不适合进行这种信号的处理。而本文采用的四阶累积量一维切片时延迟估计函数不存在三阶累积量的局限性。
3、在地震层位拾取过程中需要合理设定相关参数,这些参数关系到层位拾取的准确性,其中参考道的选择尤为重要。在分析研究两种传统的参考道选择方式的基础上,设计了一种新的参考道选择方式；这种方式在地震数据局部波形相似性较强的情况下,既克服了固定参考道方式由于横向波形变化大产生计算误差的问题；也改正了非固定参考道方式容易产生大量累计误差的缺点。
源于B P Amoco(英国石油阿莫科)公司的分频技术是通过数学变换将地震数据变换到频率域或时频域,然后沿其频率轴作频率切片,最后利用单频切片进行储层预测的一种解释技术。目前从各类文献资料来看,已有的分频技术算法主要有：傅氏变换方法、线性时频分析方法、时频分布方法等。本论文首次提出了基于Wigner双谱对角切片的分频技术,并将其应用在油气检测中,取得如下成果：
1、为了解决Wigner双谱对角切片存在的交叉干扰项问题,采用模糊域核函数滤波抑制交叉项,并推导了Wigner双谱对角切片的模糊函数计算公式。
2、在充分研究锥形核函数与指数核函数的基础上,利用锥形核函数表达式中的指数函数与指数核函数结合,给出了一个新的核函数。数值模拟结果表明新核函数兼具上述两种核函数的优点,对时延轴上及坐标轴外的交叉项都有很强的抑制作用。
3、通过坐标移动的方法,使Wigner双谱对角切片的模糊函数信号项的中心点与新核函数中心点重合。从而解决了直接进行模糊域滤波致使新核函数对交叉项抑制能力下降的问题。
4、为了解决Wigner双谱对角切片三维数据体数据量太大,致使matlab程序报错：“内存溢出”的问题。对分频技术的流程进行了改进,避免了分频过程中生成Wigner双谱对角切片三维数据体。
结合国内外的研究基础以及本人对这一领域的认识,本文论述的两类方法还需要在以下三个方面进行深入研究：
1、本文所给出的四阶累积量一维切片是基于非参数化估计方法得到的。该方法具有简单易实现的优点,但是在有限数据长度的情况下,存在估计方差较大的缺点。估计方差直接影响到计算结果的准确性,因此可以采用估计方差较小的参数化方法给出相应的地震信号时延估计算子。
2、由Wigner双谱对角切片模糊函数图可以看出,有效信号与交叉项的间距比较近,两信号分量的延迟时越小,间距越近,这不利于薄层的分辨。因此可以对Wigner双谱对角切片模糊函数的计算公式进行改造,加大信号项与交叉项的间距,提高对薄层的分辨能力。
3、模糊域核函数滤波法在有效抑制交叉项的同时降低了时频分辨率。因此可以利用重排理论或自适应最优核设计等时频分布理论抑制交叉项,在兼顾交叉项抑制能力的同时进一步提高时频聚集性。
As the oil and gas exploration level deepens, the oil and gas exploration difficulties are increasing. Owing to the complicated conditions of exploration, the SNR and resolution of data are very low. thereby seriously impact on effect of processing and interpretation. On the condition that weak signal, there is particularly important to propose a new method of signal detection for the new exploration object. As a mathematical tool describe random signal HOS theory has been initial applied in the exploration area; based on this theory, two kinds of methods were discussed by this article with the view of inhibit coherent gauss noise to interfere with the seismic horizon extracting and mend frequency-divided technique and improve the time-frequency resolution.
As the base of oil and gas detection, seismic horizon extracting appears more and more important. To improve the efficiency, people propose many ways, such as artificial neural network, pattern recognition and cross-correlation, etc. The cross-correlation way has the best stability and applies the most widely. But when the noise of the data has strong relevance, cross-correlation way pick up the time delay of noise, bring about the error of seismic horizon extracting. This paper is the full use of the transverse wave comparability and one-dimensional slice of cross-fourth-order cumulants is immune to Gaussian noise, and propose a method of automatic extracting seismic horizon based on one-dimensional slice of fourth-order cumulants, there are the following specific innovation points:
1, in 1993 tugnait gave the time delay formula based on one-dimensional slice of fourth-order cumulants, the formula uses of variable length analyzing window. When data processing uses of this variable length analyzing window, there is a problem of producing great influence by bad trace, the instability calculation results, and inadequate time-delay. To avoid above problems, this paper uses the more robust and fixed length analysis window, and according to the actual need to change the location of delay the parameter.
2, when the underground media is even, the seismic signal is a kind random signal of symmetry distribution of bordering on generalized Gaussian distribution, skewness is zero. The three order cumulant of symmetrical distribution random signal snooze is zero, so it is not fit for processing such signals. But the time delay formula based on one-dimensional slice of fourth-order cumulants doesn't has this limitation.
3. in process of extracting seismic horizon needs to reasonably setup parameters, these parameters concern the accuracy of horizon extracting, and the choice of referenced trace is especially important. Based on the study of traditional choice pattern of referenced trace, a new choice pattern of referenced trace has been devised; this way overcome the problem that the fixed referenced trace pattern leads calculation error because of transverse wave change:and also correct the shortcoming of floating referenced trace leads cumulative error.
Frequency-divided technique deriving from B P Amoco is a resolution technique to transforms seismic data to frequency domain or time-frequency domain through mathematical transform, through it. cut frequency axis into slices, make use of slices to predicate reservoirs finally. At present sorts of document considered, existing frequency-divided technique include:The information from various sources, the existing businesses of technology are mainly:Fourier transformation, linear frequency analysis, the frequency distribution.etc. This paper in order to mend frequency-divided technique and improve the time-frequency resolution, make use of the high time-frequency resolution specialty of Wigner bispectrum diagonal slice, first propose the frequency-divided technique based on the Wigner bispectrum diagonal slice and apply it on the oil and gas detection, achieved following results:
1, in order to solve the problem of cross-term interference in Wigner bispectrum diagonal slice, through fuzzy fields'kernel wave-filtering method for restraining cross-term interference and derivate formula of Wigner bispectrum diagonal slice fuzzy functions.
2, based on fully studying cone-shaped kernel and exponential kernel, through combine exponential function in cone-shaped kernel with exponential kernel and give a new kernel. Numerical simulations indicated that the new kernel function has the advantages of above two kernels, and has a strong inhibition to cross-term interference in delay axis and beyond axis.
3, by way of moving coordinate to superpose the center point between fuzzy functions signal terms and new kernel. Thereby solve a problem that the new kernel couldn't be capable of restraining cross-term interference because of filtering in fuzzy fields directly.
4, in order to solve the problem of program error messages:"memory overflow' because that datasize of 3D data volume is too massive. So the frequency-divided technique procedure is improved, avoiding generating Wigner bispectrum diagonal slice3D data volume.
In accordance with research base from home and abroad as well as this field knowledge of myself, two kinds of methods were discussed by this article need to be intensive studied from following three areas:
1, one-dimensional slice of fourth-order cumulants of this paper is based on non-parametric estimation method. This method is simple to implement, but its estimation variance is excessive, in the case of finite length of data. Estimation variance directly impact on the accuracy of the results, therefore it can make us of little variance parametric estimation method to give seismic signal delay estimation operator.
2, it can be seen from Wigner bispectrum diagonal slice fuzzy functions that space between effective signal and cross-term is closer, the delay is the less. This goes against resolving the thin bed. The formula of Wigner bispectrum diagonal slice fuzzy functions, and increases the space between effective signal and cross-term, improving ability of resolving the thin bed.
3, while effectively restraining cross-term, fuzzy field's wave-filtering method reduces the time-frequency resolution. So may make us of rearrangement theory or adaptive optimal-kernel and so on to restrain cross-term, and further improve time-frequency aggregation.
作为油气检测的基础,地震层位自动拾取的工作显得越来越重要。为了提高层位拾取的工作效率,人们提出了许多地震层位自动拾取方法,如人工神经网络方法、模式识别方法、互相关方法等。上述方法中互相关方法稳定性最好,应用也最广泛。但是当地震资料中的噪声具有强相关性时,互相关方法会拾取噪声间的时间延迟值,致使层位拾取结果出现误差。本文充分利用地震层位横向波形相似性原理以及四阶累积量一维切片对高斯噪声免疫的特点,提出了基于四阶累积量一维切片的地震层位自动拾取方法,具体有如下创新点：
1、1993年Tugnait给出了基于四阶累积量一维切片的信号时间延迟估计公式,公式中采用的是可变长度的分析时窗。在地震勘探数据处理中,采用可变长度分析时窗计算时,存在受坏道影响大、计算结果失稳、时移量拾取不足等问题；因此为了避免上述问题,本论文采用稳健性更好的固定长度的分析时窗,并且根据实际需要对延迟时参数的位置作了相应的改变。
2、当地下介质是分层比较均匀的情况下,地震信号是一种近似于广义高斯分布的、偏度为零的具有对称分布的随机信号。对于对称分布的随机信号,其三阶累积量为零,因此三阶累积量已经不适合进行这种信号的处理。而本文采用的四阶累积量一维切片时延迟估计函数不存在三阶累积量的局限性。
3、在地震层位拾取过程中需要合理设定相关参数,这些参数关系到层位拾取的准确性,其中参考道的选择尤为重要。在分析研究两种传统的参考道选择方式的基础上,设计了一种新的参考道选择方式；这种方式在地震数据局部波形相似性较强的情况下,既克服了固定参考道方式由于横向波形变化大产生计算误差的问题；也改正了非固定参考道方式容易产生大量累计误差的缺点。
源于B P Amoco(英国石油阿莫科)公司的分频技术是通过数学变换将地震数据变换到频率域或时频域,然后沿其频率轴作频率切片,最后利用单频切片进行储层预测的一种解释技术。目前从各类文献资料来看,已有的分频技术算法主要有：傅氏变换方法、线性时频分析方法、时频分布方法等。本论文首次提出了基于Wigner双谱对角切片的分频技术,并将其应用在油气检测中,取得如下成果：
1、为了解决Wigner双谱对角切片存在的交叉干扰项问题,采用模糊域核函数滤波抑制交叉项,并推导了Wigner双谱对角切片的模糊函数计算公式。
2、在充分研究锥形核函数与指数核函数的基础上,利用锥形核函数表达式中的指数函数与指数核函数结合,给出了一个新的核函数。数值模拟结果表明新核函数兼具上述两种核函数的优点,对时延轴上及坐标轴外的交叉项都有很强的抑制作用。
3、通过坐标移动的方法,使Wigner双谱对角切片的模糊函数信号项的中心点与新核函数中心点重合。从而解决了直接进行模糊域滤波致使新核函数对交叉项抑制能力下降的问题。
4、为了解决Wigner双谱对角切片三维数据体数据量太大,致使matlab程序报错：“内存溢出”的问题。对分频技术的流程进行了改进,避免了分频过程中生成Wigner双谱对角切片三维数据体。
结合国内外的研究基础以及本人对这一领域的认识,本文论述的两类方法还需要在以下三个方面进行深入研究：
1、本文所给出的四阶累积量一维切片是基于非参数化估计方法得到的。该方法具有简单易实现的优点,但是在有限数据长度的情况下,存在估计方差较大的缺点。估计方差直接影响到计算结果的准确性,因此可以采用估计方差较小的参数化方法给出相应的地震信号时延估计算子。
2、由Wigner双谱对角切片模糊函数图可以看出,有效信号与交叉项的间距比较近,两信号分量的延迟时越小,间距越近,这不利于薄层的分辨。因此可以对Wigner双谱对角切片模糊函数的计算公式进行改造,加大信号项与交叉项的间距,提高对薄层的分辨能力。
3、模糊域核函数滤波法在有效抑制交叉项的同时降低了时频分辨率。因此可以利用重排理论或自适应最优核设计等时频分布理论抑制交叉项,在兼顾交叉项抑制能力的同时进一步提高时频聚集性。
As the oil and gas exploration level deepens, the oil and gas exploration difficulties are increasing. Owing to the complicated conditions of exploration, the SNR and resolution of data are very low. thereby seriously impact on effect of processing and interpretation. On the condition that weak signal, there is particularly important to propose a new method of signal detection for the new exploration object. As a mathematical tool describe random signal HOS theory has been initial applied in the exploration area; based on this theory, two kinds of methods were discussed by this article with the view of inhibit coherent gauss noise to interfere with the seismic horizon extracting and mend frequency-divided technique and improve the time-frequency resolution.
As the base of oil and gas detection, seismic horizon extracting appears more and more important. To improve the efficiency, people propose many ways, such as artificial neural network, pattern recognition and cross-correlation, etc. The cross-correlation way has the best stability and applies the most widely. But when the noise of the data has strong relevance, cross-correlation way pick up the time delay of noise, bring about the error of seismic horizon extracting. This paper is the full use of the transverse wave comparability and one-dimensional slice of cross-fourth-order cumulants is immune to Gaussian noise, and propose a method of automatic extracting seismic horizon based on one-dimensional slice of fourth-order cumulants, there are the following specific innovation points:
1, in 1993 tugnait gave the time delay formula based on one-dimensional slice of fourth-order cumulants, the formula uses of variable length analyzing window. When data processing uses of this variable length analyzing window, there is a problem of producing great influence by bad trace, the instability calculation results, and inadequate time-delay. To avoid above problems, this paper uses the more robust and fixed length analysis window, and according to the actual need to change the location of delay the parameter.
2, when the underground media is even, the seismic signal is a kind random signal of symmetry distribution of bordering on generalized Gaussian distribution, skewness is zero. The three order cumulant of symmetrical distribution random signal snooze is zero, so it is not fit for processing such signals. But the time delay formula based on one-dimensional slice of fourth-order cumulants doesn't has this limitation.
3. in process of extracting seismic horizon needs to reasonably setup parameters, these parameters concern the accuracy of horizon extracting, and the choice of referenced trace is especially important. Based on the study of traditional choice pattern of referenced trace, a new choice pattern of referenced trace has been devised; this way overcome the problem that the fixed referenced trace pattern leads calculation error because of transverse wave change:and also correct the shortcoming of floating referenced trace leads cumulative error.
Frequency-divided technique deriving from B P Amoco is a resolution technique to transforms seismic data to frequency domain or time-frequency domain through mathematical transform, through it. cut frequency axis into slices, make use of slices to predicate reservoirs finally. At present sorts of document considered, existing frequency-divided technique include:The information from various sources, the existing businesses of technology are mainly:Fourier transformation, linear frequency analysis, the frequency distribution.etc. This paper in order to mend frequency-divided technique and improve the time-frequency resolution, make use of the high time-frequency resolution specialty of Wigner bispectrum diagonal slice, first propose the frequency-divided technique based on the Wigner bispectrum diagonal slice and apply it on the oil and gas detection, achieved following results:
1, in order to solve the problem of cross-term interference in Wigner bispectrum diagonal slice, through fuzzy fields'kernel wave-filtering method for restraining cross-term interference and derivate formula of Wigner bispectrum diagonal slice fuzzy functions.
2, based on fully studying cone-shaped kernel and exponential kernel, through combine exponential function in cone-shaped kernel with exponential kernel and give a new kernel. Numerical simulations indicated that the new kernel function has the advantages of above two kernels, and has a strong inhibition to cross-term interference in delay axis and beyond axis.
3, by way of moving coordinate to superpose the center point between fuzzy functions signal terms and new kernel. Thereby solve a problem that the new kernel couldn't be capable of restraining cross-term interference because of filtering in fuzzy fields directly.
4, in order to solve the problem of program error messages:"memory overflow' because that datasize of 3D data volume is too massive. So the frequency-divided technique procedure is improved, avoiding generating Wigner bispectrum diagonal slice3D data volume.
In accordance with research base from home and abroad as well as this field knowledge of myself, two kinds of methods were discussed by this article need to be intensive studied from following three areas:
1, one-dimensional slice of fourth-order cumulants of this paper is based on non-parametric estimation method. This method is simple to implement, but its estimation variance is excessive, in the case of finite length of data. Estimation variance directly impact on the accuracy of the results, therefore it can make us of little variance parametric estimation method to give seismic signal delay estimation operator.
2, it can be seen from Wigner bispectrum diagonal slice fuzzy functions that space between effective signal and cross-term is closer, the delay is the less. This goes against resolving the thin bed. The formula of Wigner bispectrum diagonal slice fuzzy functions, and increases the space between effective signal and cross-term, improving ability of resolving the thin bed.
3, while effectively restraining cross-term, fuzzy field's wave-filtering method reduces the time-frequency resolution. So may make us of rearrangement theory or adaptive optimal-kernel and so on to restrain cross-term, and further improve time-frequency aggregation.
引文
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