高分辨率Radon变换及其在地震资料处理中的应用
发布时间：2019-01-05 17:55
【摘要】：地震资料处理是地震勘探中重要环节之一,为了得到好的结果,地震资料处理方法形形色色,不同处理方法各有特点。Radon变换被引入到地球物理领域后,在地震资料处理的多方面发挥着重要作用。本文主要研究的是Radon变换在地震资料处理中的应用,从变换基本原理出发,着重介绍了地球物理领域中Radon变换的几种基本形式,有线性Radon变换、抛物线Radon变换、双曲线Radon变换、多项式Radon变换,给出了频率域Radon变换及时间域Radon变换的求解形式和求解方法。本文重点从快速Ra don变换(即λ-f域)重建地震数据和高分辨率抛物线Radon变换压制多次两方面展开应用研究。常规Radon变换地震数据重建,主要是利用正反Radon变换迭代,最终实现缺失地震数据的重建。虽然在频率域计算Radon变换具有较快的计算速度,但由于重建需要较多次的迭代,其计算效率仍不高,由此本文使用λ-f域Radon变换重建地震数据,该方法是由Brahim Abbad提出的一种快速抛物线Radon变换的计算方法,频率域计算需要重复计算正变换算子,λ-f域只用计算一次,同时可以通过调节λ的取值可以减少迭代次数,因此能从减少算子计算次数以及迭代次数两方便提高地震数据重建效率。多次波压制是地震资料处理中的一个难点,Radon变换利用Radon域一次波同多次波的可分离性能较为有效的压制多次波。常规Radon变换因其变换精度低,导致在Radon域分辨能力有限,对多次波的压制效果差,1999年Sacchi提出了高分辨率Radon变换,成为了现在压制多次波的主流方法。Radon变换正反变换算子并非可逆算子,常规Radon变换在计算时没有考虑模型信息,高分辨率Radon变换在计算时充分考虑到模型先验信息,根据模型信息重新设计计算算子,使得正变换结果更加符合模型。高分辨率Radon变换破坏了原先算子矩阵的To eplitz结构,此时的算子为Hermite矩阵,可以用Choleskey分解、LU分解、共轭梯度等方法求解,本文采用共轭梯度法求解。将高分辨率Radon变换应用到实际多次波压制中,与商业软件结果对比分析,验证了本文处理效果的正确性。Radon变换具有灵活的变换形式,将不同的Radon变换应用到适合其变换特性的地震资料处理中能取得较好的应用效果,本文通过数值实验和实际地震资料处理可以得到以下认识,λ-f域Radon变换重建地震数据计算效率高,高分辨率抛物线Radon变换压制多次波效果较好,线性Radon变换对线性面波具有较好的压制效果。Radon变换在地震数据处理领域应用广泛,在诸多方面已经达到了应用的标准。但由于Radon变换算子本身的非可逆性,所以Radon变换的分辨率、保幅性以及计算效率三方面是该方法的重点研究方向。
[Abstract]:Seismic data processing is one of the important links in seismic exploration. In order to obtain good results, the seismic data processing methods are various, and different processing methods have their own characteristics. Radon transform was introduced into the field of geophysics. It plays an important role in many aspects of seismic data processing. In this paper, the application of Radon transform in seismic data processing is mainly studied. Based on the basic principle of transformation, several basic forms of Radon transformation in geophysics are introduced, including linear Radon transform, parabola Radon transform, hyperbolic Radon transform. Polynomial Radon transform, the solution form and method of Radon transform in frequency domain and Radon transform in time domain are given. This paper focuses on the application of fast Ra don transform (位 -f domain) reconstruction of seismic data and suppression of high resolution parabola Radon transform. Conventional Radon transform is mainly used to reconstruct seismic data by using positive and negative Radon transform iteration, and finally the missing seismic data is reconstructed. Although the calculation of Radon transform in frequency domain is very fast, the calculation efficiency is still not high because the reconstruction needs more iterations. Therefore, the 位 -f domain Radon transform is used to reconstruct seismic data in this paper. This method is proposed by Brahim Abbad to calculate the fast parabola Radon transform. The frequency domain calculation needs to calculate the positive transformation operator repeatedly, the 位 -f domain is calculated only once, and the iteration times can be reduced by adjusting the value of 位. Therefore, the efficiency of seismic data reconstruction can be improved by reducing the number of operator computations and iterations. Multiple suppression is a difficult problem in seismic data processing. Radon transform can suppress multiple waves effectively by using the separability of primary wave and multiple wave in Radon domain. Because of the low accuracy of conventional Radon transform, the resolution in Radon domain is limited and the suppression effect of multiple waves is poor. In 1999, Sacchi proposed high resolution Radon transform. The forward and inverse transform operators of Radon transform are not invertible operators, the conventional Radon transform does not consider the model information in calculation, and the prior model information is fully taken into account in the calculation of high resolution Radon transform. According to the model information, the calculation operator is redesigned to make the positive transformation result more consistent with the model. The high-resolution Radon transform destroys the To eplitz structure of the original operator matrix, and the operator is a Hermite matrix, which can be solved by Choleskey decomposition, LU decomposition, conjugate gradient, etc. In this paper, the conjugate gradient method is used to solve the problem. The high resolution Radon transform is applied to the practical multiple suppression, and compared with the commercial software results, the correctness of the processing effect of this paper is verified. The Radon transform has a flexible transformation form. The application of different Radon transform to seismic data processing suitable for its transformation characteristics can obtain good results. In this paper, the following conclusions can be obtained through numerical experiments and actual seismic data processing. Radon transform in 位 -f domain has high computational efficiency, high resolution parabola Radon transform has better suppression effect on multiple waves, linear Radon transform has better suppression effect on linear surface wave. Radon transform is widely used in the field of seismic data processing. It has reached the standard of application in many aspects. However, due to the non-reversibility of the Radon transform operator itself, the resolution, amplitude preservation and computational efficiency of the Radon transform are the main research directions of the method.
【学位授予单位】：成都理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.44
本文编号：2402110
[Abstract]:Seismic data processing is one of the important links in seismic exploration. In order to obtain good results, the seismic data processing methods are various, and different processing methods have their own characteristics. Radon transform was introduced into the field of geophysics. It plays an important role in many aspects of seismic data processing. In this paper, the application of Radon transform in seismic data processing is mainly studied. Based on the basic principle of transformation, several basic forms of Radon transformation in geophysics are introduced, including linear Radon transform, parabola Radon transform, hyperbolic Radon transform. Polynomial Radon transform, the solution form and method of Radon transform in frequency domain and Radon transform in time domain are given. This paper focuses on the application of fast Ra don transform (位 -f domain) reconstruction of seismic data and suppression of high resolution parabola Radon transform. Conventional Radon transform is mainly used to reconstruct seismic data by using positive and negative Radon transform iteration, and finally the missing seismic data is reconstructed. Although the calculation of Radon transform in frequency domain is very fast, the calculation efficiency is still not high because the reconstruction needs more iterations. Therefore, the 位 -f domain Radon transform is used to reconstruct seismic data in this paper. This method is proposed by Brahim Abbad to calculate the fast parabola Radon transform. The frequency domain calculation needs to calculate the positive transformation operator repeatedly, the 位 -f domain is calculated only once, and the iteration times can be reduced by adjusting the value of 位. Therefore, the efficiency of seismic data reconstruction can be improved by reducing the number of operator computations and iterations. Multiple suppression is a difficult problem in seismic data processing. Radon transform can suppress multiple waves effectively by using the separability of primary wave and multiple wave in Radon domain. Because of the low accuracy of conventional Radon transform, the resolution in Radon domain is limited and the suppression effect of multiple waves is poor. In 1999, Sacchi proposed high resolution Radon transform. The forward and inverse transform operators of Radon transform are not invertible operators, the conventional Radon transform does not consider the model information in calculation, and the prior model information is fully taken into account in the calculation of high resolution Radon transform. According to the model information, the calculation operator is redesigned to make the positive transformation result more consistent with the model. The high-resolution Radon transform destroys the To eplitz structure of the original operator matrix, and the operator is a Hermite matrix, which can be solved by Choleskey decomposition, LU decomposition, conjugate gradient, etc. In this paper, the conjugate gradient method is used to solve the problem. The high resolution Radon transform is applied to the practical multiple suppression, and compared with the commercial software results, the correctness of the processing effect of this paper is verified. The Radon transform has a flexible transformation form. The application of different Radon transform to seismic data processing suitable for its transformation characteristics can obtain good results. In this paper, the following conclusions can be obtained through numerical experiments and actual seismic data processing. Radon transform in 位 -f domain has high computational efficiency, high resolution parabola Radon transform has better suppression effect on multiple waves, linear Radon transform has better suppression effect on linear surface wave. Radon transform is widely used in the field of seismic data processing. It has reached the standard of application in many aspects. However, due to the non-reversibility of the Radon transform operator itself, the resolution, amplitude preservation and computational efficiency of the Radon transform are the main research directions of the method.
【学位授予单位】：成都理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.44
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