【摘要】：地震資料處理是地震勘探中重要環(huán)節(jié)之一,為了得到好的結果,地震資料處理方法形形色色,不同處理方法各有特點。Radon變換被引入到地球物理領域后,在地震資料處理的多方面發(fā)揮著重要作用。本文主要研究的是Radon變換在地震資料處理中的應用,從變換基本原理出發(fā),著重介紹了地球物理領域中Radon變換的幾種基本形式,有線性Radon變換、拋物線Radon變換、雙曲線Radon變換、多項式Radon變換,給出了頻率域Radon變換及時間域Radon變換的求解形式和求解方法。本文重點從快速Ra don變換(即λ-f域)重建地震數(shù)據(jù)和高分辨率拋物線Radon變換壓制多次兩方面展開應用研究。常規(guī)Radon變換地震數(shù)據(jù)重建,主要是利用正反Radon變換迭代,最終實現(xiàn)缺失地震數(shù)據(jù)的重建。雖然在頻率域計算Radon變換具有較快的計算速度,但由于重建需要較多次的迭代,其計算效率仍不高,由此本文使用λ-f域Radon變換重建地震數(shù)據(jù),該方法是由Brahim Abbad提出的一種快速拋物線Radon變換的計算方法,頻率域計算需要重復計算正變換算子,λ-f域只用計算一次,同時可以通過調節(jié)λ的取值可以減少迭代次數(shù),因此能從減少算子計算次數(shù)以及迭代次數(shù)兩方便提高地震數(shù)據(jù)重建效率。多次波壓制是地震資料處理中的一個難點,Radon變換利用Radon域一次波同多次波的可分離性能較為有效的壓制多次波。常規(guī)Radon變換因其變換精度低,導致在Radon域分辨能力有限,對多次波的壓制效果差,1999年Sacchi提出了高分辨率Radon變換,成為了現(xiàn)在壓制多次波的主流方法。Radon變換正反變換算子并非可逆算子,常規(guī)Radon變換在計算時沒有考慮模型信息,高分辨率Radon變換在計算時充分考慮到模型先驗信息,根據(jù)模型信息重新設計計算算子,使得正變換結果更加符合模型。高分辨率Radon變換破壞了原先算子矩陣的To eplitz結構,此時的算子為Hermite矩陣,可以用Choleskey分解、LU分解、共軛梯度等方法求解,本文采用共軛梯度法求解。將高分辨率Radon變換應用到實際多次波壓制中,與商業(yè)軟件結果對比分析,驗證了本文處理效果的正確性。Radon變換具有靈活的變換形式,將不同的Radon變換應用到適合其變換特性的地震資料處理中能取得較好的應用效果,本文通過數(shù)值實驗和實際地震資料處理可以得到以下認識,λ-f域Radon變換重建地震數(shù)據(jù)計算效率高,高分辨率拋物線Radon變換壓制多次波效果較好,線性Radon變換對線性面波具有較好的壓制效果。Radon變換在地震數(shù)據(jù)處理領域應用廣泛,在諸多方面已經達到了應用的標準。但由于Radon變換算子本身的非可逆性,所以Radon變換的分辨率、保幅性以及計算效率三方面是該方法的重點研究方向。
[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.
【學位授予單位】：成都理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：P631.44

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