High Resolution Radon Transform And Applications

In the past 30 years, the Radon transform in the seismic data processing has attracted the attention of many scholars, the Radon transform itself in the Radon transform characteristic of the physical characteristics of the domain market more intuitive clear to comparative analysis. In recent years, in the Radon transform algorithm, there has been a new development so that the pros and cons of the Radon transform fidelity, accuracy and speed of transformation has been greatly increased. Fourier projection famous theorem (also known as the projection slice theorem) that Radon transform and the Fourier transform of a clear relationship has been proven, n-dimensional Fourier transform equivalent Radon transform and a Fourier transform. This is Radon transform to the rapid development and application of one of the reasons. With the development of digital signal processing, discrete Radon transform method to solve the problem and also the accuracy of continuous improvement. Based on the characteristics and needs of Radon transform can be derived in the form of a flexible and diverse. Radon transform precision Radon transform domain can improve the resolution of data can be greatly suppressed discrete computing in the truncation artifacts, can better follow-up processing applications. In this paper, in recent years the popularity of the Radon transform methods and discrete numerical algorithm to make summarized.According path can be integral to Radon transform respectively linear, parabolic, polynomial, hyperbolic, elliptic transform. Phase shift hyperbolic Dix hyperbolic equation is far offset error for the larger substitute. Compared with conventional transformation, far offset hyperbolic reflection energy is better focused.Linear, parabolic, polynomial Radon transform operator has invariance when, in the frequency domain can be achieved. Time - the spatial domain into the frequency of the problem - to solve the spatial domain, the benefits of doing so is the speed of Fourier transform is very fast and can be carried out in each frequency component Radon transform, and avoid solving all the time ~ offset the speed of the large sample matrix problems, and enhance the computing speed. Toeplitz operator matrix structure of (uniform sampling parameters), can be used Levinsion fast recursive algorithm to solve.High resolution Radon transform is a frequency domain space sparse bound algorithm, in the inversion iteration process, in accordance with the results of the previous iteration, through Bayesian principles will be weighted matrix and the results of the previous iteration link be new weighted matrix; weighted matrix and then solve the equation, the frequency domain by the sparse solution. As operator matrix weighted matrix does not have the presence of Toeplitz structure, but still Hermite matrix, we can use the Cholesky decomposition method, LU decomposition method, the faster algorithm is conjugate gradient algorithm.Because, after all, the parabolic Radon transform limited precision, and the existence of stability in the frequency domain problem. In foreign countries, some scholars have begun studying time - space domain to direct calculation precision hyperbolic Radon transform algorithm, the algorithm used in least squares method to the most rapid decline in law. Conjugate gradient method fast convergence, the process for stability and the high accuracy solution, which has greatly improved its calculation speed.Because of discrete computing, the Radon transform has truncation artifacts, by the least squares inversion of traditional and this artifact can not be effectively curbed. Compared with the least squares inversion and high resolution Radon transform after the results, which were better than the former.2D mask filter method is a direct damped least-squares algorithm used to suppress the effects of truncation artifacts method. Radon domain adaptive use of wave field separation method reduced time and space truncation effects. The method is to use the main ideas Radon domain truncation effect of trajectory "pick up" lateral shear line of energy "residual." Pick up option is to cut Radon domain exists outside of the weaker signal convergence "Imprint", as a separation similar to the printing of "Mask", shielding the corresponding signal. 2D mask filter technique to suppress the Radon transform many waves, the two will be obvious benefits: 1, multiple reflections of the separation was better. 2, a wave of energy to better reservations. Seismic exploration, identification and elimination of multiple wave seismic exploration session is facing long-term problems. If the seismic record wave reflection on the many strong energy, and sometimes to cover up a wave of energy, the existence of multiple waves, making lower-resolution seismic data, and the effective interference wave of people identification, make follow-up velocity analysis, migration imaging, and even brought great difficulties to explain. Therefore, the study multiple wave, and then eliminate multiple or effective suppression of multiple wave is not only a very important theoretical and technical value and a practical application value and direct economic benefits. In the suppression of multiple methods, the various forms of Radon transform played an important role, but also commonly used in industrial production methods. Based on the difference between the normal day-to eliminate many of the principles of Radon transform not only can eliminate many surface wave can also eliminate multiple layer.VSP data from the wave field is the main method used FK filtering method, median filtering andτ-p transform (radon transform)。FK filtering method is based on the speed between the positive and negative direction of the poor, the transformation to the f-k domain, upstream waves in the wave number of negative plane, descending wave in the wave number is flat, so a wave field separation, but the methods and frequency space false Rieber hybrid phenomenon, will lead to different quadrants of the energy together, that is, between the impact of the wave field can not be completely eliminated. Median filtering method based on trace between wave and consistency of assumptions, but in different formation lithology receive the downlink wave and the assumption that there are contradictions, thus affecting the separation, the effect of wave downlink, and because of boundary conditions trace less than in the last offset by the separation of amplitude distortion of the wave field is relatively large. Radon transform compared to the frequency domain, the process of transformation by reducing the curvature slope, will effectively eliminate the shortage of space at sampling frequency phenomenon, with high-resolution Radon transform, but also can improve the precision of separation.Surface wave suppression, and random noise in seismic data processing is an important issue, these disturbances through the frequency domain filtering, and not very good, the elimination of effective frequency domain signal interference wave band joined some of these overlap. FK filtering used in the production domain speed filtering method to suppress surface wave, application processing after the Radon transform method can be achieved better results.Radon transform irregular observing systems in the wave field separation can be very good applications. Radon transform the discrete structure in the Radon transform Toeplitz uniform sampling parameters, the loss of some trace or from the transformation, the situation remained effective, in the irregular observing system wave field seismic data applications can still maintain separation accuracy and efficiency. Through theoretical model spreadsheet, and elaborated in the Radon transform deletion trace, trace from changes in circumstances still be accurate separation wave field, the prediction of the tunnel ahead of the reflected wave data processing, is the tunnel forecast extraction process reflection examples.Looking Radon transform PS waves can also be separated, data reconstruction, sparse data interpolation, velocity analysis, migration and other aspects of the application well.