Independent Component Analysis And Its Application On Multiple Attenuation

Independent component analysis (ICA) derived from blind source separation (BSS) is a new method for finding underlying factors or components from multivariate (multidimensional) statistical data. The goal of ICA is to recover the unobserved source signals without any prior information given only the sensor observations that are unknown linear mixtures of the independent sources. Recently, because of a few assumptions on surroundings, ICA has become one of the exciting new topic, both in the field of data mining and more generally in image processing, feature extraction, telecommunications, financial time series analysis.In the paper, we mainly discuss its applications in the seismic signals processing, including the multiple attenuation in the records of seismic explosion and the separation of seismic converted-wave and multiple reflected-waves in sedimentary basin.Seismic data is the important information resource of geological prospect and exploration. And the multiple reflections are often one of the most serious problems in seismic surveying which influence the authenticity and the reliability of seismic imaging badly and interfere the seismic interpretation, so as to increase the cost of seismic exploitation. At the present time, the methods of the multiple attenuation are divided into two categories. One is the filtering approaches based on the differences between the primary and the multiple. The other is the prediction and subtraction approaches based on wave-equation. Without any a priori information and neither structural nor material information about the subsurface geology, the latter become an effective method and the main developing trend in the field of attenuating the multiple, and that, more and more scholars realized that the subtraction step in the prediction and subtraction approaches based on wave-equation is the sticking point. The effective method of subtraction can not only solve the disaccord between the predictive multiple and the real multiple, but also reduce the complex of calculation during the course of prediction largely. However, the energy minimum criterion (least-squares criterion) which is based on the second-order statistics is adopted by the almost existing multiple subtraction methods. From a theoretical point of view, only if the primary and the multiple are normal, the multiple can be removed totally. But in general, the above assumption is invalid in the real seismic data, so that there will remain survival multiple in the primary which is induced by the optimal criterion based on second-order statistics.After working over a variety of the existing multiple attenuation methods and the ICA theory, we try to use the ICA technique for solving the problem of the multiple subtraction in order to hurdle the obstacle in the energy function based on second-order statistics. We view the seismic data and the predictive multiples as the observed signals, the primary and the real multiples as the source signals, so the subtraction can be treated as a processing of blind source separation. Because of no normal assumption in ICA technique, accordingly, we can settle the problem appeared in the second-order statistics method.In this paper, the free-surface related multiple and the internal multiple are depicted for making out that the major amount of the multiple energy in seismic data is related to the large reflectivity of the free-surface. Next, it demonstrates the rationality of BSS equivalent to multiple subtraction theoretically and brings forwards general ICA model for the real seismic data. At last, we use the synthetical data for validating the proposed method in this paper. It makes the single trace as an example, deduces the time-distance equation of first-order free-surface related multiple, second-order free-surface related multiple and the primary of the first subsurface and the one of the second subsurface in detail. As a result, the two primaries are almost reserved absolutely. Therefore, the proposed method in this paper is effective for the multiple attenuation.There are some strong velocity discontinuities or transitions in the earth's curst and upper mantle, which can be recognized by tracing converted-wave phases in seismic wave records. However, when seismic stations are set in sedimentary area, the recorded converted-wave information will be masked by the recorded multiple reflected-waves caused by sedimentary formations. In this case, it is hard to identify the velocity discontinuity from receiver function. Now there are not many effective methods to separate the mixed seismic converted wave and multiple reflected-waves. In this paper, a new method is proposed based on Independent Component Analysis (ICA) to implement the separation of seismic converted-wave and multiple reflected-waves recorded in sedimentary basin.On the base of analyzing the features of seismic signals, we do preliminary studies and try to apply ICA in seismic signals separation. We suppose that the seismic records of each station set in the sedimentary area are some linear mixture of seismic converted-wave and multiple reflected-waves.The specific operation is: synthesizing 11 seismic records at distance of 25°~35°; in time domain, we included two close seismic records in one group and used Fast-ICA to separate two signals from them, supposing that separated signals were converted-wave and multiple reflected-waves respectively. The results show that ICA method to separate converted and reflected wave is feasible. But due to the ambiguity of basic ICA, the separated signal is of sign undetermined. So the extended ICA should be studied and applied in the subject of the paper to overcome the problem, thus better effects will be obtained.