Study And Application Of High-dimensional Seismic Data Processing With Tensor Theory

It is difficult to implement seismic exploration in the complicated geological environment, since its low quality of seismic data of 3D seismic exploration is used to get the 3D subsurface geological body information, at the same time it is more suitable in complicated geological surface condition than 2D seismic exploration.From previous studies, it provides a better exploration result because of the full use of the seismic data and valuable information. Hence, a better way to get the seismic exploration result under the complicated geological surface condition is to make the best of the characteristics of high dimension seismic data and related information.This dissertation aims to study the characteristics of the valid signal(such as reflected wave and refracted wave) on common shot gather and common receiver gather of seismic data. Then, we analyzed every independent variable in general time-distance equation and proposes high-dimensional data structure of seismic data,judging the connection of 2D and 3D seismic data under the high-dimensional data structure from every dimensionality.In order to analyze and study about the method to processing high-dimensional seismic data, this dissertation provides the definition and features of numerical tensor and transferred the high-dimensional seismic data analysis into tonsor analysis. What is more, this thesis adopted the concept of tensor space and of seismic data space.Based on the definition and features of numerical tensor, it treated the seismic data as a numerical tensor under the standard of data structure while treated the seismic data processing as the operation of numerical tensor. Meanwhile, based on the theory of tensor space, the seismic data under standard data structure is abstracted as an element of the seismic data space, the seismic data processing under standard data structure abstracted as a mapping of the seismic data space. Therefore, it provides the theory for the operation of seismic data in the tensor space. This dissertation focuses on the various numerical methods within this structure.As for the methodology part, this dissertation studied diverse methods to obtain the result, such as tonsor’s higher-order singular value decomposition and reconstruction methods to realize the operation of tensor interpolation andapproximation, scatter plots fitting and smoothing methods based on the thin sheet surface model to reach the second order tensor smooth fitting, Robust locally weighted regression and smoothing scatter plots to get the higher-order tensor smooth fitting. As a result, this thesis provides various mathematic to process the seismic data in the tensor space.Through the above mathematical tools, this dissertation provides the method of seismic data recovery and random noise suppression in tensor space. In this method,high-order singular value decomposition method is used to decompose the high dimensional seismic data in tensor space, and the decomposed seismic data are reconstructed with lower rank. By reconstructing the missing or abnormal data in seismic data, the data is normalized, and the random noise is suppressed at the same time. In addition. This dissertation provides the method of residual static correction in tensor space. The method in the existing based on first arrival wave residual static correction method, changes the conventional respectively in common shot domain and common receiver domain method in the higher-dimensional seismic tensor data, fits and smooths this tensor in shot-receiver united domain. Compared with the conventional residual static correction method, this method has better effect, and also can overcome abnormal data influence on the results of static correction.To summarize, this dissertation provides a high-dimensional seismic processing thought in tensor space using the tensor numerical methods based on the tonsor and tensor space theory. Data recovery and random noise suppression, and residual static correction method are provided in this dissertation as examples. These high-dimensional methods achieved an outstanding result, they may be useful in the dealing of the seismic data processed under the complicated geological surface condition. Besides, such thought can provide ideas for other high-dimensional seismic processing methods in tensor space.