Toeplitz矩阵的循环延拓及其分析与应用

In this paper, we have presented the combined preconditioner which is derived from k =±-1~(1/2) circulant extensions of the real symmetric positive-definite Toeplitz matrices, proved it with great efficiency and stability and shown that it is easy to make error analysis and to remove the boundary effect with the combined preconditioner. This paper has also presented the methods for the direct and inverse computation of the real Toeplitz sets of equations and discussed many problems correspondingly, especially replaced the Toeplitz matrices with the combined preconditoners for analysis. The paper has also discussed the spectral analysis and boundary effect. Finally, as an application in geophysics, the paper makes some discussion about the squared root of a real matrix which comes from the Laplace algorithm.

基于结构分析地震资料去噪方法研究

With the development of oil and gas exploration, the exploration of the continental oil and gas turns into the exploration of the subtle oil and gas reservoirs from the structural oil and gas reservoirs in China. The reserves of the found subtle oil and gas reservoirs account for more than 60 percent of the in the discovered oil and gas reserves. Exploration of the subtle oil and gas reservoirs is becoming more and more important and can be taken as the main orientation for the increase of the oil and gas reserves. The characteristics of the continental sedimentary facies determine the complexities of the lithological exploration. Most of the continental rift basins in East China have entered exploration stages of medium and high maturity. Although the quality of the seismic data is relatively good, this areas have the characteristics of the thin sand thickness, small faults, small range of the stratum. It requests that the seismic data have high resolution. It is a important task how to improve the signal/noise ratio of the high frequency of seismic data. In West China, there are the complex landforms, the deep embedding the targets of the prospecting, the complex geological constructs, many ruptures, small range of the traps, the low rock properties, many high pressure stratums and difficulties of boring well. Those represent low signal/noise ratio and complex kinds of noise in the seismic records. This needs to develop the method and technique of the noise attenuation in the data acquisition and processing. So that, oil and gas explorations need the high resolution technique of the geophysics in order to solve the implementation of the oil resources strategy for keep oil production and reserves stable in Ease China and developing the crude production and reserves in West China. High signal/noise ratio of seismic data is the basis. It is impossible to realize for the high resolution and high fidelity without the high signal/noise ratio. We play emphasis on many researches based on the structure analysis for improving signal/noise ratio of the complex areas. Several methods are put forward for noise attenuation to truly reflect the geological features. Those can reflect the geological structures, keep the edges of geological construction and improve the identifications of the oil and gas traps. The ideas of emphasize the foundation, give prominence to innovate, and pay attention to application runs through the paper. The dip-scanning method as the center of the scanned point inevitably blurs the edges of geological features, such as fault and fractures. We develop the new dip scanning method in the shap of end with two sides scanning to solve this problem. We bring forward the methods of signal estimation with the coherence, seismic wave characteristc with coherence, the most homogeneous dip-sanning for the noise attenuation using the new dip-scanning method. They can keep the geological characters, suppress the random noise and improve the s/n ratio and resolution. The rutine dip-scanning is in the time-space domain. Anew method of dip-scanning in the frequency-wavenumber domain for the noise attenuation is put forward. It use the quality of distinguishing between different dip events of the reflection in f-k domain. It can reduce the noise and gain the dip information. We describe a methodology for studying and developing filtering methods based on differential equations. It transforms the filtering equations in the frequency domain or the f-k domain into time or time-space domains, and uses a finite-difference algorithm to solve these equations. This method does not require that seismic data be stationary, so their parameters can vary at every temporal and spatial point. That enhances the adaptability of the filter. It is computationally efficient. We put forward a method of matching pursuits for the noise suppression. This method decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. It can extract the effective signal from the noisy signal and reduce the noise. We introduce the beamforming filtering method for the noise elimination. Real seismic data processing shows that it is effective in attenuating multiples and internal multiples. The s/n ratio and resolution are improved. The effective signals have the high fidelity. Through calculating in the theoretic model and applying it to the real seismic data processing, it is proved that the methods in this paper can effectively suppress the random noise, eliminate the cohence noise, and improve the resolution of the seismic data. Their practicability is very better. And the effect is very obvious.

利用宽频带台阵资料研究华北地区地壳及上地幔间断面结构

Intense tectonic renovation has occurred in the eastern continent of china since Mesozoic, as evidenced by the high heat flow, widespread magma extrusion and volcanic activities, and development of large sedimentary basins. To explain the cause and mechanism for the tectonic process in this period, some researchers have put forward various models, such as mantle plume, subduction of the Pacific slab, Yangtze Block-North China Block collision, etc. Their seismological evidence, however, is still scarce..During the period from 2000 to 2003, large temporary seismic arrays were established in North China by the Institute of the Geology and Geophysics, Chinese Academy of Sciences. Total 129 portable seismic stations were linearly emplaced across the western and eastern boundaries of the Bohai Bay Basin, and accumulated a large amount of high-quality data. Moreover, abundant data were also collected at the capital digital seismic network established in the ninth five-year period of national economic and social development. These provide an unprecedented opportunity for us to study the deep structure and associated geodynamic mechanism of lithospheric processes in North China using seismological techniques.Seismology is a kind of observation-based science. The development of seismic observations greatly promotes the improvement of seismologic theory and methodology. At the beginning of this thesis, I review the history of seismic observation progress, and present some routine processing techniques used in the array seismology. I also introduce two popular seismic imaging methods (receiver function method and seismic tomography).Receiver function method has been widely used to study the crustal and upper mantle structures, and many relevant research results have been published. In this thesis I elaborate the theory of this method, including the basic concept of receiver functions and the methodology for data pre-processing, stacking and migration. I also address some problems often encountered in practical applications of receiver function imaging.By using the teleseismic data collected at the temporary seismic arrays in North China, in particular, the traveltime information of P-to-S conversion and multiple reverberations of the Moho discontinuity, I obtain the distributions of the crustal thickness and the poisson ratio at the northwest boundary area of the Bohai Bay Basin and discuss the geological implications of the results.Through detailed intestigations on the crustal structural feature around the middle part of the Tanlu fault, considerable disparity in poisson ratios is found in the western and eastern sides of the Tanlu fault. Moreover, an obvious Moho offset is coincidently observed at the same surface location. A reasonable density model for the Tanlu fault area is also derived by simulating the observed gravity variations. Both receiver function study and gravity anomaly modeling suggest that the crustal difference between the western and eastern sides of the Tanlu fault is mainly resulted from their different compositions.With common conversion point imaging of receiver functions, I estimate the depths of the upper and lower boundaries of the mantle transition zone, i.e., the 410 and 660 km discontinuities, beneath most part of the North China continent The thickness of the transition zone (TTZ) in the study area is calculated by subtracting the depth of .410 km discontinuity from that of the 660km discontinuity. The resultant TTZ is 10-15 km larger in the east than in the west of the study area. Phase transitions at the 410 km and the 660 km discontinuities are known to have different Clapeyron slopes. Therefore, the TTZ is sensitive to the temperature changes in the transition zone. Previous studies have shown that the TTZ would be smaller in the mantle plume areas and become larger when the remnants of subducted slabs are present The hypothesis of mantle plume cannot give a reasonable interpretation to the observed TTZ beneath North China, Instead, the receiver function imaging results favor a dynamic model that correlates the thermal structure of the mantle transition zone and associated upper mantle dynamics of North China to the Pacific plate subduction process.