Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transfo...Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transform domain, we can improve the accuracy and stability of the reconstruction by transforming it to a sparse optimization problem. In this paper, we propose a mathematical model for the sparse reconstruction of data based on the LO-norm minimization. Furthermore, we discuss two types of the approximation algorithm for the LO- norm minimization according to the size and characteristics of the geophysical data： namely, the iteratively reweighted least-squares algorithm and the fast iterative hard thresholding algorithm. Theoretical and numerical analysis showed that applying the iteratively reweighted least-squares algorithm to the reconstruction of potential field data exploits its fast convergence rate, short calculation time, and high precision, whereas the fast iterative hard thresholding algorithm is more suitable for processing seismic data, moreover, its computational efficiency is better than that of the traditional iterative hard thresholding algorithm.展开更多
革命圣地延安的拉丁化《新文字报》(《Sin w enzBao》),是陕甘宁边区出版发行的拼音文字报刊。它虽然存在的时间不长,但在当时边区开展的新文字扫盲运动中,发挥过重要作用,给人们留下了难忘的印象。抗日战争前夕,为了宣传抗日救亡活动,...革命圣地延安的拉丁化《新文字报》(《Sin w enzBao》),是陕甘宁边区出版发行的拼音文字报刊。它虽然存在的时间不长,但在当时边区开展的新文字扫盲运动中,发挥过重要作用,给人们留下了难忘的印象。抗日战争前夕,为了宣传抗日救亡活动,上海地下共青团曾秘密出版过拉丁化新文字报——《我们的世界》(《womenceiShgie》)。1937年到1938年初,陕甘宁边区曾办过一批新文字扫盲班。展开更多
Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are...Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.展开更多
Greater attention has been paid to vintage-merge processing of seismic data and extracting more valuable information by the geophysicist. A match filter is used within many important areas such as splicing seismic dat...Greater attention has been paid to vintage-merge processing of seismic data and extracting more valuable information by the geophysicist. A match filter is used within many important areas such as splicing seismic data, matching seismic data with different ages and sources, 4-D seismic monitoring, and so on. The traditional match filtering method is subject to many restrictions and is usually difficult to overcome the impact of noise. Based on the traditional match filter, we propose the wavelet domain L1 norm optimal matching filter. In this paper, two different types of seismic data are decomposed to the wavelet domain, different detailed effective information is extracted for Ll-norm optimal matching, and ideal results are achieved. Based on the model test, we find that the L1 norm optimal matching filter attenuates the noise and the waveform, amplitude, and phase coherence of result signals are better than the conventional method. The field data test shows that, with our method, the seismic events in the filter results have better continuity which achieves the high precision seismic match requirements.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.41074133)
文摘Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transform domain, we can improve the accuracy and stability of the reconstruction by transforming it to a sparse optimization problem. In this paper, we propose a mathematical model for the sparse reconstruction of data based on the LO-norm minimization. Furthermore, we discuss two types of the approximation algorithm for the LO- norm minimization according to the size and characteristics of the geophysical data： namely, the iteratively reweighted least-squares algorithm and the fast iterative hard thresholding algorithm. Theoretical and numerical analysis showed that applying the iteratively reweighted least-squares algorithm to the reconstruction of potential field data exploits its fast convergence rate, short calculation time, and high precision, whereas the fast iterative hard thresholding algorithm is more suitable for processing seismic data, moreover, its computational efficiency is better than that of the traditional iterative hard thresholding algorithm.
文摘革命圣地延安的拉丁化《新文字报》(《Sin w enzBao》),是陕甘宁边区出版发行的拼音文字报刊。它虽然存在的时间不长,但在当时边区开展的新文字扫盲运动中,发挥过重要作用,给人们留下了难忘的印象。抗日战争前夕,为了宣传抗日救亡活动,上海地下共青团曾秘密出版过拉丁化新文字报——《我们的世界》(《womenceiShgie》)。1937年到1938年初,陕甘宁边区曾办过一批新文字扫盲班。
文摘Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.
基金sponsored by the Natural Science Foundation of China(No.41074075)Graduate Innovation Fund by Jilin University(No.20121070)
文摘Greater attention has been paid to vintage-merge processing of seismic data and extracting more valuable information by the geophysicist. A match filter is used within many important areas such as splicing seismic data, matching seismic data with different ages and sources, 4-D seismic monitoring, and so on. The traditional match filtering method is subject to many restrictions and is usually difficult to overcome the impact of noise. Based on the traditional match filter, we propose the wavelet domain L1 norm optimal matching filter. In this paper, two different types of seismic data are decomposed to the wavelet domain, different detailed effective information is extracted for Ll-norm optimal matching, and ideal results are achieved. Based on the model test, we find that the L1 norm optimal matching filter attenuates the noise and the waveform, amplitude, and phase coherence of result signals are better than the conventional method. The field data test shows that, with our method, the seismic events in the filter results have better continuity which achieves the high precision seismic match requirements.
