Seismic imaging of complicated underground structures with severe surface undulation(i.e.,double complex areas)is challenging owing to the difficulty of collecting the very weak reflected signal.Enhancing the weak sig...Seismic imaging of complicated underground structures with severe surface undulation(i.e.,double complex areas)is challenging owing to the difficulty of collecting the very weak reflected signal.Enhancing the weak signal is difficult even with state-of-the-art multi-domain and multidimensional prestack denoising techniques.This paper presents a time–space dip analysis of offset vector tile(OVT)domain data based on theτ-p transform.The proposed N-th root slant stack method enhances the signal in a three-dimensionalτ-p domain by establishing a zero-offset time-dip seismic attribute trace and calculating the coherence values of a given data sub-volume(i.e.,inline,crossline,time),which are then used to recalculate the data.After sorting,the new data provide a solid foundation for obtaining the optimal N value of the N-th root slant stack,which is used to enhance a weak signal.The proposed method was applied to denoising low signal-to-noise ratio(SNR)data from Western China.The optimal N value was determined for improving the SNR in deep strata,and the weak seismic signal was enhanced.The results showed that the proposed method effectively suppressed noise in low-SNR data.展开更多
The authors construct self-similar solutions for an N-dimensional transport equation,where the velocity is given by the Riezs transform.These solutions imply nonuniqueness of weak solution.In addition,self-similar sol...The authors construct self-similar solutions for an N-dimensional transport equation,where the velocity is given by the Riezs transform.These solutions imply nonuniqueness of weak solution.In addition,self-similar solution for a one-dimensional conservative equation involving the Hilbert transform is obtained.展开更多
Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method...Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the(2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the(2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water.展开更多
基金supported by the Scientific Research Foundation of Yunnan Provincial Education Department(2018JS752)the National Natural Science Foundation of China(11801240)
文摘Seismic imaging of complicated underground structures with severe surface undulation(i.e.,double complex areas)is challenging owing to the difficulty of collecting the very weak reflected signal.Enhancing the weak signal is difficult even with state-of-the-art multi-domain and multidimensional prestack denoising techniques.This paper presents a time–space dip analysis of offset vector tile(OVT)domain data based on theτ-p transform.The proposed N-th root slant stack method enhances the signal in a three-dimensionalτ-p domain by establishing a zero-offset time-dip seismic attribute trace and calculating the coherence values of a given data sub-volume(i.e.,inline,crossline,time),which are then used to recalculate the data.After sorting,the new data provide a solid foundation for obtaining the optimal N value of the N-th root slant stack,which is used to enhance a weak signal.The proposed method was applied to denoising low signal-to-noise ratio(SNR)data from Western China.The optimal N value was determined for improving the SNR in deep strata,and the weak seismic signal was enhanced.The results showed that the proposed method effectively suppressed noise in low-SNR data.
基金Project supported by the MCINN (Spain) (No.MTM2008-03754)the ERC (No.StG-203138CDSIF)
文摘The authors construct self-similar solutions for an N-dimensional transport equation,where the velocity is given by the Riezs transform.These solutions imply nonuniqueness of weak solution.In addition,self-similar solution for a one-dimensional conservative equation involving the Hilbert transform is obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055,11275072Innovative Research Team Program of the National Science Foundation of China under Grant No.61021104+3 种基金National High Technology Research and Development Program under Grant No.2011AA010101Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213Talent FundK.C.Wong Magna Fund in Ningbo University
文摘Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the(2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the(2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water.
