Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, de...Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, developed by A.C.Lazer, Schauder fixed point theorem and the Leray-Schauder degree theory, respectively.展开更多
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
A general n-th order spectral transform and a technique for inverting this transform is described in this paper and the usefulness of the whole procedure is illustrated by the solution of a system of nonlinear Klein G...A general n-th order spectral transform and a technique for inverting this transform is described in this paper and the usefulness of the whole procedure is illustrated by the solution of a system of nonlinear Klein Gordon equations.展开更多
文摘Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, developed by A.C.Lazer, Schauder fixed point theorem and the Leray-Schauder degree theory, respectively.
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.
文摘A general n-th order spectral transform and a technique for inverting this transform is described in this paper and the usefulness of the whole procedure is illustrated by the solution of a system of nonlinear Klein Gordon equations.
