Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Usin...Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.展开更多
Depth migration can image complex structures with high accuracy,thereby stimulating the increasingly urgent demands for developing depth-domain inversions and interpretations in industry.The well-seismic calibration i...Depth migration can image complex structures with high accuracy,thereby stimulating the increasingly urgent demands for developing depth-domain inversions and interpretations in industry.The well-seismic calibration in the depth domain serves as a crucial cornerstone for these interpretations and inversions.Well data provide a partial cognition of underground media.Seismic data must be accurately calibrated with well data to expand this cognition outward.Depth-domain seismic data are non-stationary,transforming traditional,mature time-domain well calibration methods unsuitable for direct application to depth-domain seismic data.Therefore,researchers usually adopt a domain transformation strategy to complete well-seismic calibration in the time domain and then convert the calibration results into the depth domain.However,this method inevitably introduces additional error accumulation caused by domain transformation.On the basis of a comprehensive review of previous research,we propose a direct depth-domain well-seismic calibration method.This method is based on the synthesis of the depth-domain seismic records and the extraction of the depth-domain generalized seismic wavelets.We introduce constrained dynamic warping with maximum stretch depth constraint and directly match seismic data with well data in the depth domain.The actual processing results show that the method improves the efficiency of the depth-domain well-seismic calibration and produces a reliable relationship between seismic and well depths after two to four iterations.展开更多
基金Supported by the Foundation of the National Natural Science of China( No.1 0 0 71 0 39) and the Foundation of Edu-cation Commission of Jiangsu Province
文摘Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.
基金supported by the National Natural Science Foundation of China(No.U23B20158)CNOOC major technology project(KJGG2022-0104)。
文摘Depth migration can image complex structures with high accuracy,thereby stimulating the increasingly urgent demands for developing depth-domain inversions and interpretations in industry.The well-seismic calibration in the depth domain serves as a crucial cornerstone for these interpretations and inversions.Well data provide a partial cognition of underground media.Seismic data must be accurately calibrated with well data to expand this cognition outward.Depth-domain seismic data are non-stationary,transforming traditional,mature time-domain well calibration methods unsuitable for direct application to depth-domain seismic data.Therefore,researchers usually adopt a domain transformation strategy to complete well-seismic calibration in the time domain and then convert the calibration results into the depth domain.However,this method inevitably introduces additional error accumulation caused by domain transformation.On the basis of a comprehensive review of previous research,we propose a direct depth-domain well-seismic calibration method.This method is based on the synthesis of the depth-domain seismic records and the extraction of the depth-domain generalized seismic wavelets.We introduce constrained dynamic warping with maximum stretch depth constraint and directly match seismic data with well data in the depth domain.The actual processing results show that the method improves the efficiency of the depth-domain well-seismic calibration and produces a reliable relationship between seismic and well depths after two to four iterations.
