Beamlet sources have strong local and directional character and can easily accomplish local illumination and migration. Besides, they provide better migration results than conventional migration methods. We introduce ...Beamlet sources have strong local and directional character and can easily accomplish local illumination and migration. Besides, they provide better migration results than conventional migration methods. We introduce the basic principles of beamlet prestack depth migration that includes a windowed Fourier transform and frame theory. We explain the Gabor-Daubechies （G-D） frame based on a Gaussian function. Beamlet decomposition provides information on the local space and direction of wavefield. We synthesize the beamlet source and beamlet records in the wavelet domain using both rectangle and Gaussian windows and then extrapolate the synthesized data with a Fourier finite-difference operator. We test the method using the standard Marmousi model. By comparing and analyzing the migration results of single directional beamlet and beamlets with different windows and directions, we demonstrate the validity of the prestack depth migration with Gaussian beamlets method.展开更多
Let M be a d × d expansive matrix, and FL2（Ω） be a reducing subspace of L2（Rd）. This paper characterizes bounded measurable sets in Rd which are the supports of Fourier transforms of M-refinable frame functi...Let M be a d × d expansive matrix, and FL2（Ω） be a reducing subspace of L2（Rd）. This paper characterizes bounded measurable sets in Rd which are the supports of Fourier transforms of M-refinable frame functions. As applications, we derive the characterization of bounded measurable sets as the supports of Fourier transforms of FMRA （W-type FMRA） frame scaling functions and MRA （W-type MRA） scaling functions for FL2（Ω）, respectively. Some examples are also provided.展开更多
基金This project is sponsored by the National Natural Science Foundation （40474041）, CNPC Young Innovation Fund （04E7040）, the Post-doctoral Research Station of Zhongyuan 0ilfield, Jiangsu 0ilfield, and CNPC Geophysical Laboratories at the China University of Petroleum （East China）.
文摘Beamlet sources have strong local and directional character and can easily accomplish local illumination and migration. Besides, they provide better migration results than conventional migration methods. We introduce the basic principles of beamlet prestack depth migration that includes a windowed Fourier transform and frame theory. We explain the Gabor-Daubechies （G-D） frame based on a Gaussian function. Beamlet decomposition provides information on the local space and direction of wavefield. We synthesize the beamlet source and beamlet records in the wavelet domain using both rectangle and Gaussian windows and then extrapolate the synthesized data with a Fourier finite-difference operator. We test the method using the standard Marmousi model. By comparing and analyzing the migration results of single directional beamlet and beamlets with different windows and directions, we demonstrate the validity of the prestack depth migration with Gaussian beamlets method.
基金Supported by Beijing Natural Science Foundation (No.1122008)the Scientific Research Common Programof Beijing Municipal Commission of Education (No.KM201110005030)
文摘Let M be a d × d expansive matrix, and FL2（Ω） be a reducing subspace of L2（Rd）. This paper characterizes bounded measurable sets in Rd which are the supports of Fourier transforms of M-refinable frame functions. As applications, we derive the characterization of bounded measurable sets as the supports of Fourier transforms of FMRA （W-type FMRA） frame scaling functions and MRA （W-type MRA） scaling functions for FL2（Ω）, respectively. Some examples are also provided.
