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Gao C.,Jilin University | Gao C.,Laboratory for Integrated Geophysical Interpretation Theory | Sun J.,Jilin University | Sun J.,Laboratory for Integrated Geophysical Interpretation Theory
Jilin Daxue Xuebao (Diqiu Kexue Ban)/Journal of Jilin University (Earth Science Edition) | Year: 2015

To disclose the influence of the efficiency and the precision of the local plane wave decomposition method on Gaussian beam migration, we analyze three local plane wave decomposition methods in time domain, frequency domain, and frequency-wavenumber domain, and deduce the formulae of these three methods. The comparison of computational accuracy and efficiency are showed based on the characters of the local plane wave decomposition in different domains. The comparative analysis indicates that the local plane wave decomposition in frequency-wavenumber domain is not only more accurate but also more efficient, and can provide precise data for migration. ©, 2015, Jilin University Press. All right reserved.

Gao C.,Jilin University | Gao C.,Laboratory for Integrated Geophysical Interpretation Theory | Sun J.-G.,Jilin University | Sun J.-G.,Laboratory for Integrated Geophysical Interpretation Theory | And 8 more authors.
Chinese Journal of Geophysics (Acta Geophysica Sinica) | Year: 2015

The traditional ray method don't perform well in the caustic and shadow region because its image accuracy is low. While the 2D Gaussian beam prestack depth migration in the frequency domain is less efficient because it needs calculation of Green function of all frequencies at imaging points. To solve these problems, we propose a novel method of 2D Gaussian beam migration of common-shot records in the time domain. In Gaussian beam migration, the source and recorded wavefield are both based on the Green functions staked by Gaussian beam from the source point and the receive point. Thus we can use the source wavefield and the recorded wavefield to generate the migrated image. Amplitude and exponential terms are both complex numbers, as Green function is complex and the traveltime expressed by the exponential term is called complex traveltime. This complex traveltime at the image point is determined by the second-order Taylor expansion of the nearest point's traveltime in the center ray. With the image condition, the migration formula is a triple integral of the horizontal slowness, vertical slowness and frequency, and the integrand is also a complex number. Focused on the real part of the integrand, the triple integral is reduced to a double integral by transforming the integral variable time to frequency using the Fourier transform. In the triple integral with the real part of the integrand, we change the sequence, and transform the frequency to the time by the Fourier transform to get the result that is two-fold integral of the horizontal slowness and the vertical slowness at the image time. The image time in the formula is the summation of the complex traveltime from the source point to the image point and that from the receiver point to the image point. Because the amplitude is a complex number, so the result with the imaginary of the amplitude is needed to transform the product of the Green function and the seismic data with the Hilbert transform. Then the triple integral becomes a double integral of the horizon slowness and the vertical slowness, and the image formula becomes the summation of two double integrals. The validity of the new method is proved on a complex numerical model. Using the Marmousi data set, the imaging result and computational efficiency of Gaussian beam migration in the time domain is compared with the method in the frequency domain. We can find that the image results of these two methods are similar, while the migration algorithm in the time domain takes less computing time. Then we compare the imaging result of Gaussian beam migration with that of Kirchhoff migration on the Sigsbee model. The migration result of Gaussian beam migration is clearer, especially for the region under the high-velocity geologic body. Gaussian beam migration section can show clear interfaces and even faults under this body which appears as migration illusion in the Kirchhoff migration. The result compared with the migrated imaging result based on the ray method indicates that Gaussian beam migration in the time domain has a higher accuracy. In this article, we present a novel method of 2D common-shot Gaussian beam migration in the time domain by employing the Fourier transform and the Hilbert transform. The ability of this method to deal with complicated models has been validated using the Marmousi data set and Sigsbee data set. Furthermore, because of holding the similar integral kernels, this method can be applied to other types of Gaussian beam migration straightforwardly, such as common-offset, common-receiver, common-midpoint and even 3D conditions. ©, 2015, Science Press. All right reserved.

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