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Viscoacoustic prestack reverse time migration based onthe optimal time-space domain high-order finite-difference method

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Applied Geophysics 2014年第1期11卷 50-62,116页

作者：赵岩刘洋任志明中国石油大学油气资源与探测国家重点实验室北京102249 中国石油大学CNPC物探重点实验室北京102249

Prestack reverse time migration （RTM） is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of the steps of RTM is solving thewave equation and extrapolating the wave field forward and backward; therefore, solvingaccurately and efficiently the wave equation affects the imaging results and the efficiencyof RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference （FD） method to solve the viscoacoustic wave equation. Dispersion analysis andnumerical simulations show that the optimal time-space domain FD method is more accurateand suppresses the numerical dispersion. We use hybrid absorbing boundary conditions tohandle the boundary reflection. We also use source-normalized cross-correlation imagingconditions for migration and apply Laplace filtering to remove the low-frequency *** modeling suggests that the viscoacoustic wave equation RTM has higher imagingresolution than the acoustic wave equation RTM when the viscosity of the subsurface isconsidered. In addition, for the wave field extrapolation, we use the adaptive variable-lengthFD operator to calculate the spatial derivatives and improve the computational efficiencywithout compromising the accuracy of the numerical solution.

关键词： Reverse time migration, Viscoacoustic, Optimization, adaptive, Time-spacedomain finite-difference

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Local generalized empirical estimation of regression

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Science China Mathematics 2004年第1期47卷 114-127页

作者： Doksum Kjell Department of Statistics University of California at Berkeley CA 94720 USA

Let f(x) be the density of a design variable X and m(x) = E[Y|X = x] the regression function. Then m(x)= G(x)/f(x), where G(x)= m(x)f(x). The Dirac δ-function is used to define a generalized empirical function Gn(x) for G(x) whose expectation equals G(x). This generalized empirical function exists only in the space of Schwartz distributions,so we introduce a local polynomial of order p approximation to Gn(.) which provides estimators of the function G(x) and its derivatives. The density f(x) can be estimated in a similar manner. The resulting local generalized empirical estimator (LGE) of m(x) is exactly the Nadaraya-Watson estimator at interior points when p = 1, but on the boundary the estimator automatically corrects the boundary effect. Asymptotic normality of the estimator is established. Asymptotic expressions for the mean squared errors are obtained and used in bandwidth selection. Boundary behavior of the estimators is investigated in details. We use Monte Carlo simulations to show that the proposed estimator with p = 1 compares favorably with the Nadaraya-Watson and the popular local linear regression smoother.

关键词： boundary adaptive, Dirac δ-function, local polynomial, local empirical, Nadaraya-Watson estimator.

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