A fast algorithm for prestack Gaussian beam migration adopting the steepest descent approximation

In the past, prestack Gaussian beam migration adopted the steepest descent approximation to reduce the dimension of the integrals and speed up the computation. However, the simplified formula by the steepest descent approximation was still in the frequency domain, and it had to be evaluated at each frequency. To solve this problem, we present a fast algorithm by changing the order of the integrals. The innermost integral is regarded as a two-dimensional continuous function with respect to the real part and the imaginary part of the total traveltime. A lookup table corresponding to the value of the innermost integral is constructed at the sampling points. The value of the innermost integral at one imaging point can be obtained through interpolation in the constructed lookup table. The accuracy and efficiency of the fast algorithm are validated with the Marmousi dataset. The application to the Sigsbee2A dataset shows a good result.

[1]  D. Hale.  Computational aspects of Gaussian beam migration , 1992 .

[2]  Yingcai Zheng,et al.  Least-squares Gaussian beam migration , 2015 .

[3]  Roelof Versteeg,et al.  The Marmousi experience; velocity model determination on a synthetic complex data set , 1994 .

[4]  David H. Johnston.  Interpretation redefined for the year 2000, Part 1 , 1994 .

[5]  Samuel H. Gray,et al.  Amplitude calculations for 3D Gaussian beam migration using complex-valued traveltimes , 2010 .

[6]  M. M. Popov,et al.  Computation of wave fields in inhomogeneous media — Gaussian beam approach , 1982 .

[7]  Samuel H. Gray,et al.  Prestack Gaussian-beam depth migration in anisotropic media , 2007 .

[8]  N. R. Hill,et al.  Gaussian beam migration , 1990 .

[9]  D. Hale.  Migration by the Kirchhoff, slant stack, and Gaussian beam methods , 1992 .

[10]  Samuel H. Gray,et al.  Gaussian beam migration of common-shot records , 2005 .

[11]  Zheng-Zheng Zhou,et al.  Subsalt imaging for exploration, production, and development: A review , 2011 .

[12]  Yue Yu.  Amplitude-preserved Gaussian beam migration under complex topographic conditions , 2012 .

[13]  Arie Verdel,et al.  Depth migration by the Gaussian beam summation method , 2010 .

[14]  Tariq Alkhalifah,et al.  Gaussian beam depth migration for anisotropic media , 1995 .

[15]  N. E. Yadari.  True-amplitude vector-acoustic imaging: Application of Gaussian beams , 2015 .

[16]  M. Popov.  A new method of computation of wave fields using Gaussian beams , 1982 .

[17]  J. Paffenholz,et al.  SIGSBEE_2A Synthetic Subsalt Dataset - Image Quality as Function of Migration Algorithm and Velocity Model Error , 2002 .

[18]  Samuel H. Gray,et al.  True-amplitude Gaussian-beam migration , 2009 .

[19]  N. R. Hill,et al.  Prestack Gaussian‐beam depth migration , 2001 .

[20]  Samuel H. Gray.  Gaussian beam migration of common-shot records , 2004 .

[21]  S. Gray,et al.  Converted‐wave beam migration with sparse sources or receivers , 2015 .