Determination of finite-difference weights using scaled binomial windows

Type
Article

Authors
Chu, Chunlei
Stoffa, Paul L.

Date
2012-05

Abstract
The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.

Citation
Chu, C., & Stoffa, P. L. (2012). Determination of finite-difference weights using scaled binomial windows. GEOPHYSICS, 77(3), W17–W26. https://doi.org/10.1190/geo2011-0336.1

Acknowledgements
Stoffa would like to acknowledge the King Abdullah Universityof Science and Technology for their support of his research. We aregrateful to associate editor Stig Hestholm and the reviewers for theirconstructive comments which helped improve the original manuscript.We thank ConocoPhillips for permission to publishthis work.

Publisher
Society of Exploration Geophysicists

Journal
GEOPHYSICS

DOI
10.1190/geo2011-0336.1

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