Determination of finite-difference weights using scaled binomial windows

Chunlei Chu, Paul L. Stoffa

Research output: Contribution to journalArticlepeer-review

82 Citations (SciVal)

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.
Original languageEnglish (US)
Pages (from-to)W17-W26
Number of pages1
JournalGEOPHYSICS
Volume77
Issue number3
DOIs
StatePublished - May 2012
Externally publishedYes

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