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A Simple and Efficient Space Domain Implementation of the Turning Bands Method
Author(s) -
Dietrich C. R.
Publication year - 1995
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/94wr01457
Subject(s) - circulant matrix , simple (philosophy) , line (geometry) , fourier transform , fast fourier transform , algorithm , covariance , embedding , discrete fourier transform (general) , process (computing) , frequency domain , function (biology) , space (punctuation) , computer science , domain (mathematical analysis) , mathematics , mathematical analysis , short time fourier transform , fourier analysis , geometry , statistics , artificial intelligence , philosophy , epistemology , evolutionary biology , biology , operating system
Given a correlation function c ( x ) with x in R n , the turning bands method (TBM( for n = 2 and 3 constructs realizations of an n ‐dimensional and stationary process Y ∼ N (O, c ( x )) from appropriately summed line processes. Therefore an implementation of TBM calls naturally for fast and accurate generations of line realizations. These have generally been generated by a spectral approach since the Fourier transform of the line covariances is linked in a very simple fashion to the n ‐dimensional Fourier transform of c ( x ). However, we show that in many instances a space domain implementation of TBM, with line realizations obtained from a circulant embedding method, has advantages over a spectral implementation in that without increase in computational costs (1) the line realizations display exactly the required covariance structure, (2) knowledge of the spectral density of the process Y is not required, and (3) fine tuning of line process parameters is not needed.