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Error analysis of phase screen method in 3‐D
Author(s) -
Cheng Ningya,
Cheng Chuen Hon,
Toksöz M. Nafi
Publication year - 1996
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/96gl01601
Subject(s) - operator (biology) , error analysis , formalism (music) , term (time) , commutator , inverse , differential operator , phase (matter) , square root , mean squared error , mathematical analysis , partial differential equation , mathematics , physics , geometry , statistics , quantum mechanics , art , musical , biochemistry , chemistry , lie conformal algebra , repressor , transcription factor , visual arts , gene , lie group
The purpose of the research presented in this paper is to do an error analysis of the phase screen method for forward and inverse wave propagation calculations in 3D heterogeneous acoustic media. The differential operator formalism approach is used, which provides new insight into the phase screen method. Under the assumptions that backscattering and commutator term of operators R and Q are negligible, we derive a partial differential equation and its solution corresponding to the phase screen method. The errors introduced in these derivations are also obtained. For a one‐step (δ z ) phase screen calculation, the leading error term is in the first order of k 0 Δ z and proportional to the error from splitting the square‐root operator Q . The propagation angle should be less than 40 degrees to control the error from the splitting operator Q under 5%.