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High‐accuracy two‐interval approximation for normal‐moveout function in a multi‐layered anisotropic model
Author(s) -
Blias Emil
Publication year - 2013
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/1365-2478.12059
Subject(s) - computation , offset (computer science) , anisotropy , approximation error , interval (graph theory) , normal moveout , inversion (geology) , function (biology) , linear approximation , regional geology , function approximation , approximation theory , born approximation , mathematics , mathematical analysis , algorithm , computer science , geology , physics , optics , scattering , telmatology , hydrogeology , quantum mechanics , nonlinear system , seismology , combinatorics , biology , tectonics , evolutionary biology , machine learning , artificial neural network , programming language , geotechnical engineering
ABSTRACT This paper discusses reducing computation costs for traveltime calculations in multi‐layered anisotropic models. Fomel and Stovas ([Fomel S., 2010]) suggested a two‐ray five‐parameter approximation that they named ‘generalized’ because it reduces to several known three‐parameter forms. Model tests, demonstrated by the authors, showed that this generalized approximation provided very high accuracy, implying it can be used in place of the exact moveout function in modelling, migration and traveltime inversion. However, detailed model studies show that for some models, with a high‐velocity layer, this approximation leads to significant errors. I develop a new three‐ray eight‐parameter approximation that provides higher accuracy and can replace the exact traveltime function that requires numerical ray calculations for each receiver. I call it a ‘two‐interval approximation’ because it uses two different equations for two offset intervals. Model tests show that this two‐interval approximation can bring much higher accuracy compared to the generalized approximation due to the use of an additional reference ray. The two‐interval new approximation can be used instead of exact traveltimes for many practical purposes.