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Estimation of a two‐dimensional seismic compressional‐wave velocity distribution by iterative tomographic imaging
Author(s) -
Zhu Xianhuai,
McMechan George A.
Publication year - 1989
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/ima.1850010103
Subject(s) - slowness , ray tracing (physics) , geology , refraction , tomography , matrix (chemical analysis) , iterative method , geometry , geodesy , optics , mathematical analysis , mathematics , algorithm , physics , seismology , materials science , composite material
Two‐dimensional velocity distributions may be estimated using iterative tomographic imaging. The medium is parameterized as a grid of small rectangular elements, each of which has constant (unknown) slowness ( s ); the data are refraction travel‐times ( t ) picked from the real data, which are transmitted between sources and recorders both located on the Earth's surface. Slowness estimation is performed by solution of the system of equations t = Ds T where D is a matrix of ray segment lengths, and T denotes the vector transpose. The solution involves minimization of the difference between the real and predicted travel‐times and is equally applicable to under and over‐determined problems. As matrix D is very large it cannot be inverted directly, and a row‐action, simultaneous iterative reconstruction technique is used. Predicted travel‐times are obtained by vectorized ray tracing. Rays are updated every few iterations so that they are internally consistent with the velocity estimated by tomography. The wider the source and recording apertures, the greater the depths that can be imaged. Rays refracted at the shallowest depths contain independent constraints that cannot be replaced by increasing the amount of data refracted at greater depths.