ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
In this paper, by using the multiscale operator and based on the Beylkin's formula [J. Math. Phys. 26, 99–108 (1985)], the inversion method of velocity singularities is presented, and by applying the multiscale operator to upward scattered data represented by the Kirchhoff approximation, the multiscale imaging formula is shown. For the band-limited inverse problem, based on the multiscale imaging formula in this paper, the behavior of the velocity singularities can be analyzed across the multiscale and the formula to reconstruct the velocity is obtained from the output of the multiscale operator interpreted in the terms of the Kirchhoff-approximate data. Particularly, at wide offset and even postcritical case, for the full-band input data, the same result with Beylkin's in the above reference about the velocity discontinuities is obtained. Our method in this paper can suppress the effects of the noise in the real world data and analyze the effect produced by band-limited input data. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.531411
Permalink