IMAGING OF VELOCITY SINGULARITIES WITH MULTISCALE OPERATORS

In this paper, by using the multiscale operator and based on the Beylk in'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 approx imation, the multiscale imaging formula is shown. For the band-limited inverse problem, based on the multiscale imaging formula in this pape r, the behavior of the velocity singularities can be analyzed across t he 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 i s obtained. Our method in this paper can suppress the effects of the n oise in the real world data and analyze the effect produced by band-li mited input data. (C) 1996 American Institute of Physics.