The stationary phase analysis of the Kirchhoff-type demigrated field |
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| Authors: | Jian-Guo Sun |
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| Institution: | (1) Department of Pulmonary Diseases, Institute for Cardiovascular Research, VU University Medical Center, De Boelelaan 1117, 1081 HV Amsterdam, The Netherlands;(2) Department of Physics and Medical Technology, Institute for Cardiovascular Research, VU University Medical Center, Amsterdam, The Netherlands;(3) Department of Cardiology, Leiden University Medical Center, Leiden, The Netherlands;(4) Department of Physiology, Institute for Cardiovascular Research, VU University Medical Center, Amsterdam, The Netherlands;(5) BMEYE B.V., Amsterdam, The Netherlands |
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| Abstract: | In the literature, stationary phase analysis of Kirchhoff-type demigrated fields is carried out mainly under the following
two conditions: (1) The considered isochrone and the target reflector are tangential to each other; (2) The spatial duration
of the wavelet of the depthmigrated image is short. For the isochrones that are not tangential to the target reflector and
for the depth-migrated images that have a large spatial duration, the published stationary phase equation for the demigrated
field will become invalid. For performing the stationary phase analysis of the Kirchhoff-type demigrated field under the conditions
that the considered isochrone and the target reflector are not tangential to each other and that the spatial duration of the
wavelet of the depth-migrated image is not short (the general conditions), I derive the formulas for the factors appearing
in the stationary phase formula in two dimensions, from which I find that for different isochrones the horizontal coordinates
of the stationary point of the depth difference function are different. Also, the equation for the Kirchhoff-type demigrated
field consists of two parts. One is the true-amplitude demigrated signal and the other is the amplitude distortion factor.
From these facts the following two conclusions can be drawn: (1) A demigrated signal is composed of many depth-migrated images
and one depth-migrated image trace provides only one sample to the demigrated signal; and (2) The amplitude distortion effect
is an effect inherent in the Kirchhoff-type demigration and cannot be eliminated during demigration. If this effect should
be eliminated, one should do an amplitude correction after demigration. |
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| Keywords: | Kirchhoff-type demigration stationary phase analysis amplitude distortion |
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