The relation between Gaussian beams and Maslov asymptotic theory |
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Authors: | Luděk Klime? Reviewer I P?en?ík |
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Institution: | (1) Institute of Geophysics, Charles University, Prague |
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Abstract: | Summary The application of Maslov asymptotic theory in a general 3-D mixed subspace of 6-D complex phase space is proposed to obtain the integral superpositions of Gaussian packets and beams. The ray method and the superposition of plane waves (Maslov method of Chapman and Drummond 7]) are special limiting cases of the above mentioned approach. The same high-frequency asymptotic expansion formulae for seismic body waves were derived previously in 8] using the Gaussian beam method.
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![gcy](/content/j0317567508831v2/xxlarge1075.gif) n![rcy](/content/j0317567508831v2/xxlarge1088.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) m a![ncy](/content/j0317567508831v2/xxlarge1085.gif) m a n![rcy](/content/j0317567508831v2/xxlarge1088.gif) ¶rt;![lcy](/content/j0317567508831v2/xxlarge1083.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) ![zhcy](/content/j0317567508831v2/xxlarge1078.gif) ![iecy](/content/j0317567508831v2/xxlarge1077.gif) ![ncy](/content/j0317567508831v2/xxlarge1085.gif) ¶rt;![lcy](/content/j0317567508831v2/xxlarge1083.gif) n![ocy](/content/j0317567508831v2/xxlarge1086.gif) ![lcy](/content/j0317567508831v2/xxlarge1083.gif) ![ucy](/content/j0317567508831v2/xxlarge1091.gif) ![chcy](/content/j0317567508831v2/xxlarge1095.gif) ![iecy](/content/j0317567508831v2/xxlarge1077.gif) u u m![iecy](/content/j0317567508831v2/xxlarge1077.gif) ![gcy](/content/j0317567508831v2/xxlarge1075.gif) a![lcy](/content/j0317567508831v2/xxlarge1083.gif) ![softcy](/content/j0317567508831v2/xxlarge1100.gif) ![ncy](/content/j0317567508831v2/xxlarge1085.gif) ![ycy](/content/j0317567508831v2/xxlarge1099.gif) ![scy](/content/j0317567508831v2/xxlarge1089.gif) n![iecy](/content/j0317567508831v2/xxlarge1077.gif) n![ocy](/content/j0317567508831v2/xxlarge1086.gif) u u a![ucy](/content/j0317567508831v2/xxlarge1091.gif) ![scy](/content/j0317567508831v2/xxlarge1089.gif) ![scy](/content/j0317567508831v2/xxlarge1089.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) ![vcy](/content/j0317567508831v2/xxlarge1074.gif) ![ycy](/content/j0317567508831v2/xxlarge1099.gif) na![kcy](/content/j0317567508831v2/xxlarge1082.gif) m![ocy](/content/j0317567508831v2/xxlarge1086.gif) u n![ucy](/content/j0317567508831v2/xxlarge1091.gif) ![chcy](/content/j0317567508831v2/xxlarge1095.gif) ![kcy](/content/j0317567508831v2/xxlarge1082.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) . ![Scy](/content/j0317567508831v2/xxlarge1057.gif) 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m![scy](/content/j0317567508831v2/xxlarge1089.gif) n![iecy](/content/j0317567508831v2/xxlarge1077.gif) ua![lcy](/content/j0317567508831v2/xxlarge1083.gif) ![softcy](/content/j0317567508831v2/xxlarge1100.gif) ![ncy](/content/j0317567508831v2/xxlarge1085.gif) ![ycy](/content/j0317567508831v2/xxlarge1099.gif) u n![rcy](/content/j0317567508831v2/xxlarge1088.gif) ¶rt;![iecy](/content/j0317567508831v2/xxlarge1077.gif) ![lcy](/content/j0317567508831v2/xxlarge1083.gif) ![softcy](/content/j0317567508831v2/xxlarge1100.gif) ![ncy](/content/j0317567508831v2/xxlarge1085.gif) ![ycy](/content/j0317567508831v2/xxlarge1099.gif) u ![scy](/content/j0317567508831v2/xxlarge1089.gif) ![lcy](/content/j0317567508831v2/xxlarge1083.gif) ![ucy](/content/j0317567508831v2/xxlarge1091.gif) a![yacy](/content/j0317567508831v2/xxlarge1103.gif) u n![rcy](/content/j0317567508831v2/xxlarge1088.gif) ¶rt;![lcy](/content/j0317567508831v2/xxlarge1083.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) ![zhcy](/content/j0317567508831v2/xxlarge1078.gif) ![iecy](/content/j0317567508831v2/xxlarge1077.gif) ![ncy](/content/j0317567508831v2/xxlarge1085.gif) ![ncy](/content/j0317567508831v2/xxlarge1085.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) ![gcy](/content/j0317567508831v2/xxlarge1075.gif) n ¶rt;![khcy](/content/j0317567508831v2/xxlarge1093.gif) ¶rt;a. ![Tcy](/content/j0317567508831v2/xxlarge1058.gif) ![zhcy](/content/j0317567508831v2/xxlarge1078.gif) a![mcy](/content/j0317567508831v2/xxlarge1084.gif) ![ycy](/content/j0317567508831v2/xxlarge1099.gif) ![vcy](/content/j0317567508831v2/xxlarge1074.gif) ![ycy](/content/j0317567508831v2/xxlarge1099.gif) ![scy](/content/j0317567508831v2/xxlarge1089.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) ![kcy](/content/j0317567508831v2/xxlarge1082.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) a m m![ncy](/content/j0317567508831v2/xxlarge1085.gif) ![ycy](/content/j0317567508831v2/xxlarge1099.gif) a u nm mu![chcy](/content/j0317567508831v2/xxlarge1095.gif) ![iecy](/content/j0317567508831v2/xxlarge1077.gif) ![scy](/content/j0317567508831v2/xxlarge1089.gif) u ![fcy](/content/j0317567508831v2/xxlarge1092.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) ![rcy](/content/j0317567508831v2/xxlarge1088.gif) ![mcy](/content/j0317567508831v2/xxlarge1084.gif) ![ucy](/content/j0317567508831v2/xxlarge1091.gif) ![lcy](/content/j0317567508831v2/xxlarge1083.gif) ![bcy](/content/j0317567508831v2/xxlarge1073.gif) ![ycy](/content/j0317567508831v2/xxlarge1099.gif) u a![ncy](/content/j0317567508831v2/xxlarge1085.gif) ![softcy](/content/j0317567508831v2/xxlarge1100.gif) ![shchcy](/content/j0317567508831v2/xxlarge1097.gif) n![ocy](/content/j0317567508831v2/xxlarge1086.gif) ![lcy](/content/j0317567508831v2/xxlarge1083.gif) ![ucy](/content/j0317567508831v2/xxlarge1091.gif) ![chcy](/content/j0317567508831v2/xxlarge1095.gif) ![iecy](/content/j0317567508831v2/xxlarge1077.gif) ![ncy](/content/j0317567508831v2/xxlarge1085.gif) ![mcy](/content/j0317567508831v2/xxlarge1084.gif) m ¶rt;![ocy](/content/j0317567508831v2/xxlarge1086.gif) a![ucy](/content/j0317567508831v2/xxlarge1091.gif) ![scy](/content/j0317567508831v2/xxlarge1089.gif) ![scy](/content/j0317567508831v2/xxlarge1089.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) ![vcy](/content/j0317567508831v2/xxlarge1074.gif) ![ycy](/content/j0317567508831v2/xxlarge1099.gif) n![ucy](/content/j0317567508831v2/xxlarge1091.gif) ![chcy](/content/j0317567508831v2/xxlarge1095.gif) ![kcy](/content/j0317567508831v2/xxlarge1082.gif) ![ocy](/content/j0317567508831v2/xxlarge1086.gif) 8].
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