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Published byStewart Rodgers Modified over 8 years ago
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Reverse Time Migration of Prism Waves for Salt Flank Delineation
Wei Dai, WesternGeco Gerard T. Schuster, King Abdullah University of Science and Technology Sep 25, 2013
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Outline Introduction and motivation Theory Numerical Results Summary
L model Salt model Summary
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Introduction Problem: Vertical boundaries (salt flanks) are difficult to image because they are usually not illuminated by primary reflections. Solution: Prism waves contain valuable information.
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Conventional Method When the known boundaries are embedded in the velocity model, conventional RTM can migrate prism waves correctly.
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Recorded Trace ๐
๐ ๐ = ๐
๐ ๐ ๐ + ๐
๐ (๐|๐)
Time (s) 2
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Horizontal Reflector Embedded in the Velocity
Z (km) 3 X (km) 6 Z (km) 3 Conventional RTM Image
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๐ ๐๐๐ (๐)= ๐ ๐ ๐ ๐พ โ (๐)๐ฎ โ ๐ ๐ ๐ฎ โ ๐ ๐ ๐
๐ ๐
Reverse Time Migration Formula ๐ ๐๐๐ (๐)= ๐ ๐ ๐ ๐พ โ (๐)๐ฎ โ ๐ ๐ ๐ฎ โ ๐ ๐ ๐
๐ ๐ Angular Freq. Source Spectrum Greenโs functions Input Data Z (km) 3 ๐ ๐ฎ ๐ ๐ = ๐ฎ ๐ ๐ ๐ + ๐ฎ ๐ (๐|๐) ๐ฎ ๐ ๐ = ๐ฎ ๐ ๐ ๐ + ๐ฎ ๐ (๐|๐)
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๐ ๐๐๐ ๐ = ๐ ๐ ๐ ๐พ โ ๐ ๐ฎ ๐ โ ๐ ๐ + ๐ฎ ๐ โ ๐ ๐ ๐ฎ ๐ โ ๐ ๐ + ๐ฎ ๐ โ ๐ ๐
๐ ๐๐๐ ๐ = ๐ ๐ ๐ ๐พ โ ๐ ๐ฎ ๐ โ ๐ ๐ + ๐ฎ ๐ โ ๐ ๐ ๐ฎ ๐ โ ๐ ๐ + ๐ฎ ๐ โ ๐ ๐ [ ๐
๐ ๐ ๐ + ๐
๐ ๐ ๐ ] = ๐ ๐ ๐ ๐พ โ ๐ [ ๐ฎ ๐ โ ๐ ๐ ๐ฎ ๐ โ ๐ ๐ ๐
๐ ๐ ๐ + ๐ฎ ๐ โ ๐ ๐ ๐ฎ ๐ โ ๐ ๐ ๐
๐ ๐ ๐ Ellipses + ๐ฎ ๐ โ ๐ ๐ ๐ฎ ๐ โ ๐ ๐ ๐
๐ ๐ ๐ + ๐ฎ ๐ โ ๐ ๐ ๐ฎ ๐ โ ๐ ๐ ๐
๐ ๐ ๐ Rabbit Ears + ๐ฎ ๐ โ ๐ ๐ ๐ฎ ๐ โ ๐ ๐ ๐
๐ ๐ ๐ + ๐ฎ ๐ โ ๐ ๐ ๐ฎ ๐ โ ๐ ๐ ๐
๐ ๐ ๐ Prism Wave Kernels + Other terms.] Z (km) 3 X (km) 6
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Migration of Prism Waves
๐ ๐๐๐ = ๐ ๐ ๐ ๐พ โ ๐ ๐ฎ ๐ โ ๐ ๐ ๐ฎ ๐ โ ๐ ๐ ๐
๐ ๐ ๐ ๐ฎ ๐ ๐ ๐ = ๐ ๐ ๐ ๐ โฒ ๐ฎ ๐ ๐ โฒ ๐ ๐ฎ ๐ ๐ โฒ ๐ ๐
๐โฒ Born Modeling Z (km) 3 X (km) 6
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Migration of Prism Waves
๐ฅ ๐ ๐ฅ ๐ ๐ฅ 2 Z (km) ๐ฅ 1 3 ๐ฅ 2 โฒ ๐ฅ ๐ โ ๐ฅ 2 โฒ ๐ + ๐ฅ 2 โ ๐ฅ ๐ ๐ = ๐ ๐ ๐ Z (km) 3 X (km) 6
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Migration of Prism Waves
๐ ๐๐๐ = ๐ ๐ ๐ ๐พ โ ๐ ๐ฎ ๐ โ ๐ ๐ ๐ฎ ๐ โ ๐ ๐ ๐
๐ ๐ ๐ ๐ฎ ๐ ๐ ๐ = ๐ ๐ ๐ ๐ โฒ ๐ฎ ๐ ๐ โฒ ๐ ๐ฎ ๐ ๐ โฒ ๐ ๐
๐โฒ Born Modeling Z (km) 3 X (km) 6
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Migration of Prism Waves
Z (km) 3 Z (km) 3 X (km) 6
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Outline Introduction and motivation Theory Numerical Results Summary
L model Salt model Summary
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The L Model Model size: 301 x 601 Source freq: 20 hz shots: 32
geophones: 601 Z (km) 3 X (km) 6
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A Shot Gather of the L Model
Time (s) 6.4 X (km) 6
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Prism Wavepath Z (km) 3 Z (km) 3 X (km) 6
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RTM Image /w Smooth Velocity
Z (km) 3 X (km) 6 Z (km) 3 Migration Image of Prism Waves
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The Salt Model Model size: 601 x 601 Source freq: 20 hz shots: 601
Model size: 601 x 601 Source freq: 20 hz shots: 601 Z (km) geophones: 601 6 X (km) 6
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A Shot Gather of the Salt Model
Time (s) 10 X (km) 6
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RTM with Smooth Velocity
Migration Velocity RTM Image Z (km) 6 X (km) 6 X (km) 6
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If the Horizontal Reflectors are embedded in the velocity
Migration Velocity RTM Image Z (km) 6 X (km) 6 X (km) 6
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New Method Migration Velocity Conv. RTM Image Prism Wave Image
Z (km) 6 Migration Velocity Conv. RTM Image Prism Wave Image RTM Image Z (km) X (km) 6 6 X (km) 6
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New Method Migration Velocity Prism Wave Image Filtered RTM Image
Z (km) 6 Migration Velocity X (km) 6 Prism Wave Image Filtered RTM Image Z (km) 6 X (km) 6
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Final Image Horizontal Final Image RTM Image Vertical Z (km) 6 Z (km)
Z (km) 6 Horizontal Final Image RTM Image Vertical Z (km) X (km) 6 6 X (km) 6
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Summary I propose a new method to migrate prism waves separately. Avoid the modification of migration velocity. Reduce cross interference between different waves by migrating different waves in separated steps. Limitations Computational cost is doubled.
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Thanks
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