• journal_title：Geophysics
• Contributor：Kenneth P. Bube ; Tamas Nemeth ; Joseph P. Stefani ; Wei Liu ; Kurt T. Nihei ; Ray Ergas ; Linbin Zhang
• Publisher：Society of Exploration Geophysicists
• Date：2012-
• Format：text/html
• Language：en
• Identifier：10.1190/geo2011-0249.1
• journal_abbrev：Geophysics
• issn：0016-8033
• volume：77
• issue：5
• firstpage：T157
• section：Seismic Modeling and Wave Propagation

We derive and compare first-order wave propagation systems for variable-tilt elastic and acoustic tilted transversely isotropic (TTI) media. Acoustic TTI systems are commonly used in reverse-time migration. Starting initially with homogeneous vertical transversely isotropic (VTI) media, and then extending to heterogeneous variable-tilt TI media, we derive a pseudoacoustic <mml:math display="inline"><mml:mrow><mml:mn>5</mml:mn><mml:mo>×</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:math>5×5 first-order system of differential equations by setting the shear-wave speeds to zero and simplifying the full-elastic system accordingly. This <mml:math display="inline"><mml:mn>5</mml:mn><mml:mo>×</mml:mo><mml:mn>5</mml:mn></mml:math>5×5 system conserves a complete energy, but only when the anelliptic anisotropy parameter <mml:math display="inline"><mml:mi>η</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:math>η>0. For <mml:math display="inline"><mml:mi>η</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>η=0 (including isotropic media), the system allows linearly time-growing and spatially nonpropagating nonphysical solutions frequently taken for numerical noise. We modified this <mml:math display="inline"><mml:mn>5</mml:mn><mml:mo>×</mml:mo><mml:mn>5</mml:mn></mml:math>5×5 acoustic first-order system by changing the stress variables to obtain a system that stays stable for <mml:math display="inline"><mml:mi>η</mml:mi><mml:mo>≥</mml:mo><mml:mn>0</mml:mn></mml:math>η≥0. This system for homogeneous VTI media is generalized to heterogeneous variable-tilt TI media by rotating the stress and strain variables in the full elastic system before setting the shear-wave speeds to zero; the system obtained can be greatly simplified by combining the rotational terms, resulting in only one rotation and extra lower-order terms compared to the <mml:math display="inline"><mml:mrow><mml:mn>5</mml:mn><mml:mo>×</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:math>5×5 first-order acoustic system for VTI media. This new system can be simplified further by neglecting the lower-order terms. Both systems (with and without lower-order terms) conserve the same complete energy. Finally, the corresponding <mml:math display="inline"><mml:mn>9</mml:mn><mml:mo>×</mml:mo><mml:mn>9</mml:mn></mml:math>9×9 full elastic system for variable-tilt acoustic TI media can be used for the purposes of benchmarking.