Wave-equation common-angle gathers for converted waves Paul Sava & Sergey Fomel Bureau of Economic Geology University of Texas at Austin

Imaging condition Image Source wavefield Receiver wavefield Wavefield reconstruction Imaging sketch S R Angle decomposition Angle-dependent reflectivity

Wavefield reconstruction Source wavefield Receiver wavefield S R

Imaging condition Rickett & Sava (2002) Biondi & Symes (2004) Sava & Fomel (2005) Claerbout (1985) Space shift: h={h x,h y,h z } Location: m={x,y,z}

Angle decomposition Reflection angle Azimuth angle Space shift: h={h x,h y,h z } Location: m={x,y,z} Message: images obtained by space-shift imaging contain sufficient information for converted-wave angle decomposition!

Angle decomposition

PP reflection geometry psps prpr 2p m 2p h

PS reflection geometry psps prpr 2p h 2p m

PS reflection geometry psps prpr 2p h 2p m

PS reflection geometry 3 relations, can eliminate 2 variables:

PS transformation Example: eliminate  and. 3 relations, can eliminate 2 variables. Sava & Fomel (2005)

PS transformation (2D) Example: eliminate  and. 3 relations, can eliminate 2 variables. Weglein & Stolt (1985) Sava & Fomel (2003)

Angle decomposition algorithm

Example distance depth v P =2 km/s v S =1 km/s

PP dataPS data surface offset time surface offset time

PP image distance depth

PS image distance depth

PP offset-gatherPS offset-gather space-shift depth space-shift depth

PP angle-gatherPS angle-gather tan(  0 ) depth tan(  0 ) depth PP transformation

PP angle-gatherPS angle-gather depth PS transformation tan(  0 )tan(  )

Example 2 distance depth acquisition shots: 51 at 0.2km receivers: 401 at 0.025km Modified from Baina et al. (2005):

PP dataPS data surface offset time surface offset time

PP imagePS image distance depth distance depth Uneven amplitude

PP offset-gathersPS offset-gathers depth space-shift

PP angle-gathersPS angle-gathers depth angle

PP angle-gatherPS angle-gather angle depth angle depth PP transformation

PP angle-gatherPS angle-gather angle depth angle depth PS transformation

PP angle-gathersPS angle-gathers depth angle Normal polarity

PP angle-gathersPS angle-gathers depth angle Reversed polarity

PP stackPS stack distance depth distance depth

Conclusions Angle decomposition for converted-waves Space-shift imaging condition –Independent of extrapolation method –Contains all required information Real challenge: what are the velocity models?