Angle-domain parameters computed via weighted slant-stack Claudio GuerraSEP-131

Motivation Post migration processes in the reflection-angle domain –migration-velocity analysis –residual multiple attenuation –AVA –regularization of the least-squares inverse imaging Compensate for illumination problems in ADCIGs

Outline Introduction Weighted OFF2ANG Results Conclusions

Introduction SEP125 - Valenciano and Biondi –Compute the Hessian in the angle domain by chaining operators T *, H and T. S(m) = ½||Lm h – d obs || 2 = ½||LTm  – d obs || 2  2 S(m)/  m 2 = T * L * LT H(x,  ; x ’,  ’ ) = T * ( ,h) H ( x, h ; x ’, h ’ ) T( ,h) H(x,  ; x ’,  ’ ) – angle-domain Hessian H ( x, h ; x ’, h ’) – offset-domain Hessian m  – ADCIGm h – SODCIG T( ,h) – angle-to-offset transformation T * ( ,h) – offset-to-angle transformation L – modeling operatorL * - migration

angle Introduction SEP125 - Valenciano and Biondi –“The Hessian... in the angle dimension lacks of resolution to be able to interpret which angles get more illumination.” offset depth offset angle depth

Weighted OFF2ANG Assymptotic approximation of Kirchhoff Migration –Main contribution comes from the vicinity of the stationary point Bleistein(1987) and Tygel et.al(1993) –migration with two different weights –division of the migrated images t z M(x,z) x –  * N(  *,t)

Weighted OFF2ANG – phase behavior Slant – stack Q – ADCIGP – SODCIG  – stacking line f (z) – wavelet z r – reflector A – amplitude h – subsurface offset  – reflection angle – rho filter

Weighted OFF2ANG – phase behavior Slant – stack Q – ADCIG  – phase function f (z) – wavelet A – amplitude h * – stationary offset  – reflection angle

Weighted OFF2ANG Weighted Slant – stack – ADCIG  – phase function f (z) – wavelet A – amplitude h * – stationary offset  – reflection angle

Results Sigsbee2b depth cmp

Results – Input data offset depth offset SODCIGDiagonal of the Hessian

Results –ADCIGs angle angle angle depth angle angle angle depth angle angle angle Main diagonal

Results – Angle sections 15 o 30 o 40 o depth cmp depth cmp depth cmp depth cmp depth cmp depth cmp Main diagonal

Results – Amplitude correction angle angle angle depth angle angle angle depth Main diagonal

Results – Amplitude correction 15 º angle section depth cmp depth cmp 30 º angle section depth cmp 45 º angle section Main diagonal

Results – Amplitude correction depth cmp Angle stack

Main diagonal5 th off-diagonal Results – 0 o Off-diagonals depth cmp 15 th off-diagonal

Main diagonal5 th off-diagonal Results – 15º Off-diagonals depth cmp 15 th off-diagonal

Conclusions Alternative approach to transform the Hessian to the angle domain Well balanced ADCIGs –Better angle-stack Off-diagonal terms –Still no direct application