Parameterization, stacking, and with the CRS Stack method - PowerPoint PPT Presentation

Parameterization, Motivation stacking & inversion of locally coherent events with the CRS Stack method Conventional depth imaging requires a macrovelocity Jürgen Mann model. Motivation Some common approaches: Introduction Travelt. tomography ◮ analysis of residual moveouts in depth-migrated Velocity analysis Objective common-image gathers (CIGs) CRS stack ➥ migration velocity analysis (MVA) Basic concepts Wavefield attributes ◮ direct inversion of traveltimes (and slopes) picked in Inversion prestack data Analytic approach Model-based approach ➥ traveltime tomography (stereo tomography) Conclusions ◮ inversion based on stacking velocities ➥ stacking velocity analysis & Dix inversion ☞ differences in applicability and complexity! Objective: W I T combine advantages to obtain initial model

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann ◮ requires extensive picking in prestack data Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann ◮ requires extensive picking in prestack data Motivation ➥ often difficult, especially in 3-D Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann ◮ requires extensive picking in prestack data Motivation ➥ often difficult, especially in 3-D Introduction Travelt. tomography ◮ optimum model matches forward-modeled and Velocity analysis Objective picked traveltimes CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann ◮ requires extensive picking in prestack data Motivation ➥ often difficult, especially in 3-D Introduction Travelt. tomography ◮ optimum model matches forward-modeled and Velocity analysis Objective picked traveltimes CRS stack ◮ no stacking and traveltime approximations required Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann ◮ requires extensive picking in prestack data Motivation ➥ often difficult, especially in 3-D Introduction Travelt. tomography ◮ optimum model matches forward-modeled and Velocity analysis Objective picked traveltimes CRS stack ◮ no stacking and traveltime approximations required Basic concepts Wavefield attributes ◮ limitations due to Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann ◮ requires extensive picking in prestack data Motivation ➥ often difficult, especially in 3-D Introduction Travelt. tomography ◮ optimum model matches forward-modeled and Velocity analysis Objective picked traveltimes CRS stack ◮ no stacking and traveltime approximations required Basic concepts Wavefield attributes ◮ limitations due to Inversion Analytic approach ◮ chosen model description (smooth, blocky, . . . ) Model-based approach Conclusions W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann ◮ requires extensive picking in prestack data Motivation ➥ often difficult, especially in 3-D Introduction Travelt. tomography ◮ optimum model matches forward-modeled and Velocity analysis Objective picked traveltimes CRS stack ◮ no stacking and traveltime approximations required Basic concepts Wavefield attributes ◮ limitations due to Inversion Analytic approach ◮ chosen model description (smooth, blocky, . . . ) Model-based approach ◮ forward-modeling method Conclusions W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann ◮ requires extensive picking in prestack data Motivation ➥ often difficult, especially in 3-D Introduction Travelt. tomography ◮ optimum model matches forward-modeled and Velocity analysis Objective picked traveltimes CRS stack ◮ no stacking and traveltime approximations required Basic concepts Wavefield attributes ◮ limitations due to Inversion Analytic approach ◮ chosen model description (smooth, blocky, . . . ) Model-based approach ◮ forward-modeling method Conclusions Extensions: W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann ◮ requires extensive picking in prestack data Motivation ➥ often difficult, especially in 3-D Introduction Travelt. tomography ◮ optimum model matches forward-modeled and Velocity analysis Objective picked traveltimes CRS stack ◮ no stacking and traveltime approximations required Basic concepts Wavefield attributes ◮ limitations due to Inversion Analytic approach ◮ chosen model description (smooth, blocky, . . . ) Model-based approach ◮ forward-modeling method Conclusions Extensions: ◮ picking of locally coherent reflection events: traveltime plus local dip W I T

Parameterization, Traveltime tomography stacking & inversion of locally coherent events with the CRS Stack method Basic properties: Jürgen Mann ◮ requires extensive picking in prestack data Motivation ➥ often difficult, especially in 3-D Introduction Travelt. tomography ◮ optimum model matches forward-modeled and Velocity analysis Objective picked traveltimes CRS stack ◮ no stacking and traveltime approximations required Basic concepts Wavefield attributes ◮ limitations due to Inversion Analytic approach ◮ chosen model description (smooth, blocky, . . . ) Model-based approach ◮ forward-modeling method Conclusions Extensions: ◮ picking of locally coherent reflection events: traveltime plus local dip ➥ stereo tomography W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann ◮ coherence analysis along second-order CMP Motivation traveltime approximation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann ◮ coherence analysis along second-order CMP Motivation traveltime approximation Introduction ➥ locally coherent event Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann ◮ coherence analysis along second-order CMP Motivation traveltime approximation Introduction ➥ locally coherent event Travelt. tomography Velocity analysis Objective ◮ coarse picking in velocity spectra CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann ◮ coherence analysis along second-order CMP Motivation traveltime approximation Introduction ➥ locally coherent event Travelt. tomography Velocity analysis Objective ◮ coarse picking in velocity spectra CRS stack ➥ simplified picking Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann ◮ coherence analysis along second-order CMP Motivation traveltime approximation Introduction ➥ locally coherent event Travelt. tomography Velocity analysis Objective ◮ coarse picking in velocity spectra CRS stack ➥ simplified picking Basic concepts Wavefield attributes ◮ interpolation Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann ◮ coherence analysis along second-order CMP Motivation traveltime approximation Introduction ➥ locally coherent event Travelt. tomography Velocity analysis Objective ◮ coarse picking in velocity spectra CRS stack ➥ simplified picking Basic concepts Wavefield attributes ◮ interpolation ☞ smooth stacking velocity model Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann ◮ coherence analysis along second-order CMP Motivation traveltime approximation Introduction ➥ locally coherent event Travelt. tomography Velocity analysis Objective ◮ coarse picking in velocity spectra CRS stack ➥ simplified picking Basic concepts Wavefield attributes ◮ interpolation ☞ smooth stacking velocity model Inversion Analytic approach Model-based approach Dix inversion: Conclusions W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann ◮ coherence analysis along second-order CMP Motivation traveltime approximation Introduction ➥ locally coherent event Travelt. tomography Velocity analysis Objective ◮ coarse picking in velocity spectra CRS stack ➥ simplified picking Basic concepts Wavefield attributes ◮ interpolation ☞ smooth stacking velocity model Inversion Analytic approach Model-based approach Dix inversion: Conclusions def ◮ assumption of 1-D model, v RMS = v stack or def = v DMO v RMS W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann ◮ coherence analysis along second-order CMP Motivation traveltime approximation Introduction ➥ locally coherent event Travelt. tomography Velocity analysis Objective ◮ coarse picking in velocity spectra CRS stack ➥ simplified picking Basic concepts Wavefield attributes ◮ interpolation ☞ smooth stacking velocity model Inversion Analytic approach Model-based approach Dix inversion: Conclusions def ◮ assumption of 1-D model, v RMS = v stack or def = v DMO v RMS ◮ conversion of RMS velocities to interval velocities W I T

Parameterization, Velocity analysis and Dix inversion stacking & inversion of locally coherent events with the CRS Stack method Stacking velocity analysis: Jürgen Mann ◮ coherence analysis along second-order CMP Motivation traveltime approximation Introduction ➥ locally coherent event Travelt. tomography Velocity analysis Objective ◮ coarse picking in velocity spectra CRS stack ➥ simplified picking Basic concepts Wavefield attributes ◮ interpolation ☞ smooth stacking velocity model Inversion Analytic approach Model-based approach Dix inversion: Conclusions def ◮ assumption of 1-D model, v RMS = v stack or def = v DMO v RMS ◮ conversion of RMS velocities to interval velocities ◮ fails for significant dip/curvature W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Initial model beyond Dix inversion: Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Initial model beyond Dix inversion: ◮ no picking in prestack data Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Initial model beyond Dix inversion: ◮ no picking in prestack data Motivation Introduction ◮ retain coherence based analysis Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Initial model beyond Dix inversion: ◮ no picking in prestack data Motivation Introduction ◮ retain coherence based analysis Travelt. tomography Velocity analysis Objective Required tools: CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Initial model beyond Dix inversion: ◮ no picking in prestack data Motivation Introduction ◮ retain coherence based analysis Travelt. tomography Velocity analysis Objective Required tools: CRS stack Basic concepts ◮ a generalized stacking velocity analysis Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Initial model beyond Dix inversion: ◮ no picking in prestack data Motivation Introduction ◮ retain coherence based analysis Travelt. tomography Velocity analysis Objective Required tools: CRS stack Basic concepts ◮ a generalized stacking velocity analysis Wavefield attributes Inversion ➥ Common-Reflection-Surface Stack Analytic approach Model-based approach Conclusions W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Initial model beyond Dix inversion: ◮ no picking in prestack data Motivation Introduction ◮ retain coherence based analysis Travelt. tomography Velocity analysis Objective Required tools: CRS stack Basic concepts ◮ a generalized stacking velocity analysis Wavefield attributes Inversion ➥ Common-Reflection-Surface Stack Analytic approach Model-based approach ◮ a suitable inversion method Conclusions W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Initial model beyond Dix inversion: ◮ no picking in prestack data Motivation Introduction ◮ retain coherence based analysis Travelt. tomography Velocity analysis Objective Required tools: CRS stack Basic concepts ◮ a generalized stacking velocity analysis Wavefield attributes Inversion ➥ Common-Reflection-Surface Stack Analytic approach Model-based approach ◮ a suitable inversion method Conclusions ➥ NIP-wave tomography W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Initial model beyond Dix inversion: ◮ no picking in prestack data Motivation Introduction ◮ retain coherence based analysis Travelt. tomography Velocity analysis Objective Required tools: CRS stack Basic concepts ◮ a generalized stacking velocity analysis Wavefield attributes Inversion ➥ Common-Reflection-Surface Stack Analytic approach Model-based approach ◮ a suitable inversion method Conclusions ➥ NIP-wave tomography Final model beyond second-order approximation: W I T

Parameterization, Objective stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Initial model beyond Dix inversion: ◮ no picking in prestack data Motivation Introduction ◮ retain coherence based analysis Travelt. tomography Velocity analysis Objective Required tools: CRS stack Basic concepts ◮ a generalized stacking velocity analysis Wavefield attributes Inversion ➥ Common-Reflection-Surface Stack Analytic approach Model-based approach ◮ a suitable inversion method Conclusions ➥ NIP-wave tomography Final model beyond second-order approximation: ➥ tomography with model-based diffraction traveltimes W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography Velocity analysis Objective t 2 ( ∆ x , h ) =( t 0 + 2 p · ∆ x ) 2 CRS stack Basic concepts � � ∆ x T M x ∆ x + h T M h h Wavefield attributes + 2 t 0 Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography Velocity analysis Objective t 2 ( ∆ x , h ) =( t 0 + 2 p · ∆ x ) 2 CRS stack Basic concepts � � ∆ x T M x ∆ x + h T M h h Wavefield attributes + 2 t 0 Inversion Analytic approach Model-based approach � p = 1 2 ∂ t / ∂ x � Conclusions � t 0 zero-offset traveltime ( ∆ x = 0 , h = 0 ) 2 ∂ 2 t / ∂ h 2 � h source/receiver offset M h = 1 � � ∆ x midpoint displacement ( ∆ x = 0 , h = 0 ) 2 ∂ 2 t / ∂ x 2 � p horizontal slowness M x = 1 � � ( ∆ x = 0 , h = 0 ) W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography ◮ fully automated coherence-based application Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography ◮ fully automated coherence-based application Velocity analysis Objective ◮ high-density analysis CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography ◮ fully automated coherence-based application Velocity analysis Objective ◮ high-density analysis CRS stack Basic concepts ➥ no pulse stretch, high resolution Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography ◮ fully automated coherence-based application Velocity analysis Objective ◮ high-density analysis CRS stack Basic concepts ➥ no pulse stretch, high resolution Wavefield attributes Inversion ◮ spatial stacking operator Analytic approach Model-based approach Conclusions W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography ◮ fully automated coherence-based application Velocity analysis Objective ◮ high-density analysis CRS stack Basic concepts ➥ no pulse stretch, high resolution Wavefield attributes Inversion ◮ spatial stacking operator Analytic approach Model-based approach ➥ much more prestack traces used Conclusions W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography ◮ fully automated coherence-based application Velocity analysis Objective ◮ high-density analysis CRS stack Basic concepts ➥ no pulse stretch, high resolution Wavefield attributes Inversion ◮ spatial stacking operator Analytic approach Model-based approach ➥ much more prestack traces used Conclusions ➥ enhanced signal/noise ratio W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography ◮ fully automated coherence-based application Velocity analysis Objective ◮ high-density analysis CRS stack Basic concepts ➥ no pulse stretch, high resolution Wavefield attributes Inversion ◮ spatial stacking operator Analytic approach Model-based approach ➥ much more prestack traces used Conclusions ➥ enhanced signal/noise ratio ◮ additional stacking parameters related to first and second traveltime derivatives W I T

Parameterization, Common-Reflection-Surface stack stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Generalization of stacking velocity analysis: Motivation ◮ second-order approximation of traveltime Introduction Travelt. tomography ◮ fully automated coherence-based application Velocity analysis Objective ◮ high-density analysis CRS stack Basic concepts ➥ no pulse stretch, high resolution Wavefield attributes Inversion ◮ spatial stacking operator Analytic approach Model-based approach ➥ much more prestack traces used Conclusions ➥ enhanced signal/noise ratio ◮ additional stacking parameters related to first and second traveltime derivatives ☞ geometrical interpretation W I T

Parameterization, CRS wavefield attributes in 2-D stacking & inversion of locally coherent events with the CRS Stack method Geometrical interpretation of stacking parameters: Jürgen Mann R R ξ ξ NIP N Motivation Introduction α α Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes NIP NIP Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, CRS wavefield attributes in 2-D stacking & inversion of locally coherent events with the CRS Stack method Geometrical interpretation of stacking parameters: Jürgen Mann R R ξ ξ NIP N Motivation Introduction α α Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes NIP NIP Inversion Analytic approach Model-based approach Conclusions Emergence direction and curvatures of hypothetical wavefronts: W I T

Parameterization, CRS wavefield attributes in 2-D stacking & inversion of locally coherent events with the CRS Stack method Geometrical interpretation of stacking parameters: Jürgen Mann R R ξ ξ NIP N Motivation Introduction α α Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes NIP NIP Inversion Analytic approach Model-based approach Conclusions Emergence direction and curvatures of hypothetical wavefronts: ◮ exploding point source W I T

Parameterization, CRS wavefield attributes in 2-D stacking & inversion of locally coherent events with the CRS Stack method Geometrical interpretation of stacking parameters: Jürgen Mann R R ξ ξ NIP N Motivation Introduction α α Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes NIP NIP Inversion Analytic approach Model-based approach Conclusions Emergence direction and curvatures of hypothetical wavefronts: ◮ exploding point source ☞ normal-incidence-point (NIP) wave W I T

Parameterization, CRS wavefield attributes in 2-D stacking & inversion of locally coherent events with the CRS Stack method Geometrical interpretation of stacking parameters: Jürgen Mann R R ξ ξ NIP N Motivation Introduction α α Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes NIP NIP Inversion Analytic approach Model-based approach Conclusions Emergence direction and curvatures of hypothetical wavefronts: ◮ exploding point source ☞ normal-incidence-point (NIP) wave ◮ exploding reflector W I T

Parameterization, CRS wavefield attributes in 2-D stacking & inversion of locally coherent events with the CRS Stack method Geometrical interpretation of stacking parameters: Jürgen Mann R R ξ ξ NIP N Motivation Introduction α α Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes NIP NIP Inversion Analytic approach Model-based approach Conclusions Emergence direction and curvatures of hypothetical wavefronts: ◮ exploding point source ☞ normal-incidence-point (NIP) wave ◮ exploding reflector ☞ normal wave W I T

Parameterization, stacking & inversion of CRS wavefield attributes in 3-D locally coherent events with the CRS Stack method Normal Wavefront Jürgen Mann z Motivation x Introduction Travelt. tomography Velocity analysis Objective y CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions Central Ray NIP Wavefront ☞ slowness vector and curvature matrices! W I T (Höcht, 2002)

Parameterization, Reformulation of traveltime formula stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Reformulation of traveltime formula stacking & inversion of locally coherent events with the CRS Stack In terms of traveltime derivatives: method Jürgen Mann t 2 ( ∆ x , h ) =( t 0 + 2 p · ∆ x ) 2 Motivation � � ∆ x T M x ∆ x + h T M h h + 2 t 0 Introduction Travelt. tomography Velocity analysis Objective � p = 1 2 ∂ t / ∂ x � CRS stack � ( ∆ x = 0 , h = 0 ) Basic concepts t 0 zero-offset traveltime Wavefield attributes 2 ∂ 2 t / ∂ h 2 � h source/receiver offset M h = 1 � Inversion � ∆ x midpoint displacement ( ∆ x = 0 , h = 0 ) Analytic approach Model-based approach p horizontal slowness 2 ∂ 2 t / ∂ x 2 � M x = 1 Conclusions � � ( ∆ x = 0 , h = 0 ) W I T

Parameterization, Reformulation of traveltime formula stacking & inversion of locally coherent events with the CRS Stack In terms of kinematic wavefield attributes: method Jürgen Mann t 2 ( ∆ x , h ) =( t 0 + 2 p · ∆ x ) 2 Motivation � � ∆ x T M x ∆ x + h T M h h + 2 t 0 Introduction Travelt. tomography Velocity analysis Objective p = 1 v 0 ( sin α cos ψ , sin α sin ψ ) T CRS stack Basic concepts t 0 zero-offset traveltime Wavefield attributes h source/receiver offset M h = 1 v 0 DK NIP D T Inversion ∆ x midpoint displacement Analytic approach Model-based approach p horizontal slowness M x = 1 v 0 DK N D T Conclusions W I T

Parameterization, Reformulation of traveltime formula stacking & inversion of locally coherent events with the CRS Stack In terms of kinematic wavefield attributes: method Jürgen Mann t 2 ( ∆ x , h ) =( t 0 + 2 p · ∆ x ) 2 Motivation � � ∆ x T M x ∆ x + h T M h h + 2 t 0 Introduction Travelt. tomography Velocity analysis Objective p = 1 v 0 ( sin α cos ψ , sin α sin ψ ) T CRS stack Basic concepts t 0 zero-offset traveltime Wavefield attributes h source/receiver offset M h = 1 v 0 DK NIP D T Inversion ∆ x midpoint displacement Analytic approach Model-based approach p horizontal slowness M x = 1 v 0 DK N D T Conclusions α , ψ azimuth & emergence angle of normal ray D transformation ray-centered/global coordinates K NIP , K N curvature matrix of NIP/normal wavefront W I T v 0 near-surface velocity

Parameterization, Inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann ◮ CRS attributes are well-suited for inversion Motivation Introduction ➥ NIP-wave tomography Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann ◮ CRS attributes are well-suited for inversion Motivation Introduction ➥ NIP-wave tomography Travelt. tomography Velocity analysis + Independent picks Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann ◮ CRS attributes are well-suited for inversion Motivation Introduction ➥ NIP-wave tomography Travelt. tomography Velocity analysis + Independent picks Objective + Picking only in stacked section CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann ◮ CRS attributes are well-suited for inversion Motivation Introduction ➥ NIP-wave tomography Travelt. tomography Velocity analysis + Independent picks Objective + Picking only in stacked section CRS stack + Highly automated Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann ◮ CRS attributes are well-suited for inversion Motivation Introduction ➥ NIP-wave tomography Travelt. tomography Velocity analysis + Independent picks Objective + Picking only in stacked section CRS stack + Highly automated Basic concepts Wavefield attributes + Vivid inversion scheme Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann ◮ CRS attributes are well-suited for inversion Motivation Introduction ➥ NIP-wave tomography Travelt. tomography Velocity analysis + Independent picks Objective + Picking only in stacked section CRS stack + Highly automated Basic concepts Wavefield attributes + Vivid inversion scheme Inversion – Inherent restriction to second order Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann ◮ CRS attributes are well-suited for inversion Motivation Introduction ➥ NIP-wave tomography Travelt. tomography Velocity analysis + Independent picks Objective + Picking only in stacked section CRS stack + Highly automated Basic concepts Wavefield attributes + Vivid inversion scheme Inversion – Inherent restriction to second order Analytic approach Model-based approach ◮ Proposed two-step strategy Conclusions W I T

Parameterization, Inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann ◮ CRS attributes are well-suited for inversion Motivation Introduction ➥ NIP-wave tomography Travelt. tomography Velocity analysis + Independent picks Objective + Picking only in stacked section CRS stack + Highly automated Basic concepts Wavefield attributes + Vivid inversion scheme Inversion – Inherent restriction to second order Analytic approach Model-based approach ◮ Proposed two-step strategy Conclusions ◮ NIP-wave tomography for high-quality initial model W I T

Parameterization, Inversion stacking & inversion of locally coherent events with the CRS Stack method Jürgen Mann ◮ CRS attributes are well-suited for inversion Motivation Introduction ➥ NIP-wave tomography Travelt. tomography Velocity analysis + Independent picks Objective + Picking only in stacked section CRS stack + Highly automated Basic concepts Wavefield attributes + Vivid inversion scheme Inversion – Inherent restriction to second order Analytic approach Model-based approach ◮ Proposed two-step strategy Conclusions ◮ NIP-wave tomography for high-quality initial model ◮ Drop analytic approximation, switch to model-based diffraction traveltimes W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann ◮ Diffraction traveltimes well suited for inversion: Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann ◮ Diffraction traveltimes well suited for inversion: Motivation Introduction + no dependence on reflector structure Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann ◮ Diffraction traveltimes well suited for inversion: Motivation Introduction + no dependence on reflector structure Travelt. tomography Velocity analysis + very simple imaging condition Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann ◮ Diffraction traveltimes well suited for inversion: Motivation Introduction + no dependence on reflector structure Travelt. tomography Velocity analysis + very simple imaging condition Objective – Diffraction events only present for true diffractors! CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann ◮ Diffraction traveltimes well suited for inversion: Motivation Introduction + no dependence on reflector structure Travelt. tomography Velocity analysis + very simple imaging condition Objective – Diffraction events only present for true diffractors! CRS stack Basic concepts ◮ NIP-wave theorem: Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann ◮ Diffraction traveltimes well suited for inversion: Motivation Introduction + no dependence on reflector structure Travelt. tomography Velocity analysis + very simple imaging condition Objective – Diffraction events only present for true diffractors! CRS stack Basic concepts ◮ NIP-wave theorem: Wavefield attributes ◮ up to second order: Inversion Analytic approach zero-offset diffraction traveltime ≡ CMP traveltime Model-based approach Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann ◮ Diffraction traveltimes well suited for inversion: Motivation Introduction + no dependence on reflector structure Travelt. tomography Velocity analysis + very simple imaging condition Objective – Diffraction events only present for true diffractors! CRS stack Basic concepts ◮ NIP-wave theorem: Wavefield attributes ◮ up to second order: Inversion Analytic approach zero-offset diffraction traveltime ≡ CMP traveltime Model-based approach ◮ CMP reflection traveltimes available from the data Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann ◮ Diffraction traveltimes well suited for inversion: Motivation Introduction + no dependence on reflector structure Travelt. tomography Velocity analysis + very simple imaging condition Objective – Diffraction events only present for true diffractors! CRS stack Basic concepts ◮ NIP-wave theorem: Wavefield attributes ◮ up to second order: Inversion Analytic approach zero-offset diffraction traveltime ≡ CMP traveltime Model-based approach ◮ CMP reflection traveltimes available from the data Conclusions ◮ approximate description of hypothetical diffraction traveltimes for all offsets W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann ◮ Diffraction traveltimes well suited for inversion: Motivation Introduction + no dependence on reflector structure Travelt. tomography Velocity analysis + very simple imaging condition Objective – Diffraction events only present for true diffractors! CRS stack Basic concepts ◮ NIP-wave theorem: Wavefield attributes ◮ up to second order: Inversion Analytic approach zero-offset diffraction traveltime ≡ CMP traveltime Model-based approach ◮ CMP reflection traveltimes available from the data Conclusions ◮ approximate description of hypothetical diffraction traveltimes for all offsets ➥ data-derived second-order diffraction traveltimes W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltimes with the CRS Stack method Jürgen Mann ◮ Diffraction traveltimes well suited for inversion: Motivation Introduction + no dependence on reflector structure Travelt. tomography Velocity analysis + very simple imaging condition Objective – Diffraction events only present for true diffractors! CRS stack Basic concepts ◮ NIP-wave theorem: Wavefield attributes ◮ up to second order: Inversion Analytic approach zero-offset diffraction traveltime ≡ CMP traveltime Model-based approach ◮ CMP reflection traveltimes available from the data Conclusions ◮ approximate description of hypothetical diffraction traveltimes for all offsets ➥ data-derived second-order diffraction traveltimes ➥ analytic description W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltime with the CRS Stack method Jürgen Mann Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltime with the CRS Stack method Jürgen Mann NIP-wave tomography (2D) Motivation Introduction Travelt. tomography Velocity analysis Objective CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltime with the CRS Stack method Jürgen Mann NIP-wave tomography (2D) ◮ data space Motivation Introduction � � , ∂ 2 t � � x 0 , t 0 , ∂ t Travelt. tomography � � Velocity analysis � � ∂ h 2 ∂ x Objective � � ( x 0 , h = 0 ) ( x 0 , h = 0 ) i CRS stack Basic concepts Wavefield attributes Inversion Analytic approach Model-based approach Conclusions W I T

Parameterization, Inversion with analytic diffraction stacking & inversion of locally coherent events traveltime with the CRS Stack method Jürgen Mann NIP-wave tomography (2D) ◮ data space Motivation Introduction � � , ∂ 2 t � � x 0 , t 0 , ∂ t Travelt. tomography � � Velocity analysis � � ∂ h 2 ∂ x Objective � � ( x 0 , h = 0 ) ( x 0 , h = 0 ) i CRS stack Basic concepts Wavefield attributes ◮ model space Inversion Analytic approach ( x , z , Θ 0 ) i v ( x , z ) Model-based approach ; Conclusions W I T