Amplitude-preserved wave-equation migration Paul Sava & Biondo Biondi SEP108 (pages 1-27)

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Presentation transcript:

Amplitude-preserved wave-equation migration Paul Sava & Biondo Biondi SEP108 (pages 1-27)

Wave-equation imaging Why? –Complex wavefields –Sharp velocity variation sub-salt What? –Reflectivity function of incidence angle Imaging Migration Velocity Analysis (MVA) Amplitude vs. Angle Analysis (AVA)

Angle-Domain Common Image Gathers Applications –imaging –S/G migration (Prucha et at., 1999) –shot-profile migration (Rickett, 2001) –seismic inversion (Prucha et. al., 2001) –MVA –traveltime tomography (Clapp, 2000) –wave-equation MVA (Sava & Biondi, 2000) –C-waves –polarity reversal (Rosales, 2001) –AVA –wave-equation AVA (Gratwick, 2001)

Angle-gathers vs. offset-gathers Offset gather Angle gather

Agenda ADCIG kinematics image space data space Amplitude-preserved migration general formulation weighting function COMAZ ADCIG amplitudes spatial bandwidth temporal bandwidth RTT Applications true-amplitude migration inversion WEMVA

Reflection scheme: global view SourceReceiver V(x,y,z)  

Reflection scheme: local view   2h v 

ADCIG methods Reflection angleOffset ray-parameter k-domain (RTT) x-domain (slant-stack)

ADCIG: example

ADCIG methods: comparison Reflection angleOffset ray-parameter indirectly –function of dip directlyReflection angle less sensitivesensitiveInaccurate velocity boundaries data space –mixed with migration image space –separated from migration Computation domain

Agenda ADCIG kinematics image space data space Amplitude-preserved migration general formulation weighting function COMAZ ADCIG amplitudes spatial bandwidth temporal bandwidth RTT Applications true-amplitude migration inversion WEMVA

Spatial bandwidth khkh kzkz  max  max kzkz   max  max

Synthetic: ideal gather frequency domainspace domainamplitude

Temporal bandwidth imageangle gather dataoffset gather wide frequency band narrow frequency band  kzkz khkh kzkz khkh  khkh kzkz

Temporal bandwidth frequency domainspace domainamplitude

RTT implementation Two possibilities: –push: loop over input –pull: loop over output khkh kzkz kzkz  angle gather offset gather

push RTT offset-gatherangle-gather k-domain x-domain

pull RTT offset-gatherangle-gather k-domain x-domain

RTT amplitudes

Agenda ADCIG kinematics image space data space Amplitude-preserved migration general formulation weighting functions COMAZ ADCIG amplitudes spatial bandwidth temporal bandwidth RTT Applications true-amplitude migration inversion WEMVA

Amplitude-preserving migration Definition: the process of recovering the amplitude of the reflectivity vector given –perfect data –infinite bandwidth –infinite aperture

Modeling operator L: modeling operator A: Amplitude operator G: Reflection operator i 0 : seismic image r: reflectivity d: seismic data

Amplitude operator Clayton & Stolt (1981) L: modeling operator A: amplitude operator G: Reflection operator i 0 : seismic image r: reflectivity d: seismic data

Reflection operator L: modeling operator A: amplitude operator G: reflection operator i 0 : seismic image r: reflectivity d: seismic data Clayton & Stolt (1981) Stolt & Benson (1986)

Amplitude-preserving operator L: modeling operator A: amplitude operator G: reflection operator i 0 : seismic image r: reflectivity d: seismic data

Weighting operator modelingmigration

Agenda ADCIG kinematics image space data space Amplitude-preserved migration general formulation weighting functions COMAZ ADCIG amplitudes spatial bandwidth temporal bandwidth RTT Applications true-amplitude migration inversion WEMVA

Amplitude correction: the problem frequency domainspace domainamplitude

Jacobian: general expression image space data space

Jacobian: 2-D, image space  2h v 

Jacobian: general expression image space data space

Jacobian: 2-D, data space  2h v 

Jacobian: 2-D, flat reflectors (Wapenaar et al., 1999)

Amplitude correction: the problem frequency domainspace domainamplitude

AVA: correct amplitudes frequency domainspace domainamplitude

Agenda ADCIG kinematics image space data space Amplitude-preserved migration general formulation weighting function COMAZ ADCIG amplitudes spatial bandwidth temporal bandwidth RTT Applications true-amplitude migration inversion WEMVA

COMAZ: stationary-phase view from above 2-DCOMAZ

Amplitude component Phase-shift component COMAZ: stationary-phase correction

COMAZ: no amplitude corrections

COMAZ: all amplitude corrections

Agenda ADCIG kinematics image space data space Amplitude-preserved migration general formulation weighting function COMAZ ADCIG amplitudes spatial bandwidth temporal bandwidth RTT Applications true-amplitude migration inversion WEMVA

True-amplitude migration L: modeling operator A: amplitude operator G: reflection operator i 0 : seismic image r: reflectivity d: seismic data

True-amplitude migration: COMAZ OPERATORS L: modeling W: Jacobian A: amplitude A stat : stationary-phase G: reflection

True-amplitude migration: real data

Inversion: pseudo-unitary operators InversionMigration

Inversion: preconditioned regularization

Wave-equation MVA L: Wave-equation MVA m: slowness perturbation d: image perturbation References: SEP100, SEP103, SEP105

WEMVA: model

WEMVA: correct amplitudes

WEMVA: incorrect amplitudes

Summary The goal –Reflectivity function of reflection angle The means –correct ADCIG transformations –kinematics –amplitudes –correct migration amplitude

Applications true-amplitude migration seismic inversion AVA wave-equation MVA