Wave-equation migration velocity analysis Paul Sava* Stanford University Biondo Biondi Stanford University

Imaging=MVA+Migration Migration wavefield based Migration velocity analysis (MVA) traveltime based Compatible migration and MVA methods

Imaging: the “big picture” Kirchhoff migration traveltime tomography wavefronts wave-equation migration wave-equation MVA (WEMVA) wavefields

Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

Wavefield scattering

Wavefield scattering

Scattered wavefield Medium perturbation Wavefield perturbation

Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

Imaging: Correct velocity Background velocity Migrated image Reflectivity model What the data tell us...What migration does... location depth location depth

Imaging: Incorrect velocity Perturbed velocity Migrated image Reflectivity model What the data tell us...What migration does... location depth location depth

Wave-equation MVA: Objective Velocity perturbation Image perturbation slowness perturbation (unknown) WEMVA operator image perturbation (known) location depth location depth

–migrated images –moveout and focusing –amplitudes –parabolic wave equation –multipathing –slow –picked traveltimes –moveout –eikonal equation –fast Comparison: WEMVA vs TT Wave-equation MVATraveltime tomography

–migrated images –interpretive control –parabolic wave equation –slow –recorded data –two-way wave equation –slow Comparison: WEMVA vs WET Wave-equation MVAWave-equation tomography

Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

Image perturbations FocusingFlatness Residual process: moveout migration focusing slowness perturbation (unknown) WEMVA operator image perturbation (known) location depth angle

Image perturbations

Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

Double Square-Root Equation Fourier Finite Difference Generalized Screen Propagator Wavefield extrapolation

“Wave-equation” migration

Slowness perturbation

slowness perturbation background wavefield perturbation Wavefield perturbation

Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

Born approximation Small perturbations! Born linearization Non-linear WEMVA slowness perturbation (unknown) WEMVA operator image perturbation (known) Unit circle

Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

Applications “Image perturbation” image difference image “differential” Examples –Structural imaging –Overpressure prediction –4-D seismic monitoring –Diffraction focusing MVA

Application 1: Structural imaging Velocity analysis in complex areas multipathing high velocity contrast Full images vs. picked events Spatial focusing + offset focusing Traveltimes & amplitudes

Structural imaging: methodology DataImageVelocity Image perturbation

Location [km] Depth [km] Location [km] Depth [km] Location [km] Depth [km] Location [km] Depth [km] Structural imaging: example

Application 2: Overpressure Overpressure zone Complicated salt Complicated propagation

Overpressure: motivation Pressure creates time/moveout changes cannot be picked with enough accuracy Complicated overburden ray-based methods fail

Overpressure: methodology DataImageVelocity Image perturbation

Overpressure: proof of concept

Application 3: 4D monitoring Small traveltime changes cannot be picked with enough accuracy Amplitude variations ignored by traveltime methods Cumulative phase and amplitude effects mask deeper effects

4D monitoring: methodology DataImageVelocity 4D difference data

4D monitoring: proof of concept

Application 4: Focusing MVA Moveout information missing or hard to use Focusing information ignored by moveout / traveltime based methods focusing moveout

Focusing MVA: methodology DataImageVelocity Image perturbation

Focusing MVA: proof of concept

Agenda Theoretical background WEMVA methodology Scattering Imaging Image perturbations Wavefield extrapolation Born linearization WEMVA applications

WEMVA summary Methodology –“wave-equation” –image optimization focusing and moveouts –interpretive control Applications –any image perturbation repeated images over time optimized and reference images