Riemannian Wavefield Migration: Wave-equation migration from Topography Jeff Shragge, Guojian Shan, Biondo Biondi Stanford University Paul Sava, Sergey Fomel Bureau of Economic Geology UT Austin
The Dossier: WE Imaging Limitations Incomplete Data Computational Power Physical Inaccuracy
The Dossier: WE Imaging Limitations Incomplete Data Computational Power Physical Inaccuracy
The Dossier: WE Imaging Limitations Propagator inaccuracy (illumination) Topographic surface limitations Coordinate system not conformal to propagation direction or acquisition surface Migration physics decoupled from geometry
The Dossier: WE Imaging Limitations Propagator Inaccuracy (Illumination) Migration Physics decoupled from Geometry Difficult Steep Dip Imaging Coordinate system not conformal to propagation direction or acquisition surface
Steep Dip Imaging Accuracy of wavefield extrapolation decreases as propagating waves tend to horizontal Extrapolation Direction
The Dossier: WE Imaging Limitations Propagator Inaccuracy (Illumination) Coordinate system not conformal to propagation direction or acquisition surface Migration Physics decoupled from Geometry Difficult Steep Dip Imaging No use of Overturning waves
Using Overturning Waves Currently do not use potentially useful information provided by overturning waves Extrapolation Direction
Proposed Solution Coordinate system conformal with wavefield propagation Extrapolation Direction
The Dossier: WE Imaging Limitations Topographic Surface Limitations Coordinate system not conformal to propagation direction or acquisition surface Migration Physics decoupled from Geometry Difficult Steep Dip Imaging No use of Overturning waves Extrapolation from complex free-surface Propagator Inaccuracy (Illumination)
Free Surface Topography How to define extrapolation surface orthogonal to free surface?
The Dossier: WE Imaging Limitations Topographic Surface Limitations Coordinate system not conformal to propagation direction or acquisition surface Migration Physics decoupled from Geometry Difficult Steep Dip Imaging No use of Overturning waves Extrapolation from complex free-surface Propagator Inaccuracy (Illumination) Extrapolation from deviated boreholes
VSP Deviated Well Topography Receiver wavefield acquired in well deviated in 3-D How to define wavefield extrapolation from borehole surface?
Proposed Solution Coordinate system conformal with borehole geometry
The Dossier: WE Imaging Limitations Topographic Surface Limitations Difficult Steep Dip Imaging No use of Overturning waves Extrapolation from complex free-surface Propagator Inaccuracy (Illumination) Extrapolation from deviated boreholes Coordinate system not conformal to propagation direction or acquisition surface Migration Physics decoupled from Geometry
A Solution… Summerized Reduce Propagator Inaccuracy (Illumination) Enable W.E. imaging directly from Topographic Surfaces Perform Migration on Coordinate systems conformal to propagation direction/acquisition surface Couple Migration Physics with Geometry Improve Steep Dip Imaging Use Overturning waves No datuming at the free-surface W.E. Imaging for massive 3-D VSP data
Migration from Topography – I Make wave-equation imaging conformal with acquisition geometry
Migration from Topography – II Make wave-equation imaging conformal with acquisition geometry
Migration from Topography – III Make wave-equation imaging conformal with acquisition geometry Two requirements: i) Propagating wavefields in generalized coordinate systems ii) Creating the specific topographic coordinate system
Agenda Riemannian Wavefield Extrapolation Coordinate System Generation Example: Migration from Topography –Imaging Husky
Agenda Riemannian Wavefield Extrapolation Coordinate System Generation Example: Migration from Topography –Imaging Husky
RWE in 2-D ray-coordinates RiemannianCartesian Extrapolation Direction Orthogonal Direction
RWE: Helmholtz equation (associated) metric tensor Laplacian Coordinate system Sava and Fomel (2005)
RWE: (Semi)orthogonal coordinates
1 st order2 nd order 1 st order RWE: Helmholtz equation Ray-coordinate Interpretation α = velocity function J = geometric spreading (i.e. Jacobian) Sava and Fomel (2005)
RWE: Dispersion relation Riemannian Cartesian
RWE: Dispersion relation Riemannian Cartesian
RWE: Kinematic dispersion relation Riemannian Cartesian
RWE: Kinematic dispersion relation Riemannian Cartesian
RWE: Wavefield extrapolation Riemannian Cartesian
interpolate Extrapolation Work Flow PHYSICAL DOMAIN CANONICAL DOMAIN MODEL DOMAIN WAVEFIELD DOMAIN
Agenda Riemannian Wavefield Extrapolation Coordinate System Generation Example: Migration from Topography –Imaging Husky
Conformal Mapping Technique PHYSICAL DOMAIN O O O O O O O O O O
Conformal Mapping Technique PHYSICAL DOMAINCANONICAL DOMAIN O O O O O O O O O OOOOOOOO O O O g f -1
Conformal Mapping Technique PHYSICAL DOMAINCANONICAL DOMAIN O O O O O O O O O OOOOOOOO O O O OOOOOOO O O O g f -1
Conformal Mapping Technique PHYSICAL DOMAINCANONICAL DOMAIN O O O O O O O O O O O O O O O O O O O OOOOOOOO O O O OOOOOOO O O O g f -1 g -1 f
Conformal Mapping Technique O O O O O O O O O OOOOOOOO O O O Shot Profile Migration –use same grid for both source and receiver wavefields
RWE: Shot-profile migration Riemannian Cartesian
Single shot Imaging Work Flow interpolate PHYSICAL DOMAIN CANONICAL DOMAIN MODEL DOMAIN IMAGE DOMAIN interpolate
Agenda Riemannian Wavefield Extrapolation Coordinate System Generation Example: Migration from Topography –Imaging Husky
Husky data set – Topography 10x Surface Topography Exaggeration
Husky data set – Time Migration + Geology
TopoWEM TopoWEM Image
TopoWEM TopoWEM Image
TopoWEM + Angle Gathers TopoWEM Image
TopoWEM Angle Gathers
Kirchhoff from Flat Datum Kirchhoff Image
Kirchhoff from Flat Datum Kirchhoff Image
Kirchhoff + surface offset gathers Kirchhoff Image
TopoWEM vs. Statics+Datum Kirchhoff TopoWEM Image Kirchhoff Image
TopoWEM vs. Statics+Datum Kirchhoff TopoWEM Image Kirchhoff Image
Summary TopoWEM produced good image –Resolved near-surface structures and dips Kirchhoff migration from flat datum produced good image –Better at mid-to-basement depths but could not resolve near-surface Bottom line: statics + migration from datum is less accurate –Kinematic errors in static assumptions TopoWEM is more expensive –Requires Taylor series expansion about 2 coefficient parameters Imaging from acquisition coordinate works
Acknowledgements Anatoly Baumstein Tom Dickens Ernestine Dixon Dave Hinkley Matt Hong Linda Price Mike Rainwater Peter Traynin Joe Vanderslice Kim Wilmott Husky Oil Talisman Oil Friday Lunch Folks John Sumner No doubt many others