Seismic Imaging
A.Y. 2025/2026
Learning objectives
The course unit is aimed at providing an extensive review of the principles, techniques and applications of seismic imaging for hydrocarbon exploration.
Expected learning outcomes
By the end of the course unit students will be able to assess the effectiveness of the different seismic imaging tools with respect to the geological and geophysical complexity of the area under investigation.
The course unit aims at developing the analytical skills needed to plan and assess correctness and effectiveness of seismic imaging projects.
The course unit aims at developing the analytical skills needed to plan and assess correctness and effectiveness of seismic imaging projects.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
The course aims to provide an overview of the basic principles, techniques, and applications of seismic imaging in industry.
1. Introduction to imaging and basics of wave propagation
1.1. Remote sensing
1,2. Application of imaging techniques in the industry and in our everyday life
2. Seismic imaging techniques
2.1. 1D Imaging
2.1.1. Snell's law and wave propagation in layered media
2.1.2. Normal moveout hyperbola
2.1.3. Stack
2.2. Imaging in constant velocity media
2.2.1. Migration through diffraction stack
2.2.2. Migration through spreading along elliptical trajectories
2.3. Imaging when velocity varies with depth only (time imaging)
2.3.1. Time to depth stretching
2.4. Imaging with laterally variable velocity (depth imaging)
2.5. 2D versus 3D imaging
2.6. Mathematics of seismic imaging
2.6.1. Green's theorem
2.6.2. Imaging condition
2.7. Ray-based imaging (Kirchhoff depth migration)
2.7.1. Eikonal equation and ray tracing
2.7.2. Migration aperture
2.7.3. Anti-alias filter
2.7.4. Common reflection point gathers
2.7.5. NMO stretch and mute
2.8. Gaussian beam migration
2.9. One-way migration
2.10. Full wave imaging (Reverse Time Migration)
2.10.1. Finite difference wave equation solution
2.11. Least square migration
2.12. Anisotropic imaging
2.12.1. VTI and TTI models
2.13. True amplitude imaging
2.14. Absorption and absorption-compensated imaging
3. Velocity analysis
3.1. NMO velocity analysis
3.2. Semblance
3.3. Layered media, stacking velocity and root mean squared velocity
3.3.1. Dix's equation
3.4. Inverse problems
3.4.1. Forward operator
3.4.2. Inverse operator
3.4.3. Null space
3.4.4. Ill conditioned inverse problems
3.4.5. Regularization
3.4.6. Conjugate gradient
3.5. Velocity aalysis in presence of dipping reflectors
3.5.1. Dip Moveout operator
3.6. Ray-based tomographic velocity analysis
3.6.1. Radon transform
3.6.2. Crosswell tomography
3.6.3. Reflection tomography
3.7. Uncertainty analysis
3.7.1. Null space sampling
3.8. Migration velocity analysis
3.9. Anisotropic velocity estimation
3.10. Integration of well data
3.10.1. Markers and well misties
3.11. Industrial applications
3.12. Full wave velocity analysis (Full Waveform Inversion FWI)
3.12.1. Non-linear inverse problems
3.12.2. Full wave: challenges and opportunities
3.12.3. How to measure signal mismatches, cost functions
3.12.4. Diving waves vs reflections
3.12.5. FWI imaging
3.13. Application of Deep Learning to inverse problems
1. Introduction to imaging and basics of wave propagation
1.1. Remote sensing
1,2. Application of imaging techniques in the industry and in our everyday life
2. Seismic imaging techniques
2.1. 1D Imaging
2.1.1. Snell's law and wave propagation in layered media
2.1.2. Normal moveout hyperbola
2.1.3. Stack
2.2. Imaging in constant velocity media
2.2.1. Migration through diffraction stack
2.2.2. Migration through spreading along elliptical trajectories
2.3. Imaging when velocity varies with depth only (time imaging)
2.3.1. Time to depth stretching
2.4. Imaging with laterally variable velocity (depth imaging)
2.5. 2D versus 3D imaging
2.6. Mathematics of seismic imaging
2.6.1. Green's theorem
2.6.2. Imaging condition
2.7. Ray-based imaging (Kirchhoff depth migration)
2.7.1. Eikonal equation and ray tracing
2.7.2. Migration aperture
2.7.3. Anti-alias filter
2.7.4. Common reflection point gathers
2.7.5. NMO stretch and mute
2.8. Gaussian beam migration
2.9. One-way migration
2.10. Full wave imaging (Reverse Time Migration)
2.10.1. Finite difference wave equation solution
2.11. Least square migration
2.12. Anisotropic imaging
2.12.1. VTI and TTI models
2.13. True amplitude imaging
2.14. Absorption and absorption-compensated imaging
3. Velocity analysis
3.1. NMO velocity analysis
3.2. Semblance
3.3. Layered media, stacking velocity and root mean squared velocity
3.3.1. Dix's equation
3.4. Inverse problems
3.4.1. Forward operator
3.4.2. Inverse operator
3.4.3. Null space
3.4.4. Ill conditioned inverse problems
3.4.5. Regularization
3.4.6. Conjugate gradient
3.5. Velocity aalysis in presence of dipping reflectors
3.5.1. Dip Moveout operator
3.6. Ray-based tomographic velocity analysis
3.6.1. Radon transform
3.6.2. Crosswell tomography
3.6.3. Reflection tomography
3.7. Uncertainty analysis
3.7.1. Null space sampling
3.8. Migration velocity analysis
3.9. Anisotropic velocity estimation
3.10. Integration of well data
3.10.1. Markers and well misties
3.11. Industrial applications
3.12. Full wave velocity analysis (Full Waveform Inversion FWI)
3.12.1. Non-linear inverse problems
3.12.2. Full wave: challenges and opportunities
3.12.3. How to measure signal mismatches, cost functions
3.12.4. Diving waves vs reflections
3.12.5. FWI imaging
3.13. Application of Deep Learning to inverse problems
Prerequisites for admission
Basic knowledge of digital signal processing and calculus
Teaching methods
frontal lessons
Teaching Resources
E. Robein, Seismic Imaging: A Review of the Techniques, their Principles, Merits and Limitations, EAGE publications
Assessment methods and Criteria
During the oral exam the student must demonstrate his/her knowledge on the topics covered by the course and the ability to discuss and solve problems being presented.
Professor(s)