The course aims to provide an introduction to the basic principles and
techniques of imaging using acoustic and elastic waves, with a specific
focus on applications in the field of energy industry
D1 - Knowledge and understanding: At the end of the course, the student
will have to know the basics of the most common imaging techniques
applied to reflected data;
D2 - Ability to apply knowledge and understanding: At the end of the
course students will be able to evaluate the effectiveness of the various
seismic imaging tools according to the geological and geophysical
complexity of the investigated area
D3 - Making judgements: The course aims to develop the analytical skills
and critical spirit necessary to plan and evaluate the correctness and
effectiveness of an imaging project
D4 - Communication skills: The student must be able to describe the
fundamental principles of the methods and of the work carried out with
an appropriate technical language
D5 - The student will acquire skills that will enable him to autonomously
perfect his scientific and professional training in order to maintain an
adequate level of skills with methods of permanent training (continuing
education) in a disciplinary field in rapid technological evolution

Basic courses of Mathematics and Physics

1. Introduction to imaging and basics of wave prpoagation
1.1. Application of imaging techniques in the industry and in our
everyday life

2. Seismic imaging techniques
2.1.1. Snell’s law and wave propagation in layered media
2.1.2. Normal moveout hyperbola
2.1.3. Stack
2.2. Imaiging 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 imaigng)
2.5. 2D versus 3D imaging
2.6. Mathematics of seismic imaging
2.6.1. Green’s theorem
2.6.2. Imaging conidtion
2.7. Ray-based imaging (Kirchhoff depth migration)
2.7.1. Migration aperture
2.7.2. Anti-alias filter
2.7.3. Common reflection point gathers
2.7.4. NMO stretch and mute
2.8. Gaussian beam migration
2.9. One-way migration
2.9.1. Dispersion equation and phase shift operator
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)
3.12.1. Non-linear inverse problems
3.12.2. Full wave: challenges and opportunities
3.12.3. How to measure signal mismatches
3.12.4. Diving waves vs reflections
3.13. Application of Deep Learning to inverse problems

Robein E., Seismic Imaging: A Review of the Techniques, their Principles,
Merits and Limitations, EAGE
Robein E., Velocities, Time-imaging and Depth-imaging: Principles and
Methods, EAGE
Kak A., Slaney M., Principles of Computerized Tomographic Imaging,
available at http://www.slaney.org/pct/

1. Introduction to imaging and basics of wave propagation
1.1. 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. Imaiging 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 imaigng)
2.5. 2D versus 3D imaging
2.6. Mathematics of seismic imaging
2.6.1. Green’s theorem
2.6.2. Imaging conidtion
2.7. Ray-based imaging (Kirchhoff depth migration)
2.7.1. Migration aperture
2.7.2. Anti-alias filter
2.7.3. Common reflection point gathers
2.7.4. NMO stretch and mute
2.8. Gaussian beam migration
2.9. One-way migration
2.9.1. Dispersion equation and phase shift operator
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)
3.12.1. Non-linear inverse problems
3.12.2. Full wave: challenges and opportunities
3.12.3. How to measure signal mismatches
3.12.4. Diving waves vs reflections
3.13. Application of Deep Learning to inverse problems

Lectures and exercises

Oral exam with questions and exercises. The assessment is carried out on
the following elements: knowledge of the subject, problem solving skills,
properties of the technical-scientific language used to present it, ability to
present and construct the presentation in a logical and orderly way and
to establish any links with related topics