Introduction to imaging and foundations of wave propagation. Imaging technique application in the industry and in our everyday life. The ripple tank
Imaging techniques. Imaging in 1D media. Snell’s law and wave propagation in layered media. Normal moveout hyperbolas. Stack. Imaging in constant velocity media. Migration by hyperbola summation. Migration by the spraying approach. Imaging in v(z) media (time imaging). Two way time to depth mapping. Imaging in laterally variable velocity (depth imaging). 2D versus 3D imaging. The mathematics of seismic imaging. Green’s theorem. Imaging condition. Imaging based on rays (Kirchhoff migration). Migration aperture. Antialias filter. Common reflection point gather. NMO stretch and mute. Imaging based on gaussian beams. Imaging based on the one-way wave equation (heat equation). Phase shift operator. Full wave imaging (Reverse Time Migration). Computational complexity. Least squares migration. Imaging in anisotropic media. VTI and TTI models. Amplitude preserving imaging. Absorption and absorption compensated imaging
Velocity analysis. Velocity analysis for NMO hyperbolas. Semblance. Layered media, stacking velocity and root mean squared velocity. Dix equation. Inverse problems. Forward operators, data and model space. Inverse operators. Null space. Ill conditioned inverse problems. Regularization. Conjugate gradient. Velocity analysis and dipping reflectors. Dip Moveout Operator. Ray based velocity analysis and tomography. Radon transform. Transmission tomography. Reflection tomography. Analysis of velocity estimation uncertainty. Null space sampling. Migration velocity analysis. Anisotropic velocity model estimation. Integration with well measurements. Well marker calibration. Case histories. Full wave velocity analysis (Full Waveform Inversion). Non-linear inverse problems. FWI: potentiality and limitations. How to measure the difference between two signals. Deep learning and inverse problems. Generative Adversarial Networks