Regularization and Constraints in Seismic Inversion

 Regularization and constraints are crucial techniques in seismic inversion used to stabilize the inversion process and ensure that the resulting subsurface models are geologically realistic and physically meaningful.

 Involves adding additional information or assumptions to the inversion process to control the model's complexity and prevent overfitting to the seismic data. This is especially important when dealing with noisy or incomplete data. Regularization techniques, such as Tikhonov regularization or total variation regularization, impose smoothness, continuity, or other desirable properties on the model, helping to produce more stable and robust results. 

 Specific conditions or limits applied to the inversion process based on prior knowledge or geological expectations. These constraints can include bounds on model parameters, such as limiting the range of velocities or densities to physically plausible values, or enforcing geological features like layer boundaries or fault planes. Constraints help guide the inversion process towards solutions that are consistent with known geological structures and properties.