# Seismic Exploration Methods for Structural Studies and for Active Fault Characterization: A Review
## 3 Developments in Seismic Imaging
### Pre-Stack Depth Migration  
Migration is a fundamental step of seismic reflection processing that allows repositioning dipping reflected events to their correct spatial and temporal locations. Whether to perform migration in the time or depth domain depends on the subsurface complexity and the accuracy of the velocity model available to us. When velocity estimations are not accurate, the seismic data are migrated in time [19]. Time migration is an appropriate technique for mild to moderate lateral velocity variations. However, when the subsurface contains significant lateral velocity variations caused by complex near-surface conditions, depth migration is necessary to accurately image the subsurface structure [2]. Significant lateral velocity variations can cause strong ray deflection at the layer boundaries, resulting in non-hyperbolic arrival times of reflected events. Consequently, conventional CMP stacking, which relies on the hyperbolic displacement assumption, distorts the amplitudes and travel times associated with non-hyperbolic reflection events, leading to a deviation from an ideal zero-offset wavefield. To avoid this distortion, depth migration ideally should be performed before the stack, i.e., pre-stack depth migration (PSDM: [2; 19]). One of the earliest algorithms developed for seismic migration is the time-domain Kirchhoff migration method, which is based on the ray theory. It was first formulated by [PERSON] [52] and based on the early work of [PERSON] [53]. This method stacks all amplitudes found along hyperbolic diffraction paths in the post-stack domain. Another migration technique involves modeling a stacked section as an upcoming zero-offset wavefield generated by exploding reflectors [54]. This approach conceptualizes migration as a combination of wavefield extrapolation and imaging. The downward continuation of wavefields can be implemented using finite-difference solutions to the scalar wave equation, and migration methods based on such implementations are called finite-difference migration. [PERSON] [23] provides a comprehensive theoretical foundation of finite-difference migration and its practical aspects. Some migration algorithms involve transforming seismic data into the frequency domain before applying the imaging algorithm [55; 56; 57]. Frequency-domain migration reduces the computational cost of the imaging process, leading to faster and more efficient processing. Despite the wide range of migration algorithms used in the industry today, none of them fully meets the important criteria of handling all dips and velocity variations while still being cost-effective [58]. As discussed previously, when a reliable velocity model is available and when the subsurface structural complexity is high, seismic reflection data should be pre-stack depth migrated (PSDM). There are several imaging algorithms used in PSDM: apart from the classic Kirchhoff migration, nowadays, one of the most used methods is the reverse-time migration (RTM: [59; 60; 61]). RTM involves modeling the propagation of seismic waves in the subsurface in reverse time from the receivers to the sources. This approach produces a wavefield that in theory is free from artifacts caused by the conventional forward modeling approach, resulting in higher resolution images of the subsurface. RTM therefore is particularly effective in imaging complex geological structures. However, one of the challenges of RTM, and of the depth migration algorithms in general, is their need for an accurate estimate of the subsurface velocity model. This is where seismic tomography and FWI can be useful. For instance, FWI can be used to update the model parameters used in the RTM process to obtain more accurate and high-resolution images of the subsurface in an alternating sequence of migration and model updates [62; 63].