# Seismic Exploration Methods for Structural Studies and for Active Fault Characterization: A Review
## 4 Seismic Attributes
### Amplitude versus Offset Analysis  
Amplitude versus offset (or AVO) measures the change in seismic wave amplitude with respect to the angle of incidence (or offset) of a source-receiver pair. AVO analysis can provide insights into the physical characteristics of the subsurface, such as lithology and fluid content. It is performed on individual traces on pre-stack seismic data and typically on common midpoint gathers [116]. One of the main advantages of the AVO is its ability to differentiate between different types of fluids (oil, gas, water) and lithology [117]. The AVO response of water-bearing formations, for example, is typically different from that of gas and oil-bearing formations, which makes AVO analysis useful in determining the presence of hydrocarbons. The theoretical basis of AVO was first developed by [PERSON] [118] and [PERSON] [119], which derived the equations for plane-wave reflection amplitudes as a function of incident angle, given the P-wave and S-wave velocities and densities of the two media. [PERSON] [120] used the Zoeppritz equations to investigate the relationship between AVO and Poisson's ratio and laid the foundation for modern AVO interpretation. Inspired by [PERSON]'s work, [PERSON] [121], [PERSON] [122], [PERSON] and [PERSON] [117], among others, made groundbreaking contributions to predicting lithology from AVO. In particular, [PERSON] and [PERSON] [115] introduced the industry standard classification of reflection coefficient curves which includes the classification of bright spot, phase reversal, and dim out. This classification was developed specifically for hydrocarbon saturated formations.  
Several studies have demonstrated that the AVO analysis can be a very effective tool for fault and fracture characterization. For instance, [PERSON] [123] shows that the use of seismic azimuthal AVO can effectively estimate fracture density and strike, as they are consistent  
Figure 7: Time slices through (**a**) coherence and long-wavelength, (**b**) most-positive, and (**c**) most-negative curvature volumes. The fault/fracture patterns appear more focused on curvature time slices and are well correlated with the corresponding seismic signatures. Yellow arrows indicate a prominent acquisition footprint. From [PERSON] and [PERSON] [89]. Data courtesy of Rally Energy, Calgary.  
with known fracture indicators from various sources such as core, outcrop, production, well logs, and structural interpretations. The good correlation between seismic azimuthal AVO and fracture indicators achieved by [PERSON] [123] suggests that azimuthal AVO can provide valuable information about cross-well fracture information where other methods may not be feasible.  
[PERSON] and [PERSON] [124] used AVO inversion and fault intensity analysis to monitor hydraulic fracturing in shale-gas reservoirs together with microseismic and production data. They located faults on seismic reflection images and calculated the reservoir's mechanical properties through an AVO inversion. Their study shows that hydraulic fractures tend to occur in areas with high fault intensity, which are followed by areas with high brittleness. The presence of natural faults affects the spatial distribution of the microseismic cloud and the velocity of fluid front propagation, resulting in events that move further and faster away from the well. Additionally, the results suggest that microseismic events reactivate existing fault planes and have magnitude distributions that resemble natural seismicity.