# Inspiration for Seismic Diffraction Modelling, Separation, and Velocity in Depth Imaging
## 3 Results and Discussion  
### Detection of Faults and Fractures  
In general geology, a fracture is any kind of separation or break in a rock formation. Examples are joints or faults in which the formation is divided into two or more pieces [25]. In geology, fracture is a broad term that includes faults, fractures, and discontinuities. These fractures can provide access for fluids, such as water or hydrocarbons, to move into the rocks [26]. Therefore, the model shown in Figure 5a is the fractured basement model from the Malay Basin. The number of faults and fractures present in the igneous basement are a challenge for seismic imaging. This field produces oil from the fractured basement. For simplicity in testing the diffraction imaging algorithm and concept, we extracted a part of the fractured model, which is shown in Figure 5b. A finite difference modeling technique is performed to generate the gather data using a zero-offset configuration. Figure 6a shows the zero-offset section; diffractions are produced at the edges of the reflector and a series of diffraction curves appear on the fault plane. The amplitude of the hyperbola decreases with increasing depth because of the attenuation factor. Furthermore, the curvature of the hyperbola is higher in the shallow section than in the deeper section. A 3D projection of the hyperbolic curves is shown in Figures 2 and 3, which describe the fundamentals of the diffraction with respect to velocity and depth. The frequency-wavenumber (F-K) analysis is a standard array technique that simultaneously calculates the power distributed among different speeds and directions of approach [27]. Figure 6b shows the results in the F-K domain for the zero-offset data. Here, we can see that the amplitude from the reflection occurs at a speed of zero cycles per second. Further, the diffraction amplitude is shown away from zero with the lower amplitude. The filter, which is designed based on the dip of the frequency cut-off, removes the reflection and preserves the diffraction only by looking into the spectrum. This filter was design based on trial and error analysis. Finally, the output of the filter is shown in Figure 6c. Figure 6d shows the diffraction section, which is achieved by DFF. The reflection is removed and diffraction is enhanced. A series of diffractions appears on the fault plane. Diffraction stacking can help in fault interpretation. Figure 5: (a) Malay Basin field, which contains extensive faults and fractures in the igneous basement [28]. (b) Input initial velocity model for seismic analysis [8]. Diffraction stacking or imaging can add information to an interpreter for fault and fracture identification. The Stolt migration is applied to the diffraction and reflection data, which are shown in Figure 7a,b. The diffractions are imaged properly and the point diffractions show the locations of the faults and a probable discontinuous surface. Figure 7b shows the migrated synthetic seismic data without diffraction separation; not all of the components of the faults are illuminated, as desired. Furthermore, separating the diffractions would help us to interpret the faults, as the apex of each diffraction shows the continuity of the fault plane. Figure 7c is the amplitude spectrum of the migrated data in the time-distance (t-x) domain, which shows the amplitude distribution with the trace number. At the fault location, the amplitude is very low or near to zero because most of the migration algorithms kill the diffractions that are considered as noise. In this context, diffraction separation is needed to improve the imaging results. Figure 6: (**a**) Seismic response of the input velocity model; a series of diffractions are generated at the fault location. (**b**) The frequency–wavenumber (F-K) spectrum, which shows the amplitude distribution with wave cycles per kilometer. (**c**) F-K spectrum after application of the designed filter; only the diffraction amplitude is displayed, while the reflection amplitude has been removed.