3. Application of method in field data: Sigsbee (Gulf of Mexico)

Most information obtained from high resolution or super-resolution images is the result of careful processing. Consideration of diffraction is necessary in advanced wave modeling and processing because in conventional processing, diffractions are suppressed intentionally or implicitly [32]. In addition, the separation of these diffractions using plane wave destruction filtering could preserve the

diffracted amplitude. To prove the proposed modeling and diffraction migration results, we examined the Sigsbee 2A model to study wave extrapolation in a complex velocity field model containing a sedimentary sequence fragmented by a number of normal faults and overlapping (Figure 7a). In addition, there is a complex salt structure in the model that causes illumination problems as part of the current processing and imaging approach. These imaging problems allowed us to develop appropriate algorithms for better imaging. The Sigsbee 2A model has an absorbent free surface condition and a lower than normal water body reflection. These properties do not generate the effect of free surface multiples and lower than normal internal multiples.

For seismic imaging purposes, a zero shift design was chosen to acquire the zero offset seismic data for simplicity, as shown in Figure 7b. Advanced modeling of low-rank waves is used to obtain non-dispersive seismic. The comparison of two waves modeling the finite difference and the lower row is performed for high resolution imaging purposes. Figure 5 shows an evaluation of the results of conventional Figure 8(a) and advanced Figure 8(b) wave modeling and imaging results that indicate that saline body edges are unresolved. Modeling and imaging.

The plane wave destruction method is used to separate the diffractions from the full-wave reflection data. It is important to rely on the estimated dip of the data and to recognize an accurate determination of the sinking wave as it is an essential parameter for plane wave destruction filtering to separate diffraction and reflection. In this research, we separated the diffractions from the complete wave and tried to imagine these diffractions with a correct velocity model (Figure 9b). Figure 9a is the result of a depth-migrated image using conventional wave modeling results, which are poor compared to the results of advanced wave modeling and diffraction

Figure 7. (a) Sigsbee velocity model, from Gulf of Mexico (GOM) (b) zero-offset seismic data using low-rank approximation.

#### Figure 8.

Seismic imaging of full wave data using (a) conventional finite difference modeling and (b) advance wave modeling using low rank approximation.

Advance Wave Modeling and Diffractions for High-Resolution Subsurface Seismic Imaging DOI: http://dx.doi.org/10.5772/intechopen.81164

#### Figure 9.

Reflection and diffraction migration (a) conventional zero-offset migration, (b) diffraction migration and (c) frequency spectrum comparison of conventional full wave migration and advance wave approximation diffraction migration.

imaging. Figure 9c shows the frequency spectra of the migrated data. The original offset using classical modeling and full wave migration with Fourier migration in several steps is indicated in green, and advanced waveform modeling with diffraction migration is displayed in purple. Improvements in diffraction imaging, especially for small scale events, are highlighted in the spectrum, allowing us to achieve high resolution images with low frequency data recovery after migration. Low frequency signals from long-lived seismic data are critical values for many areas of exploration seismology and hydrocarbon prediction.
