2. 2D examples of a complex faulted model: Marmousi

The proposed methodology is tested on a model called Marmousi, created in 1988 by the French Petroleum Institute (IFP) [30]. This model contains 158 horizons with horizontal layers and series of normal faults, which makes it complex especially at the center of the model. This model length is 9.2 km and the depth is 3 km. Figure 4(a) shows the Marmousi model, in which we assume that our task is to imagine the structure of the anticline below and consider it as a reservoir. We use a Ricker wavelet at a point source with a dominant frequency of 40 Hz. The size of the horizontal grid x is 4 m and z is 4 m. Figure 4(b) shows the result of the results of the advanced wave modeling using a low rank approximation. This modeling technique is capable of carrying out different designed studies, but for this we have selected the zero shift data record.

This imaging workflow is a new development for high-resolution imaging, as shown in Figure 3. We tested the workflow by separating the diffraction and the residue and representing it separately. Figure 5(a) shows the diffraction separated using plane wave destruction filtering and Figure 5(b) is the residue after diffraction separation. Figure 6(a) shows the zero shift data migrated with full wave imaging and (b) is the imaged section combining both reflection migration and diffraction migration. This shows an improvement in the resolution especially in the amplitude of faults and small discontinuities that are not resolved by the conventional imaging method.

#### Figure 3.

A generalized diffraction separation workflow using plane wave destruction (PWD) based on estimating the slope of the data before imaging [29].

Figure 4. (a) Marmousi velocity model and (b) modeled seismic data 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 5. Separation of the seismic data (a) separated diffraction and (b) separated reflection.

#### Figure 6.

Imaging of the seismic data (a) conventional zero-offset migration, (b) reflection and diffraction migration combined and (c) frequency spectrum of the data a & b [31].

For quantitative interpretation of the results, Figure 6(c) shows a frequency spectrum for both conventional (red) and diffractive (green) imaging. Higher diffraction response. In addition, higher frequency data of 50–60 Hz is enhanced for high resolution imaging.
