SYNTHETIC EXPERIMENTS

Synthetic ¶ wave data experiments were performed on two radically different, homogeneous, transversely isotropy models to examine the feasibility of the two techniques for improved normal moveout correction and lithology discrimination based on the degree of estimated anisotropy of the medium and the degree of anellipticity. Table 1 shows the elastic properties of the models.

transversely isotropic medium c₁₁ c₃₃ c₁₃ c₄₄ c₆₆ density

Sandstone-Shale 234E6 228E6 90.0E6 68.9E6 71.3E6 2.34

Sandstone-Anisotropic shale 255E6 228E6 90.0E6 68.9E6 91.4E6 2.34

Limestone-Shale 364E6 287E6 113E6 86.9E6 114E6 2.44

Limestone-Anisotropic Shale 384E6 287E6 113E6 86.9E6 134E6 2.44

Anisotropic Shale 233E6 193E6 76.1E6 58.3E6 98.6E6 2.38

The first model was a sandstone-shale stratified medium with weakly transversely isotropy . The ¶-wave vertical velocity of the medium was 9865 ft/s, and the anisotropy factor, defined as the horizontal to vertical phase velocity ratio $v_x\over v_z$ was about 1.014. The second model was a limestone-shale subsurface with moderate anisotropy. This medium had a vertical velocity of 10850 ft/s and a moderate anisotropy factor of 1.125.

Synthetic common shot point gather were obtained by 2-dimensional finite difference modeling for the two models for analysis. The source was at a depth of 1850 ft and receivers were at the surface out to offsets of 3200 ft. The range of angles was from 0 to 60 degrees. The vertical component of synthetic common shot point gather for the sandstone-shale model and limestone-shale model are shown in Figures 4 and 5 ,respectively. For applying Byun's method, we can consider this common shot point gather as the offset VSP gather and for applying Muir's method this can be considered as common midpoint gather by considering the source is image source and the depth of common midpoint is a half of the depth of image source.

Figure 6 shows semblance analysis by using Byun's method for sandstone-shale model as a function of horizontal velocity v_x and velocity at 45 degrees, v_q. High semblance values appear at nearly horizontal velocity and smaller velocity at 45 degrees than horizontal velocity which represent very well weak anisotropy or anellipticity.

Figure 7 shows semblance analysis by using Muir's method for sandstone-shale model as a function of horizontal velocity v_x and anellipticity q. In this case, peak semblance appears near the horizontal velocity and the small value of q represents weak anisotropy. Figures 8 and 9 show semblance analysis for limestone-shale model by Byun's method and Muir's method, respectively. In both cases stacking velocity represents a somewhat bigger value than the actual horizontal velocity and anellipticity is bigger than in the case of sandstone-shale model.