7|c|Table 1 : Elastic constants for transversely isotropic solids (ft/sec) | ||||||

transversely isotropic medium | c_{11} |
c_{33} |
c_{13} |
c_{44} |
c_{66} |
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 |

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.

1/13/1998