The Perturbation Analysis Of Multipole Model Waves In A Borehole Surrounded By Equiaxial Crystallographic Anisotropic Formation

The model is liquid in a borehole surrounded by equiaxial crystallographic anisotropicis formation. Although there are seldom examples of estimating waveforms acquired by a sonic tool in well or in seismology and the application of the method is enormously restricted by its complex theoretical formulations and obscure processing, the focus of this paper is researched mode waves surrounded by equiaxial crystallographic anisotropicis formation by a sonic tool in a well theoretically and numerically. There are only three absolute elastic constants under the orthogonal coordinate system, but the symmetry of the elastic constants because of depending on θis lost under the cylinder coordinate system. However, due to the complexity of this problem, their results cannot be determined with accuracy directly. Using the perturbative method can help to resolve the problem. Hamilton's theory can be used to calculate the perturbative integral calculus. The effect on the dispersion of phase velocity of mode waves surrounded by equiaxial crystallographic anisotropicis formation in a borehole also can be gained. The thesis studies the acoustic field excited by monopole source, dipole source and quadrupole source. Simplified dispersion formulations of Multipole Model waves Based on the theory of dispersion of phase velocity of mode waves surrounded by isotropicis formation in a borehole, the formulations of mode waves are expressed by volume integrals and the displacements of unperturbed mode at a harmonic frequency. Since the displacements can be reduced to relevant functions of radius, azimuth, and Z, we can simplify volume integrals to line integrals of radius. Considering the characteristic of the integrand of radius in simplified dispersion formulations, we transform the infinitely dimensional integrals of radius into interval integrals for rapidly calculating the velocity change due to equiaxial crystallographic anisotropicis effect. From the above simplified formulations, we can directly infer that only screw mode wave velocity depends on angle φ, which denotes the azimuth angle of multipole source polarization relative to the polar angle of cylinder coordinate system, but the other guided modes such as Stoneley wave and flexural wave are independent of angle φ. These are the new results. Considering these results, it is more important to investigate the character of screw mode wave. Dispersion analysis According to the same simplification, we deduce the simplified dispersion of phase velocity of mode waves surrounded by equiaxial crystallographic anisotropicis formation in a borehole referred to a reference state where the velocity of mode waves surrounded by isotropicis formation in a borehole. Equiaxial crystallographic anisotropicis effect are all not same to the three kind of mode wave, the biggest effect is Stoneley mode wave and the smallest effect is screw mode wave, the effect of flexural mode wave is between Stoneley mode wave and screw mode wave.