This thesis provides a feasibility study on the determination of formation anisotropy parameters from logging-while-drilling (LWD) borehole acoustic measurements. For this reason, the wave propagation in fluid-filled boreholes surrounded by transverse isotropic (TI) formations is investigated in great detail using the finite-difference method. While the focus is put on quadrupole waves, the sensitivities of monopole and flexural waves are evaluated as well. All three wave types are considered with/without the presence of an LWD tool. Moreover, anisotropy-induced mode contaminants are discussed for various TI configurations. In addition, the well-known plane wave Alford rotation has been generalized to cylindrical borehole waves of any order, except for the monopole. This formulation has been extended to allow for non-orthogonal multipole firings, and associated inversion methods have been developed to compute formation shear principal velocities and accompanying polarization directions, utilizing various LWD (cross-) quadrupole measurements.:1 Introduction
1.1 Borehole acoustic configurations
1.2 Wave propagation in a fluid-filled borehole in the absence of a logging tool
1.3 Wave propagation in a fluid-filled borehole in the presence of a logging tool
1.4 Anisotropy
2 Theory
2.1 Stiffness and compliance tensor
2.1.1 Triclinic symmetry
2.1.2 Monoclinic symmetry
2.1.3 Orthotropic symmetry
2.1.4 Transverse isotropic (TI) symmetry
2.1.5 Isotropy
2.2 Reference frames
2.3 Seismic wave equations for a linear elastic, anisotropic medium
2.3.1 Basic equations
2.3.2 Integral transforms
2.3.3 Christoffel equation
2.3.4 Phase slowness surfaces
2.3.5 Group velocity
2.4 Solution in cylindrical coordinates for the borehole geometry
2.4.1 Special case: vertical transverse isotropy (VTI)
2.4.2 General case: triclinic symmetry
3 Finite-difference modeling of wave propagation in anisotropic media
3.1 Finite-difference method
3.2 Spatial finite-difference grids
3.2.1 Standard staggered grid
3.2.2 Lebedev grid
3.3 Heterogeneous media
3.4 Finite-difference properties and grid dispersion
3.5 Initial conditions
3.6 Boundary conditions
3.7 Parallelization
3.8 Finite-difference parameters
4 Wave propagation in fluid-filled boreholes surrounded by TI media
4.1 Vertical transverse isotropy (VTI)
4.1.1 Monopole excitation
4.1.2 Dipole excitation
4.1.3 Quadrupole excitation
4.1.4 Summary
4.2 Horizontal transverse isotropy (HTI)
4.2.1 Monopole excitation
4.2.2 Theory of cross-multipole shear wave splitting
4.2.3 Dipole excitation
4.2.4 Quadrupole excitation
4.2.5 Hexapole waves
4.2.6 Summary
4.3 Tilted transverse isotropy (TTI)
4.3.1 Monopole excitation
4.3.2 Dipole excitation
4.3.3 Quadrupole excitation
4.3.4 Summary
4.4 Anisotropy-induced mode contaminants
4.4.1 Vertical transverse isotropy (VTI)
4.4.2 Horizontal transverse isotropy (HTI)
4.4.3 Tilted transverse isotropy (TTI)
4.4.4 Summary
5 Inversion methods
5.1 Vertical transverse isotropy (VTI)
5.2 Horizontal transverse isotropy (HTI)
5.2.1 Inverse generalized Alford rotation
5.2.2 Inversion method based on dipole excitations
5.2.3 Inversion method based on quadrupole excitations
5.3 Tilted transverse isotropy (TTI)
5.4 Challenges in real measurements
5.4.1 Signal-to-noise ratio (SNR)
5.4.2 Tool eccentricity
6 Conclusions
References
List of Abbreviations and Symbols
List of Figures
List of Tables
A Integral transforms
A.1 Laplace transform
A.2 Spatial Fourier transform
A.3 Azimuthal Fourier transform
A.4 Meijer transform
B Stiffness and compliance tensor
B.1 Rotation between reference frames
B.2 Cylindrical coordinates
C Christoffel equation
C.1 Cartesian coordinates
C.2 Cylindrical coordinates
D Processing of borehole acoustic waveform array data
D.1 Time-domain methods
D.2 Frequency-domain methods
D.2.1 Weighted spectral semblance method
D.2.2 Modified matrix pencil method
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:76975 |
| Date | 07 January 2022 |
| Creators | Demmler, Christoph |
| Contributors | Buske, Stefan, Geerits, Tim W., Tang, Xiaoming, TU Bergakademie Freiberg |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 10.1190/segam2020-3426574.1 |
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