Acoustic mode waves and individual arrivals excited by a dipole source in fluid-filled boreholes |
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Authors: | XiuMei Zhang HaiLan Zhang and XiuMing Wang |
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Institution: | (1) State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China |
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Abstract: | An approach of separating individual wave arrivals for a dipole logging is presented. The branch points are treated as a type
of logarithm and the Riemann surface structure of the multivalued function is studied, that is, the displacement potential
within the borehole. Based on the theoretical analysis, the complex poles contributing to the wave field on various Riemann
sheets are investigated in detail for the case of a fast formation. It is shown that poles on Riemann sheet (0,0) are real
and form branches of modes with dispersion. Mathematically, it is demonstrated that the flexural mode has no cutoff frequency,
which is different from the traditional point of view. Poles on other relevant Riemann sheets are complex and form many branches
on the complex frequency-wavenumber plane. Further investigation on the pole and branch cut contributions indicates that the
vertical branch cut integration method has limitations in separating wave arrivals. By properly taking into account the complex
poles on various Riemann sheets together with branch cut integrations, wave arrivals are separated from the full waveforms
effectively for both the fast and slow formation models. Specially, there are complex poles on Riemann sheet (0,−1) in the
vicinity of the compressional branch cut for a slow formation with a large Poisson’s ratio, which have small imaginary parts
and contribute a lot to the p-wave arrival.
Supported by the National Natural Science Foundation of China (Grant No. 10534040) |
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Keywords: | dipole sources Riemann sheet cutoff frequency individual arrivals |
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