scholarly journals Heuristics of the Branch-Cut-and-Price-Framework SCIP

2008 ◽  
pp. 31-36 ◽  
Author(s):  
Timo Berthold
Keyword(s):  
Branch Cut

A theoretical investigation of acoustic monopole logging-while-drilling individual waves with emphasis on the collar wave and its dependence on formation

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. D1-D11 ◽  
Author(s):  
Xiaobo Zheng ◽  
Hengshan Hu
Keyword(s):  
Theoretical Analysis ◽  
Excitation Spectrum ◽  
Integral Method ◽  
Individual Component ◽  
P Wave ◽  
Residue Theorem ◽  
Full Waveform ◽  
Logging While Drilling ◽  
Traveling Speed ◽  
Branch Cut

To seek measures to weaken the collar wave signals so that the formation arrivals are observable, it is important to make theoretical analysis of separate collar wave and formation arrivals in the acoustic logging-while-drilling environment. However, until now, the collar wave signal and the formation P- and S-arrivals have never been separately calculated. We have obtained individual component waves using the residue theorem and the branch-cut integral method, including residues at leaky poles. The waveform summed up from all individual waves is shown to agree well with the full waveform calculated by real-axis integration. In particular, the formation P-wave is obtained by summing the formation leaky mode and the compressional branch-cut integral for slow formations. The collar wave is found to propagate in the borehole and the formation as well as in the collar. Although the traveling speed of the collar wave is almost irrelevant to the formation, the attenuation and excitation spectrum of the collar wave are significantly affected by the formation, which reveals that an effective collar wave weakening design should be based on a model with the formation being taken into consideration.

Phase unwrapping with the branch-cut method: role of phase-field direction

2000 ◽  
Vol 39 (26) ◽  
pp. 4802 ◽  
Author(s):  
Bernd Gutmann ◽  
Herbert Weber
Keyword(s):  
Phase Field ◽  
Phase Unwrapping ◽  
Field Direction ◽  
Cut Method ◽  
Branch Cut

Branch, Cut, and Price: Sequential and Parallel

2001 ◽  
pp. 223-260 ◽  
Author(s):  
Laszlo Ladányi ◽  
Ted K. Ralphs ◽  
Leslie E. Trotter
Keyword(s):  
Branch Cut

Compressional head waves in attenuative formations: Forward modeling and inversion

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1908-1920 ◽  
Author(s):  
Qing‐Huo Liu ◽  
Chung Chang
Keyword(s):  
Radiation Condition ◽  
Forward Modeling ◽  
Head Wave ◽  
Transmission Measurement ◽  
Processing Scheme ◽  
Straightforward Application ◽  
Head Waves ◽  
Simple Processing ◽  
The Individual ◽  
Branch Cut

We develop a method of forward modeling and inverting formation attenuation data from sonic compressional head waves in a fluid‐filled borehole using a branch‐cut integration (BCI) technique to calculate individual acoustic arrivals. We validate this approach with a real‐ axis integration (RAI) method that does not separate the individual arrivals. We show that the straightforward application of the original BCI method for lossless media gives erroneous results for attenuative formations. With a choice of the Riemann sheets satisfying the radiation condition, the new BCI method gives correct results for most lossy and lossless formations. However, modeling very slow formations needs to include the contribution of a leaky pole near the vertical branch cut. With a constant‐Q assumption, we develop a simple processing scheme to extract the formation compressional Q factor from the P head‐wave arrivals. We used experimental data from laboratory‐scale borehole measurements to invert for the compressional Q value of a Lucite block. The inverted results agree within 4.5% of an independent ultrasonic transmission measurement of Q.

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