The mechanical responses in monopole acoustic LWD and their relation with the output voltage waveform

Acoustic logging while drilling (LWD), characterised by simultaneous drilling and logging, is widely used to obtain the elastic parameters of the formation around the borehole. Most published monopole acoustic LWD simulation waveforms are routinely presented as pressure. However, these pressure waveforms disagree with the voltage waveforms recorded in the experiments. Here, to find out the reason of the inconsistent of these two waveforms, both the piezoelectric effect of the transducer and the propagation of the acoustic wave are integrally calculated with the finite-element method, obtaining the voltage waveform as well as the mechanical waveforms. The quantitative comparisons between the mechanical waveforms and the voltage waveform show that the output voltage cannot represent the pressure signal, but a combination of multiple mechanical signals. Based on the piezoelectric equation and the structure of the piezoelectric transducer used in this paper, we formulate the output voltage in terms of the four mechanical quantities, i.e. the radial strain and axial stress of the transducer as well as the acoustic pressure and the radial displacement of the borehole fluid. Furthermore, the contributions of these four mechanical quantities to different wave groups are explored. Finally, the waveforms comparisons after drill collar grooving reveal that the displacement waveform before and after grooving should also be displayed when evaluating the grooving effect instead of only the pressure waveform as in previous studies.

Phase Evolution of the Time- and Space-Like Peregrine Breather in a Laboratory

Coherent wave groups are not only characterized by the intrinsic shape of the wave packet, but also by the underlying phase evolution during the propagation. Exact deterministic formulations of hydrodynamic or electromagnetic coherent wave groups can be obtained by solving the nonlinear Schrödinger equation (NLSE). When considering the NLSE, there are two asymptotically equivalent formulations, which can be used to describe the wave dynamics: the time- or space-like NLSE. These differences have been theoretically elaborated upon in the 2016 work of Chabchoub and Grimshaw. In this paper, we address fundamental characteristic differences beyond the shape of wave envelope, which arise in the phase evolution. We use the Peregrine breather as a referenced wave envelope model, whose dynamics is created and tracked in a wave flume using two boundary conditions, namely as defined by the time- and space-like NLSE. It is shown that whichever of the two boundary conditions is used, the corresponding local shape of wave localization is very close and almost identical during the evolution; however, the respective local phase evolution is different. The phase dynamics follows the prediction from the respective NLSE framework adopted in each case.

Note on the Application of Transient Wave Packets for Wave–Ice Interaction Experiments

This paper presents the transient wave packet (TWP) technique as an efficient method for wave–ice interaction experiments. TWPs are deterministic wave groups, where both the amplitude spectrum and the associated phases are tailor-made and manipulated, being well established for efficient wave–structure interaction experiments. One major benefit of TWPs is the possibility to determine the response amplitude operator (RAO) of a structure in a single test run compared to the classical approach by investigating regular waves of different wave lengths. Thus, applying TWPs for wave–ice interaction offers the determination of the RAO of the ice at specific locations. In this context, the determination of RAO means that the ice characteristics in terms of wave damping over a wide frequency range are obtained. Besides this, the wave dispersion of the underlying wave components of the TWP can be additionally investigated between the specific locations with the same single test run. For the purpose of this study, experiments in an ice tank, capable of generating tailored waves, were performed with a solid ice sheet. Besides the generation of one TWP, regular waves of different wave lengths were generated as a reference to validate the TWP results for specific wave periods. It is shown that the TWP technique is not only applicable for wave–ice interaction investigations, but is also an efficient alternative to investigations with regular waves.

MNLS simulations of surface wave groups with directional spreading in deep and finite depth waters

We simulate focusing surface gravity wave groups with directional spreading using the modified nonlinear Schrödinger (MNLS) equation and compare the results with a fully-nonlinear potential flow code, OceanWave3D. We alter the direction and characteristic wavenumber of the MNLS carrier wave, to assess the impact on the simulation results. Both a truncated (fifth-order) and exact version of the linear dispersion operator are used for the MNLS equation. The wave groups are based on the theory of quasi-determinism and a narrow-banded Gaussian spectrum. We find that the truncated and exact dispersion operators both perform well if: (1) the direction of the carrier wave aligns with the direction of wave group propagation; (2) the characteristic wavenumber of the carrier wave coincides with the initial spectral peak. However, the MNLS simulations based on the exact linear dispersion operator perform significantly better if the direction of the carrier wave does not align with the wave group direction or if the characteristic wavenumber does not coincide with the initial spectral peak. We also perform finite-depth simulations with the MNLS equation for dimensionless depths ($$k_{\text {p}}d$$ k p d ) between 1.36 and 5.59, incorporating depth into the boundary conditions as well as the dispersion operator, and compare the results with those of fully-nonlinear potential flow code to assess the finite-depth limitations of the MNLS.

On the transmission of data packets through fiber-optic cables of uniform index

The treatment of Maxwell equations show that propagating wave of packets in fiber-optic cables is dispersive, propagating in groups, such that group velocity along certain curves in the frequency-phase velocity diagrams vanishes. It is suggested that stalling of wave groups is responsible, for bursting propagation observed in experimental measurements, causing some delay in transmission. The dispersion equations developed here, are different from those given in texts that are based on “weakly guiding approximation”. The queue of such data packets arriving at a router station is found to have a “raised tail” distribution unlike that of Poisson arrivals. For accounting the property, a Mittag–Leffler function distribution (MLFD) of probability is used following a modification of that for a Poisson process, the tail raising is shown to cause delay in transmission, and its estimate is analysed based on the theory.

Directional Coherent Wave Group From an Assimilated Non-linear Wavefield

The presence of coherent wave groups in the ocean has been so far postulated but still lacks evidence other than the indication from the radar images. Here, we attempt to reconstruct a wave field to monitor the evolution of a directional wave group based on a phase resolving two-dimensional non-linear wave model constrained by the stereo images of the ocean surface. The reconstructed wave field of around 20 wavelength squared revealed a coherent wave group compact in both propagating and transverse directions. The envelope of the wave group seems to be oriented obliquely to the propagation direction, somewhat resembling the directional soliton that was theoretically predicted and experimentally and numerically reproduced recently. A comparison with a constrained linear wave model demonstrated the coherence of the non-linear wave group that propagates for tens of wavelengths. The study elaborates a possibility of a spatially coherent short crested wave group in the directional sea.