Acoustic modes of propagation in the borehole and their relationship to rock properties

Geophysics ◽  
1982 ◽  
Vol 47 (8) ◽  
pp. 1215-1228 ◽  
Author(s):  
F. L. Paillet ◽  
J. E. White
Keyword(s):  
Elastic Solid ◽  
Body Waves ◽  
Radioactive Waste Disposal ◽  
Plane Geometry ◽  
Rock Properties ◽  
Geometry Model ◽  
Head Waves ◽  
Time Domain Response ◽  
Tube Wave ◽  
The Time Domain

Acoustic waveform measurements in boreholes have important applications in fracture hydrology and radioactive waste disposal, but ambiguities in existing interpretation techniques remain a problem. We have addressed the problem by using residue theory to predict the relative excitation of various modes contained in experimental waveforms. A plane‐geometry model involving a layer of fluid between two elastic half‐spaces is shown to provide velocity dispersion curves for propagating modes that are very similar to those for the fluid‐filled borehole. We use the plane‐geometry model to illustrate the effects of the confined borehole fluid on surface and body waves traveling along the borehole in the elastic solid. We also computed excitation functions for some of the lowest‐order symmetric modes, calculated the time‐domain response of the trapped modes following the shear head waves, and compared them to waveforms recorded in boreholes through several homogeneous formations. The insight into the mode composition of the experimental waveforms obtained in these formations is used to construct amplitude logs that should be especially sensitive to variations in the presence of fluid‐filled fractures in the borehole wall. Initial tests show the technique is most successful when the waveform is dominated by the fundamental tube wave, and yet frequencies remain relatively high. The model analysis indicates these conditions can only be obtained when the borehole diameter is not much larger than that of the logging tool.

Tube-wave monitoring as a method to detect shear modulus changes around boreholes: A case study

Geophysics ◽  
2021 ◽  
pp. 1-69
Author(s):  
Daniel Wehner ◽  
Filipe Borges ◽  
Martin Landrø
Keyword(s):  
Shear Modulus ◽  
Body Waves ◽  
Rock Properties ◽  
Step Method ◽  
Monitoring Method ◽  
Near Surface ◽  
Wave Measurements ◽  
Geological Formation ◽  
Tube Wave ◽  
Borehole Seismic

Monitoring the shear modulus of formations around boreholes is of interest for various applications, ranging from near-surface investigation to reservoir monitoring. Downhole logging tools and borehole seismic are common techniques applied to measure and characterize formation properties. These methods rely on transmitted and reflected waves to retrieve the rock properties. Wave modes travelling along the interface between the well and the formation, such as tube waves, are often considered as noise. However, tube waves are less attenuated than body waves, and contain information about the shear modulus of the formation surrounding the well. Hence, a potential use of this interface wave is of interest. As tube-wave properties depend on several parameters, e.g. well geometry, highly accurate measurements should be performed for use in inferring rock properties. We study the feasibility of tube-wave measurements as a monitoring method. Different experiments are conducted using a hydrophone array in two boreholes, with depths of 30 m and 95 m. The experiments are used to investigate how accurate the tube-wave velocity can be measured, and which parameters have most impact on the measurements. Our results suggest that it is hard to estimate the absolute shear modulus of the geological formation using tube-wave velocities only. However, it seems feasible to use them to monitor changes of the shear modulus, depending on the borehole set up and geological formation. The tube-wave monitoring can be used as a first step method to determine the depth along the well where changes occur before more accurate measurements are performed in a second step.

Estimating slowness dispersion from arrays of sonic logging waveforms

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 530-544 ◽  
Author(s):  
S. W. Lang ◽  
A. L. Kurkjian ◽  
J. H. McClellan ◽  
C. F. Morris ◽  
T. W. Parks
Keyword(s):  
Prediction Models ◽  
Temporal Frequency ◽  
Exponential Model ◽  
Dispersion Relations ◽  
The Body ◽  
Body Waves ◽  
Rock Properties ◽  
Scale Model ◽  
Receiver Array ◽  
Head Waves

Acoustic wave propagation in a fluid‐filled borehole is affected by the type of rock which surrounds the hole. More specifically, the slowness dispersion of the various body‐wave and borehole modes depends to some extent on the properties of the rock. We have developed a technique for estimating the dispersion relations from data acquired by full‐waveform digital sonic array well‐logging tools. The technique is an extension of earlier work and is based on a variation of the well‐known Prony method of exponential modeling to estimate the spatial wavenumbers at each temporal frequency. This variation, known as the forward‐backward method of linear prediction, models the spatial propagation by purely real‐valued wavenumbers. The Prony exponential model is derived from the physics of borehole acoustics under the assumption that the formation does not vary in the axial or azimuthal dimensions across the aperture of the receiver array, but can vary arbitrarily in the radial dimension. The exponential model fits the arrivals of body waves (i.e., head waves) well, because the body waves are dominated by a pole rather than a branch point. Examples of this processing applied to synthetic waveforms, laboratory scale‐model data, and field data illustrate the power of the technique and verify its ability to recover dispersion relations from sonic array data. The interpretation of the estimated dispersion in terms of rock properties is not discussed.

scholarly journals Diagnostically Oriented Experiments and Modelling of Switched Reluctance Motor Dynamic Eccentricity

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3857
Author(s):  
Jakub Lorencki ◽  
Stanisław Radkowski ◽  
Szymon Gontarz
Keyword(s):  
Time Domain ◽  
Test Bench ◽  
Switched Reluctance Motor ◽  
Industrial Applications ◽  
Switched Reluctance ◽  
Static And Dynamic Analysis ◽  
Geometry Model ◽  
Reluctance Motor ◽  
Dynamic Eccentricity ◽  
The Time Domain

The article compares the results of experimental and modelling research of switched reluctance motor at two different operational states: one proper and one with mechanical fault, i.e., with dynamic eccentricity of the rotor. The experiments were carried out on a test bench and then the results were compared with mathematical modelling of quasi-static and dynamic analysis of 2D geometry model. Finally, it was examined how the operation with dynamic eccentricity fault of the motor affected its main physical parameter—the phase current. The analysis was presented in the frequency domain using the Fast Fourier Transform (FFT); however, individual current waveforms in the time domain are also shown for comparison. Applying results of the research could increase reliability of the maintenance of SRM and enhance its application in vehicles for special purposes as well as its military and industrial applications.

Improving the time domain response of fractional order digital differentiators by windowing

2015 ◽  
Vol 107 ◽  
pp. 282-289 ◽  
Author(s):  
Chengyan Peng ◽  
Xiaochuan Ma ◽  
Geping Lin ◽  
Min Wang
Keyword(s):  
Fractional Order ◽  
Time Domain ◽  
Time Domain Response ◽  
The Time Domain

Crone pulse electromagnetic response of a conducting thin horizontal sheet—Theory and field application

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1350-1354 ◽  
Author(s):  
S. S. Rai
Keyword(s):  
Thin Sheet ◽  
Horizontal Layer ◽  
Field Application ◽  
Step Response ◽  
Electromagnetic Response ◽  
Attractive Feature ◽  
Time Domain Response ◽  
The Time Domain ◽  
Interpretation Model ◽  
Response Formula

The horizontal, conducting thin‐sheet model represents a special interest in interpretation of electromagnetic field data since it is a suitable interpretation model for the surficial conductive layer, a common occurrence in many terrains. For small thicknesses of overburden layers [Formula: see text]separation) the resolution of layer thickness and conductivity is not possible and interpretation needs to be carried out in terms of the layer conductance. An attractive feature of the thin‐sheet model is the simplicity with which the time‐domain response [Formula: see text] can be calculated. The step response of an infinitely thin layer was derived by Maxwell (1891). In this paper I derive the Crone pulse electromagnetic (PEM) response of a conducting infinitely thin horizontal layer. Applicability of the study is demonstrated by means of a field example.

Numerical computation of individual far‐field arrivals excited by an acoustic source in a borehole

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 852-866 ◽  
Author(s):  
Andrew L. Kurkjian
Keyword(s):  
Numerical Computation ◽  
The Body ◽  
Body Waves ◽  
Head Wave ◽  
Far Field ◽  
Trapped Mode ◽  
Full Waveform ◽  
Full Wave ◽  
Head Waves ◽  
Strong Shear

In this paper, I model the acoustic logging problem and numerically compute individual arrivals at far‐field receivers. The ability to compute individual arrivals is useful for examining the sensitivities of each arrival to various factors of interest, as opposed to examining the full waveform as a whole. While the numerical computation of the mode arrivals (Peterson, 1974) and the numerical computation of the first head waves (Tsang and Rader, 1979) have been previously reported, the numerical computation of the entire set of head‐wave arrivals is new and is the major contribution of this paper. Following Roever et al. (1974) and others, the full wave field is represented as a sum of contributions from both poles and branchcuts in the complex wavenumber plane. The pole contributions correspond to mode arrivals while the branch cuts are associated with the body waves (i.e., head waves). Both the pole and branch cut contributions are computed numerically and results are presented for the cases of a slow and a fast formation. The shear event in the slow formation is found to be relatively small, consistent with observations in measured data. Contrary to existing knowledge, the shear event in the fast formation is also relatively small. The apparent strong shear arrival in the full waveforms is due primarily to the trapped mode pole in the vicinity of cutoff.

scholarly journals A Reduced-Order Model for Active Suppression Control of Vehicle Longitudinal Low-Frequency Vibration

2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Donghao Hao ◽  
Changlu Zhao ◽  
Ying Huang
Keyword(s):  
Longitudinal Vibration ◽  
Estimation Method ◽  
Low Frequency ◽  
Coupling Model ◽  
Torsional Stiffness ◽  
Model Parameters ◽  
Active Suppression ◽  
Low Frequency Vibration ◽  
Time Domain Response ◽  
The Time Domain

Establishing a prediction model, with linearity and few dof (degree of freedom), is a key step for the design of a control algorithm based on the modern control theory. In this paper, such a model is needed for active suppression of vehicle longitudinal low-frequency vibration. However, many dynamic processes in the vehicle have different effects on the vibration. Therefore, a detailed coupling model is firstly established, considering the dynamics of the torsional vibrations of the driveline and the tire, the tire force nonlinearity, and the vehicle vertical and pitch vibrations. Based on this model, sensitivity analysis is conducted and the results show that the tire slip, the torsional stiffness of the half-shaft, and the tire have great influences on the longitudinal vibration. Then a three-dof model is obtained by linearizing the tire slip into damping. A parameter estimation method is designed to obtain the model parameters. Finally, the model is validated. The time domain response, error analysis, and frequency response results demonstrate that the 3-dof model has a good consistency with the detailed coupling model. It is suitable as a control-oriented model.

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