Simulation of borehole sonic waveforms in dipping, anisotropic, and invaded formations

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. E127-E139 ◽  
Author(s):  
Robert K. Mallan ◽  
Carlos Torres-Verdín ◽  
Jun Ma

A numerical simulation study has been made of borehole sonic measurements that examined shoulder-bed, anisotropy, and mud-filtrate invasion effects on frequency-dispersion curves of flexural and Stoneley waves. Numerical simulations were considered for a range of models for fast and slow formations. Computations are performed with a Cartesian 3D finite-difference time-domain code. Simulations show that presence of transverse isotropy (TI) alters the dispersion of flexural and Stoneley waves. In slow formations, the flexural wave becomes less dispersive when the shear modulus (c44) governing wave propagation parallel to the TI symmetry axis is lower than the shear modulus (c66) governing wave propagation normal to the TI symmetry axis; conversely, the flexural wave becomes more dispersive when c44 > c66. Dispersion decreases by as much as 30% at higher frequencies for the considered case where c44 < c66. Dispersion of Stoneley waves, on the other hand, increases in TI formations when c44 > c66 and decreases when c44 < c66. Dispersion increases by more than a factor of 2.5 at higher frequencies for the considered case where c44 < c66. Simulations also indicate that the impact of invasion on flexural and Stoneley dispersions can be altered by the presence of TI. For the case of a slow formation and TI, where c44 decreases from the isotropic value, separation between dispersion curves for cases with and without the presence of a fast invasion zone increases by as much as 33% for the flexural wave and by as much as a factor of 1.4 for the Stoneley wave. Lastly, presence of a shoulder bed intersecting the sonic tool at high dip angles can alter flexural dispersion significantly at low frequencies. For the considered case of a shoulder bed dipping at 80°, ambiguity in the flexural cutoff frequency might lead to shear-wave velocity errors of 8%–10%.

1964 ◽  
Vol 31 (2) ◽  
pp. 213-222 ◽  
Author(s):  
J. P. Jones

Elastic wave propagation in a medium consisting of two finite layers is considered. Two types of solutions are treated. The first is a Rayleigh train of waves. It is seen that for this case, when the wavelength becomes short, the waves approach two Rayleigh waves plus a possible Stoneley wave. When the wavelength becomes large, there are two waves; i.e., a flexural wave and an axial wave. Calculations are presented for this case. The propagation of SH waves is treated, but no calculations are presented.


Geophysics ◽  
1993 ◽  
Vol 58 (9) ◽  
pp. 1257-1269 ◽  
Author(s):  
Lasse Renlie ◽  
Arne M. Raaen

The stress relief associated with the drilling of a borehole may lead to an anisotropic formation in the vicinity of the borehole, where the properties in the radial direction differ from those in the axial and tangential directions. Thus, axial and radial compressional acoustic velocities are different, and similarly, the velocity of an axial shear‐wave depends on whether the polarization is radial or tangential. A model was developed to describe acoustic wave propagation in a borehole surrounded by a formation with stress‐relief‐induced radial transverse isotropy (RTI). Acoustic full waveforms due to a monopole source are computed using the real‐axis integration method, and dispersion relations are found by tracing poles in the [Formula: see text] plane. An analytic expression for the low‐frequency Stoneley wave is developed. The numerical results confirm the expectations that the compressional refraction is mainly given by the axial compressional velocity, while the shear refraction arrival is due to the shear wave with radial polarization. As a result, acoustic logging in an RTI formation, will indicate a higher [Formula: see text] ratio than that existing in the virgin formation. It also follows that the shear velocity may be a better indicator of a mechanically damaged zone near the borehole than the compressional velocity. The Stoneley‐wave velocity was found to decrease with the increasing degree of RTI.


1972 ◽  
Vol 62 (1) ◽  
pp. 285-299
Author(s):  
Walter L. Pilant

Abstract The equation governing elastic waves propagating along a solid-solid interface is found to have sixteen (16) independent roots on its eight (8) associated Riemann sheets. The range of existence (in terms of material parameters) for the real root corresponding to the propagation of Stoneley waves has long been known. It is found that outside this range there are two types of behavior. If the material of greater density has a velocity slightly greater than that of the material of lesser density, the unattenuated Stoneley waves make a transition to attenuated Interface waves, i.e., they leak energy away from the interface as they propagate along it. If the more dense material has a velocity more than about three times that of the less dense, then the Interface-wave root disappears and energy is propagated along the interface as Rayleigh waves. This Rayleigh-wave propagation is associated with a different root of the fundamental equation. On the other hand, if the material of greater density has a velocity much lower than that of the material of lower density (a case that is difficult to find physically), then no energy will be propagated along the interface at all. This result was unexpected. Some rather interesting behavior of the 16 roots was noted as the physical parameters were varied over a wide range. In addition to the normal collisions between pairs of roots, and between individual roots and branch points (with attendant Riemann sheet jumping), it was found that some roots go through the point at infinity and return with a change in sign. At least one unexpected case of a multiple root was found. Another case was noted in which a pair of complex roots change quadrants in the complex phase-velocity plane, leading to a discontinuity in root type. Finally, it was noted that, in a cyclic variation of the material parameters, it is possible to choose a path such that the roots, when followed individually, will not return to their original values. In fact, as many as five cycles in parameter space can be accomplished before the roots return. All this strange mathematical behavior seems to have no physical significance, but has been presented to increase understanding of the general behavior of the dispersion relations associated with elastic-wave propagation.


Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. D47-D55 ◽  
Author(s):  
Song Xu ◽  
Xiao-Ming Tang ◽  
Yuan-Da Su ◽  
Sheng-Qing Lee ◽  
Chun-Xi Zhuang

Many earth formations are characterized as transversely isotropic (TI) media. In acoustic logging through a vertical borehole, the S-wave TI property has traditionally been determined from borehole monopole Stoneley-wave measurements, but the feasibility of shear-TI estimation from dipole flexural waves has not been fully investigated. We have developed a methodology to determine the TI parameters from borehole dipole-flexural wave data. Our analysis shows that the Stoneley wave is sensitive to the TI property mainly in an acoustically slow formation, and the sensitivity diminishes when the formation becomes faster. The advantage of the flexural wave over the Stoneley wave is that the former wave is sensitive to the TI property in the slow and fast formations, provided the wave measurement is made in a broad frequency range in which the flexural-wave dispersion characteristics from low to high frequencies can be used. By calculating the theoretical flexural-wave dispersion curve for the TI formation and using it to fit the measured wave dispersion data, we can simultaneously determine the vertical and horizontal S-wave velocities, from which the S-wave TI parameter is obtained. Application of our methodology to field data processing shows that the TI parameter estimated from the flexural wave is almost identical to that from the Stoneley wave for a slow formation. For a fast formation, the flexural-wave result is more accurate and reliable compared with the Stoneley-wave result. Our study, thus, introduces a novel application of dipole acoustic logging.


Author(s):  
G. P. Tandon ◽  
J. Kang ◽  
R. Y. Kim ◽  
T. J. Whitney

Composite structures in an aircraft are susceptible to impact damage, which can occur during manufacture, service or maintenance. Recent studies show that impacts with ground support equipment are the major cause of in-service damage to composite structures in an aircraft. Other sources of impact include collision with birds, runway stones or ballistic impacts. These impacts can produce various types of damage, including fiber breakage, matrix cracking, delamination, and interfacial debonding. The results of such damage can have detrimental effects on the overall structural performance and safety. A comprehensive structural health monitoring (SHM) system provides a means to significantly reduce life-cycle costs of aerospace vehicles by providing accurate diagnostics and prognostics of structural damage to reduce unnecessary inspections and support vehicle life extension. The main objective of this paper is to develop a methodology to detect and identify the damage sources and their severity in composite laminates subjected to low velocity impact using wave propagation methods. When damage occurs in a material due to mechanical load or impact, an acoustic wave emits and propagates through the material. The material chosen for this work is a 12″ long and 12″ wide, +/− 60 degree braided composite. Two edges of the plate were fixed by clamping the plate between two steel bars and secured by bolts spaced 1″ apart, while the other two edges were free, as shown in Figure 1. In order to characterize the wave propagation and damage process, two resonant type AE sensors and four accelerometers were mounted on the specimen. The specimen was then tapped lightly with a hand-held acoustic impact hammer at several different chosen locations, and stress wave signals were monitored using a commercial dynamic signal process system which contains software capable of detecting impact source location. The impact force was kept to a minimum initially such that no damage occurred in the specimen. After this initial test, the specimens were subjected to low velocity impact using drop weight impact machine with 0.5 inch spherical indenter. The impact force was increased by a number of times until substantial damage observed while monitoring signals generated from the specimen. After each incremental impact, both acoustic hammer tapping test and nondestructive inspection such as ultrasonic C-scan and/or X-ray radiography were carried out to delineate the damage source and severity. Figure 2 is an example of C-Scan of the composite plate after a series of impacts with various drop heights. Recorded signals were analyzed to determine the origin of the source and its severity. The impact hammer produced both an extensional wave and a flexural wave in these composite plate specimens. Because of dispersive characteristics of the flexural wave, the first arrival time of the extensional wave was used for source location algorithm. Besides the source location, discussion will be given on parameters such as amplitude, energy, frequency, number of events related with impact force, and damage size in detail. As an example, Figure 3 is a plot of the measured damage size as a function of the dead-weight drop height for tests conducted on various panels. As expected, the size of the damage increases with amount of drop height (or impact energy). Thus, based on C-scan measurements, critical threshold impact height of approximately 5″ is identified for “any measurable” damage to occur. The corresponding magnitude of the impact energy is ∼ 108 in-lb. On the other hand, the critical threshold for any visual damage to be detected is approximately 502 in-lb for the laminate material investigated. In summary, a methodology has been developed for estimating the damage severity from the amplitude of the signal received. The approach entails constructing design curves relating the size of the damage to impact energy, and establishing relationships between impact energy and the magnitude of the signal. These relationships can then be used to predict the estimated size of the damage based on the amplitude of the arriving signal. A critical threshold impact energy has been identified below which “no measurable” damage occurs. Three regions of damage growth, namely, a decreasing rate with magnitude of impact energy. A constant damage growth rate characterizes the steady-state region, while damage size increases almost exponentially with impact energy in the tertiary region potentially leading to catastrophic failure.


Geophysics ◽  
1991 ◽  
Vol 56 (4) ◽  
pp. 447-460 ◽  
Author(s):  
X. M. Tang ◽  
C. H. Cheng ◽  
M. N. Toksöz

The propagation of Stoneley waves in a fluid‐filled borehole with a vertical fracture is investigated both theoretically and experimentally. The borehole propagation excites fluid motion in the fracture and the resulting fluid flow at the fracture opening perturbs the fluid‐solid interface boundary condition at the borehole wall. By developing a boundary condition perturbation technique for the borehole situation, we studied the effect of this change in the boundary condition on the Stoneley propagation. Cases of both hard and soft formations have been investigated. The fracture has minimal effects on the Stoneley velocity, except in the very low frequency range in which the Stoneley velocity drastically decreases with decreasing frequency. Significant Stoneley‐wave attenuation is produced because of the energy dissipation into the fracture. The quantitative behavior of these effects depends not only on fracture aperture and borehole radius, but also on the acoustic properties of the formation and fluid. Ultrasonic experiments were performed to measure Stoneley propagation in laboratory fracture borehole models. Aluminum and lucite were used to simulate a hard and a soft formation, respectively. Array data for wave propagation were obtained and were processed using Prony’s method to give velocity and attenuation of Stoneley waves as a function of frequency. In both hard and soft formation cases, the experimental results agreed with the theoretical predictions. The important result of this study is that it presents a quantitative relationship between the Stoneley propagation and the fracture character in conjunction with formation and fluid properties. This relationship provides a method for estimating the characteristics of a vertical fracture by means of Stoneley wave measurements.


Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 118-126 ◽  
Author(s):  
Xiaoming Tang

Many rocks exhibit transversely isotropic (TI) characteristics. For determining the TI property using acoustic logging, Stoneley waves are the only borehole wave mode that has a significant sensitivity to TI effects, especially when the formation is acoustically slow compared to the borehole fluid. This study describes a method for deriving the formation shear‐wave TI parameter from the Stoneley wave data acquired by a logging tool. It is shown that the presence of the tool in the borehole can substantially affect the Stoneley wave propagation. Fortunately, for low‐frequency Stoneley waves, the tool effect can be satisfactorily modeled using an effective modulus, regardless of the actual structure of the tool. The modulus can be determined from a calibration procedure. In the inversion processing of the Stoneley wave data, the Stoneley wave slowness is related to the weighted average of the wave's dispersion curve over the frequency range occupied by the wave spectrum. This provides a fast method for the inversion. As a processing example, this method has been applied to estimate the shear‐wave TI parameter profile for the Lewis shale formation in Braggs, Wyoming. The resulting profile delineates the shear‐wave anisotropy magnitude and variation for this shale formation.


1986 ◽  
Vol 39 (6) ◽  
pp. 853-865 ◽  
Author(s):  
M. M. Al-Mousawi

Experimental investigations in the field of longitudinal wave propagation in beams are plentiful; however, experimental studies of flexural wave propagation problems are scarce and are restricted mainly to uniform and infinite structures where the effects of reflected waves are not generally included. This review is mostly restricted to low velocity impact and does not cover the so-called high velocity impact such as those of bullets and explosives. In addition to a brief survey of classical work related to impact, this article covers publications related to experimental studies of longitudinal and flexural elastic waves due to impact. This includes the longitudinal, central as well as eccentric impact and transverse impact of two bars and the impact achieved by sphere impinging on a beam. Many workers used experimental findings to study the adequacy of various theoretical solutions of the wave propagation problem such as those by Pochhammer and Chree, Euler–Bernoulli, and the Timoshenko beam theory. The revival of interest in the recent years is due to, among other things, the advancement of experimental equipment and measurement techniques for data acquisition of stress waves and associated signals. An important application of transient waves is their use for the determination of material properties under various loading conditions and strain rates that can be studied by the split Hopkinson pressure bar techniques. The problem of longitudinal and flexural waves in bars with discontinuities of cross section are covered, and some publications on fracture of materials due to bending waves are also included. Experimental investigations demonstrate the effect of abrupt change of cross section and/or material properties on reflected and transmitted waves where reflections are to be taken into consideration when estimating the level of stresses and strains in finite beam with discontinuities. In the field of flexural wave propagation, comparison of theoretical predictions with experimental results verified and validated the adequacy of the Timoshenko theory for the determination of bending strain in finite structures, a one-dimensional theory that takes into account the effect of shear deformation and rotatory inertia.


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