The radiation of an elastic field from a plane piston source is formulated using the representation theorem, in which the Green’s function for an elastic half-space is employed. On the basis of this formulation, the radiated elastic wave field for both compressional and shear cylindrical wave sources is derived. The diffraction of elastic waves incident on a receiver that has the same geometry as that of the source and is coaxially aligned with it is studied. The authors present a procedure in which both numerical and asymptotic techniques are employed to allow them to evaluate the diffraction effects in any frequency range of interest. The elastic diffraction is compared with the acoustic diffraction and it is discovered that they differ only in the nearfield of the piston source because of the coupling between shear and compressional components in the elastic case. In the farfield, however, the elastic diffraction approaches the acoustic diffraction. With the help of ultrasonic laboratory measurements, the authors test the theoretical results and find that the theory and experiments agree well for the elastic solution. An important application of the results of this study is in attenuation measurements using pulse propagation techniques, where spectral ratio of a sample relative to a standard sample, or ratio of samples of the same material but different length is used. In the former case, the attenuation can be overestimated. While in the latter case, the attenuation can be significantly underestimated, if corrections for diffraction effects are not made.
In Vertical Seismic Profiling tube waves are generated by compressional waves impinging on subsurface fractures or permeable zones. The amplitude of tUbe waves is dependent upon the formation permeability, the length of the fracture, and on the source frequency. The generation of tube waves is formulated theoretically and the relative effects of these parameters are studied individually. Field examples are shown for open fractures in granite. From tube wave amplitudes normalized to P-wave amplitudes, calculated permeabilities are on the order of 400 millidarcys.
Full waveform acoustic well logging has become instrumental to hydrocarbon exploration because of its ability to determine in situ velocity information for P and S waves as well as the attenuation (or absorption) of seismic energy. It is therefore important that the factors infiuencing these logs be understood. In addition to formation properities, Poisson's ratio, the borehole environment, and tool centering can affect the full waveform acoustic logs. These latter factors are evaluated through modeling of elliptic boreholes and de-centralized tools in the borehole. INTRODUCTIONA number of factors affect the observed full waveform acoustic log amplitudes. Formation properities play an important role. In addition the borehole environment can cause variations. For example, borehole rugosity impedes the propagation of head waves (Morris et aI., 1964). In areas of' cavitation and washouts, critical refraction may be prevented, resulting in low amplitude waveforms. Lebreton et al. (1978) report a strong reduction in waveform amplitude proportional to an increase in mud cake thickness.Centering of the sonde and a cylindrical borehole are crucial to waveform amplitudes and arrival times. In most full waveform logging systems the tool is held centralized in the borehole by several bow type springs which press against the formation. In other systems, rubber "fingers" keep the tool centralized. The reliability of these methods in keeping the tool centralized in holes with a true circular cross section as well as in irregular holes has not been well documented. The actual amount of "rattle" that the tool experiences is not generally known.Morris estimates that moving the source one quarter of an inch (0.64 cm) off-center decreases the P wave amplitude by one half (Morris et al., 1964). This is a significant effect for such a small displacement. In experiments with a tool placed in a trough to simulate a cased borehole it was determined that moving the centralized source completely against the casing not only decreases the amplitude of the recorded waveform but also increases its complexity and reverses the apparent polarity of the first motion (Riddle, 1962). Studies by Forristall and Ingram (1969) show that an off-centered condition for a fiuid cylinder yields two types of refiected arrivals: one associated with the source waveform, and the other with its derivative.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.