Wavelength-Based Axial Resolution Limitations of Flexural Wave Dispersion Sonic Logging
- Kristoffer Walker (Now with Chevron ETC) | Qingtao Sun (Halliburton) | Ruijia Wang (Halliburton)
- Document ID
- Society of Petrophysicists and Well-Log Analysts
- SPWLA 60th Annual Logging Symposium, 15-19 June, The Woodlands, Texas, USA
- Publication Date
- Document Type
- Conference Paper
- 2019. held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors
- 7 in the last 30 days
- 109 since 2007
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Dipole sonic logging can estimate formation shear slowness in all formations and thus has important applications in lithology classification, geomechanical analysis, porosity estimation, and pore pressure prediction. A dipole transmitter is used to excite a flexural wave, which is a guided wave that travels along the borehole wall with an apparent slowness (inverse of velocity) that is dispersive. The low-frequency asymptote of this dispersion indicates the formation shear slowness, which is usually measured with a time-or frequency-domain semblance method. Modern borehole acoustic tools have an array of receivers spanning an axial aperture of 6 ft, which permits use of a subarray of receivers to sense a shorter axial length of investigation. Because smaller apertures usually increase the sharpness of a dipole sonic log, one often assumes the aperture length dictates the true axial resolution. However, it is well known that the slowness resolution power of semblance processing also depends on how much variation in phase exists across the receiver array for the slowness range that spans the true slowness. Transforming from frequency to wavenumber space is the same as saying the resolution power depends on how many wavelengths are obtained within the receiver aperture.
This paper presents numerical modeling of flexural wave propagation for fast and slow formations to show that the ability to resolve the low-frequency asymptote of thin beds is a function of bed thickness and borehole and formation parameters. Specifically shown are the results of applying frequency semblance to flexural mode waveforms created by three-dimensional (3D) finite-difference time-domain (FDTD) simulations where the thickness and velocity contrast of interbedding are precisely controlled. An equation is derived that predicts the minimum resolvable layer thickness based on the concept that a progressively thickening bed will eventually obtain a thickness that will encompass a sufficient number of wavelengths (within the frequency range of the asymptote dictated by the borehole and formation parameters) to be well resolved via semblance methods. For example, a thin bed with a 15% velocity contrast for an 8.5-in borehole does not encompass a sufficient number of wavelengths within the 2 to 4 kHz asymptote region for thin beds less than 3 ft in thickness. However, for a smaller borehole where the asymptote extends to higher frequencies or for a 3-ft bed with the same velocity contrast, such resolution is possible.
An implication of these results is that for fast formations the higher-frequency monopole/dipole refracted shear logs are more capable of higher axial resolution, provided the formation is fast enough that the refracted shear exists and is well separated from the Stoneley mode. Furthermore, shear slowness estimation algorithms that weight preferentially the higher frequencies within the asymptote region of the dispersion curve are well posed to resolve thin beds when the bed-thickness-to-wavelength ratio permits it.
|File Size||2 MB||Number of Pages||17|