Changes in P-wave velocity with different full waveform sonic transmitter centre frequency
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Full waveform sonic logging, with the transmitter set at different centre frequencies, often provides different compressional wave velocities over the same interval. There may be several reasons why these velocity differences are recovered where the source has different frequency content. Examples include: intrinsic dispersion, scattering dispersion, geometric dispersion, processing artefacts and acquisition artefacts. We acquired and analysed multifrequency monopole full waveform sonic logging data from the cored drill hole intersecting a high-permeability sandy aquifer in the Northern Gnangara Mound, Perth Basin, Western Australia. A key interval of the shallow, sand-dominated Yarragadee Formation was selected and logged four times with transmitter centre frequencies set to 1, 3, 5 and 15 kHz. We compute apparent velocity dispersion as the percentage velocity differences in the P-wave velocity recovered from full waveform sonic logs completed at different dominant transmitter centre frequencies. We find that high-permeability sediments could be placed into broad groups: cross-bedded and non-cross-bedded sandstones.We find a distinctly different relationship between apparent P-wave velocity dispersion and permeability for cross-bedded and non-cross-bedded sandstones. Cross plots for the two sediment types show a general trend of increasing apparent dispersion with increasing permeability. Grouping the sandstone layers based on sediment type, as observed from core samples, illustrates different but positive correlation between the apparent P-wave velocity dispersion and permeability in these shallow, weakly-consolidated sandstones. The cross-bedded sandstone, for its part, has a wider range of permeability than the non-cross-bedded sandstone but a smaller range of apparent P-wave velocity dispersion. Given these results, our hypothesis is that while permeability plays a role, other factors such as geometric dispersion or scattering dispersion likely contribute the net value of P-wave dispersion recovered between any two receivers. Finally the results from these experiments have shown that there exists at least a weak empirical relationship between P-wave velocity dispersion and hydraulic permeability at the field site.
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