Differences between observed and forward modelled flexural wave dispersion characteristics in cross dipole sonic logging in homogeneous formations are useful for evaluating mud invasion and for differentiating between stress-induced and fabricrelated anisotropy. In this paper we investigate the sensitivity of the dispersion effect to borehole size and mud slowness, and show the importance of taking account of the tool's mechanical properties in the forward model -particularly when the tool diameter is a substantial fraction of the well diameter. We demonstrate that a new generation of small diameter cross dipole tool has a small tool-effect in common hole sizes, and extend the dispersion model results down to hole diameters less than 4 inches; we verify the calculations with real data sets acquired in sub 4-inch wells, as well as larger wells up to a 12 inches diameter. The results are also used to examine the size of dispersion corrections needed to calculate shear slowness in situations where low frequencies from the broadband transmitter are coupled relatively weakly to the formation.
IntroductionVelocity logs are a key component in generating seismic ties, in the derivation of data used to populate mechanical earth models, and for fluids identification and related petrophysical applications. In fast formations, refracted shear waves are generally present in monopole waveforms, but shear velocity in slow (as well as fast) formations is commonly derived from flexural waves excited by dipole sources mounted in a wireline tool. Borehole flexural waves are dispersive, however. In the low frequency limit flexural waves travel at the formation shear velocity, but in the high frequency range they travel more slowly. Very often the processed shear velocity needs to be corrected to the true shear velocity according to its dispersion characteristics -Kimball (1998). In model-based dispersion correction the flexural velocity is computed in a narrow lowfrequency band and then corrected for residual dispersion effects using a theoretical model. Additionally, the dispersive behaviour can be exploited to evaluate formation alternation due to mud invasion, borehole damage or stress -in this case by comparing the observed flexural wave dispersion characteristics with the modelling results in an assumed homogeneous formation. For both applications the accuracy of the end product depends on the quality of the forward model, and an important factor in the model is the mechanical behaviour of the tool itself within the borehole.In this paper we analyze the tool effect for a new generation of small diameter cross-dipole wireline tool, and include results for holes as small as 3.8 inches (96mm) -for which we also have field data. The primary objective is to characterize the full dispersion curve as the foundation of a future study of formation stress, but we also show the utility of the result in the basic processing of shear slowness (inverse velocity).
