Quadrupole acoustic logging is used to measure shear in the logging-while-drilling (LWD) environment. Evaluation of shear slowness in quadrupole acoustic logging requires an inversion method that takes into account the dispersion of the quadrupole mode, including tool-presence effects. The inversion method was developed to adopt a semblance processing that is based on waveform back propagation, assuming a homogeneous isotropic (HI) formation model with tool-presence effects. The inversion optimizes formation shear slowness and also includes optimization of mud slowness as an internal parameter to compensate for effects of undetermined mud slowness. A fast and robust optimization technique was employed using characteristics of the quadrupole semblance map to locate the maximum semblance peak. An automatic frequency band selection minimized errors from unknown borehole parameters and environmental effects. Testing with synthetic data validates the inversion method and field results showed very good agreement with wireline measurements.
The quadrupole mode generated by a quadrupole source shows a dispersive nature over a wide-frequency band in sonic measurements. In addition, it has the advantage over flexural mode of being able to measure shear slowness in LWD environments. Because the rigid body of the LWD tool causes a strong interference between the flexural mode of the tool and that of the borehole, it is not possible to use a dipole source to determine shear. With proper design of the LWD collar, the collar and formation quadrupole arrivals are kept separate, making feasible accurate formation shear measurements. In contrast to the flexural mode excited by a dipole source, the quadrupole mode shows no asymptote to the formation shear at low frequency. Modeling studies show that the quadruple mode is a function of six borehole parameters (formation compressional and shear slowness, formation density, borehole diameter, mud slowness, and density) in case of an HI formation model. In particular, quadrupole mode has a significant sensitivity for mud slowness in fast and intermediate formations. Therefore, dispersive processing is required for estimating formation shear slowness. This leads to a model-based inversion method which optimizes shear slowness by optimizing semblance. A fast and robust optimization technique with a peaksearch method was developed by using characteristics of the semblance plane for achieving better performance than the standard nonlinear optimization method. Test results of quadrupole inversion with synthetic and field data are presented.
Assuming an HI formation model, the quadrupole dispersion curve depends on six parameters: formation compressional (DTc) and shear slowness (DTs), formation density (Rhob), borehole diameter (BHD), mud slowness (DTm), and mud density (Rhom). A sensitivity analysis is performed to analyze the dependence of the quadrupole mode on these six borehole parameters. The sensitivity analysis on an intermediate slowness HI formation model shows that the shear slowness has the highest sensitivity among all the parameters in a wide frequency range (Figure 1), though mud slowness also has a significant sensitivity. Further analysis shows that the sensitivity to mud slowness becomes smaller in slow formations, while it becomes higher in fast and intermediate formations.
