Sonic logging data are useful in a variety of applications, including seismic correlation, rock mechanics and wellbore stability, pore pressure prediction, sourceless porosity estimation, gas detection, and stress and fracture characterization. In many cases, logging-while-drilling (LWD) sonic logs provide a helpful alternative to wireline logs because of hazard avoidance, timeliness of information, rig costs, or ease of deployment, particularly in horizontal wells. Shear wave slowness logs play an important role in many applications, yet they can be problematic to obtain, particularly in slow formations where the refracted shear wave arrival is not supported. Modern LWD sonic logging tools typically use a quadrupole excitation source that can excite a quadrupole mode, or screw waves, from which the formation shear wave velocity can be derived.
A fundamental feature of screw waves excited by a quadrupole source in an LWD environment is that their nonleaky cutoff frequency slowness is the formation shear slowness. However, the slowness data near this cutoff frequency are often influenced by noise or the presence of other modes because of the low excitation amplitude. Conventional methods process the energetic, higher-frequency portion of the screw waves and perform a model-based dispersion correction to obtain the final shear slowness estimate. This model-based correction assumes a well-conditioned borehole and known borehole (e.g., caliper and mud speed) and formation parameters (e.g., density and compressional speed) and can produce erroneous results when assumptions are violated.
To overcome these difficulties, a data-driven quadrupole method was developed that operates in the frequency domain and uses all useful dispersion responses of the existing modes. The technique is an extension of the data-driven dispersion processing of wireline flexural waves for quadrupole data. The process first generates a differentiate-phase frequency-slowness coherence/semblance map and then extracts the slowness dispersion vs. frequency, which is used to compute the slowness density log along the slowness axis. An edge-detection method is then applied to capture the leading edge associated with the shear slowness and to form an initial estimate of the formation shear slowness based on slowness value at the leading peak on the slowness density log. This shear slowness forms the input to another algorithm that minimizes the misfit between the screw slowness vector and a simplified screw dispersion model to refine the shear slowness answer. The simplified screw dispersion model consists of a precomputed library of theoretical screw dispersion curves and two data-driven parameters that are used to account for errors generated by unknown inputs. The optimization process estimates both the shear slowness and screw wave dispersion response.
Field data results suggesting that reliable and high-quality shear slowness logs can be obtained over a wide range of formations are discussed.
