Inversion of shear wave slowness and attenuation from dipole acoustic logging data based on an equivalent tool theory

The presence of a sonic logging tool affects the propagation characteristics of dipole-flexural wave in a fluid-filled borehole. As a result, the tool effect should be considered during the processing and inversion of the dipole-flexural wave for acoustic properties of shear wave. We show that the presence of the tool not only changes the slowness dispersion of the flexural wave but also results in a shift of its frequency-dependent attenuation toward lower frequencies. Equivalent tool theory (ETT) can realistically model the effect of an acoustic tool on guided wave propagation. With the ETT framework, we develop a unified workflow for estimating both the shear wave slowness and attenuation from dipole array acoustic waveforms. The workflow is an extension of the model-based dispersive processing of dipole logging data. The proposed workflow involves two inversion procedures. By matching the actual dispersion data with the theoretical dispersion predicted by the ETT, we can invert the shear wave slowness and tool parameters. With the estimated shear wave slowness and other borehole parameters, we further calculate the partition coefficients of flexural waves using the ETT. Based on the concept of energy partitioning, we formulate a linear optimization problem and invert for the shear wave attenuation from the frequency-dependent dipole attenuation. We use synthetic and field data to demonstrate the effectiveness and applicability of the developed method. The results show that it is important to incorporate the tool effect when processing dipole acoustic logging data for shear wave slowness and attenuation, especially in a fast formation.