A general expression is derived for the dispersion relations and the impulse response of a radially layered borehole. The model geometry consists of a central fluid cylinder surrounded by an arbitrary number of solid annuli. A Thomson-Haskell type propagator matrix is used to relate stresses and displacements across the layers. Although the model is completely general, the geometries considered here are restricted to those of a cased bole. Layers of steel, cement, and formation surround the innermost fluid layer. Synthetic microseismograms containing all body and interface waves are calculated for a variety of model parameters.Formation body wave arrivals are relatively unaffected by the presence of a casing. They may, however, be hard to identify if cement velocities are close to or larger than those of the formation. The Stoneley and pseudoRayleigh wave arrivals are strongly influenced by the casing parameters. They respond to the combined effects of the steel, the cement, and the formation.

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Automatic methods of determining P and S velocities from full waveform acoustic logs are studied and compared. The suggested P‐wave method is an event detector which is based on threshold detection in a window near the previous picks and fine adjustment by a semblance correlation. The moveouts found by the correlation process are used to find common source P velocities as well as effective borehole compensated (BHC) P velocities. Compensated velocities are derived from waveforms from complementing tool positions which compare favorably to velocities from standard BHC sonic logs. We call the most reliable method for S waves the P‐correlated S‐method. It consists of correlating the P waveform with the rest of the record to find the S arrival. The S waveform is then correlated with the next record to determine the S velocity. This method is compared with published techniques and proves more stable and reliable. The method does not necessitate a distinct S‐wave arrival and can utilize the existence of the reflected conical wave whose phase velocity is controlled by the S velocity of the formation.

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