Compressional head waves in attenuative formations: Forward modeling and inversion

摘要

We develop a method of forward modeling and inverting formation attenuation data from sonic compressional head waves in a fluid-filled borehole using a branch-cut integration (BCI) technique to calculate individual acoustic arrivals. We validate this approach with a real-axis integration (RAI) method that does not separate the individual arrivals. We show that the straightforward application of the original BCI method for lossless media gives erroneous results for attenuative formations. With a choice of the Riemann sheets satisfying the radiation condition, the new BCI method gives correct results for most lossy and lossless formations. However, modeling very slow formations needs to include the contribution of a leaky pole near the vertical branch cut. With a constant- Q assumption, we develop a simple processing scheme to extract the formation compressional Q factor from the P head-wave arrivals. We used experimental data from laboratory-scale borehole measurements to invert for the compressional Q value of a Lucite block. The inverted results agree within 4.5% of an independent ultrasonic transmission measurement of Q.