A borehole-model-derived algorithm for estimating QP logs from full-waveform sonic logs

Abstract

We develop a processing algorithm to estimate the intrinsic seismic attenuation [Formula: see text] from P head waves of full-waveform sonic logs. The algorithm, based on an extended version of the amplitude spectral ratio (ASR) method, corrects the apparent attenuation for the effects of multiple raypaths within the borehole, geometric spreading of head waves, and formation inhomogeneity. The algorithm is derived from two ray models. The first model simulates the interaction among rays reflected within the borehole and rays reflected from layer interfaces. This model removes these reflections and extracts the leading borehole wavelet. The second model uses a single-ray model for the borehole head wave in layered formations. This model provides the transmission coefficients across the layer interfaces between the source depth and the receiver depth with sectional geometric spreading within these layers. We use these two models to simultaneously separate, correct for, and normalize the effects of the borehole, geometric spreading, and layering. Then we test the accuracy and limits of the models using the finite-difference solution of a point source in a fluid-filled borehole surrounded by uniform and layered formations. In 255 tested cases, the absolute difference between the estimated and exact divided by the exact [Formula: see text] is within 3% for more than half of the cases and 5% for more than two-thirds of the cases. The lower accuracy in the remaining cases is associated mainly with certain receiver locations with regard to the layer interfaces and is caused by the limitations of the ray models.