| Abstract: | Two techniques for the measurement of attenuation–spectral ratio and rise time techniques–were tested and compared in the laboratory. The spectral ratio technique proved to be reliable and easy to implement for intermediate values (5 < Q < 50) of attenuation. For low (Q > 50) and high attenuations, the spectral ratio technique is inaccurate. Calculating the rise time on simulated signals, we found a relation between rise time τ and the ratio travel-time to quality factor T/Q which could be approximated in intervals by the linear relation τ=τ+C*T/Q. The constants τ and C depend on the absolute value of T/Q and on the initial source signal. The rise time technique, performed on the first quarter period of the signal, enables high attenuations (Q < 5) to be measured. The determination of the relation between τ and T/Q is possible if one knows the initial source. We theoretically approximate this relation through a simulation using a realistic propagation model. With laboratory measurements made on Fontainebleau sandstone, we show that the rise time technique using the theoretical relation τ=τ(T/Q) gives comparable values of Q to those obtained from the spectral ratio technique. In borehole seismics, where it is often difficult to remove undesired signals, the rise time technique applied with the right (τ, T/Q) relation is the best method to use. |
