HOMOMORPHIC PROCESSING OF THE TUBE WAVE GENERATED DURING ACOUSTIC LOGGING

We have developed a new method to process the tube wave, which is gene rated during acoustic logging, to obtain estimates for its wavenumber, attenuation coefficient, amplitude, and phase at every frequency. To improve the accuracy of the estimates, the method can use data from mu ltiple sources and data collected at successive depths in the borehole . This new method has several advantages over other methods that are c urrently used to process acoustic logging data: the new method can obt ain accurate estimates of the wavenumber and amplitude from only a few receivers; the receivers can be irregularly spaced; and no spurious e stimates are generated. Nonetheless, this new method has one disadvant age compared to others: it can only estimate the parameters for one, h igh-amplitude wave like the tube wave. Also, like all other existing m ethods, the new method obtains only reasonable estimates for the atten uation coefficient when data from many receivers are processed.