WAVELET TRANSFORM - APPLICATION TO ACOUSTIC LOGGING

The wavelet transform can be used to develop the process which allows group and phase velocity measurement of dispersive waves. The method h as been applied to acoustic data to measure formation velocities. The behavior and the accuracy of the method have been checked on synthetic full waveform acoustic data. The method was applied to dispersive wav es of the Stoneley type and to flexural modes whose low frequency comp onents are propagated at the formation shear velocity. A raw measureme nt of the phase velocity of a flexural mode gives an estimate of the s hear velocity with an error of about 5%. The use of a wavelet transfor m yields an accurate study of dispersion and gives a shear velocity me asurement with an error of less than 1%. However, all the examples pre sented here are based on the use of synthetic data, which are not corr upted by noise and were obtained with a numerical model. This algorith m is complete, to the extent in which it enables simulation of all the seismic arrivals for the considered geometry (cylindrical borehole wi th a circular section, in an homogeneous medium). Nevertheless, such a model remains a simplified version of what will occur in reality, whe n the irregularities of the borehole, the cementing defects and the ba ckground noise may call into question the excellent precision of the r esults obtained. The process which is described in this paper must be seen as one possible method for the analysis of field data, but it sti ll has to be applied to many recordings of field data before its effec tiveness can really be proved.