Values of attenuation have been extracted from five detailed velocity surveys. Significant amounts of attenuation are observed in all five wells. Measured values of attenuation vary by a factor of 10, ranging from less than 0.1 to 0.9 dB/wavelength. Correlation of attenuation with lithology is good, considering the resolution limits of the surveys.One of the surveys was performed in West Texas, and the other four were carried out in the Gulf Coast area. The total number of recording depths in each survey varied from 3 1 to 208, with downhole recordings taken every 10 or 20 ft over key stratigraphic zones. In all five surveys, a monitor geophone was placed near the well to check for source consistency.Two of the better known previous experiments for measuring in-situ attenuation at seismic frequencies were performed by McDonal et al (1958) and Tulles and Reid (1969). These experiments differed from our present surveys in that several geophones were cemented within the boreholes at various depths. Source repeatability was therefore not a problem, and explosive sources were used with frequencies above 400 Hz. Since we were limited to one downhole geophone, we needed sources with repeatable signatures. For the land surveys we used vibrators with frequencies no greater than 80 Hz. We were more fortunate in our offshore experiment, where one of our sources had usable frequencies up to 125 Hz.
THEORY
NotationOur procedure for measuring attenuation involved constructing the spectral ratio between each downhole pulse and one particular reference pulse. A value of cumulative attenuation (CA) was then extracted from each spectral ratio and plotted as a function of geophone depth. This method allowed us to use many measurements in determining the attenuation over each depth interval.From numerous past experiments we know that the logarithm of the pulse amplitude decays at a rate roughly proportional to frequency. References to many of these experiments can be found in comprehensive articles by Hamilton (1972Hamilton ( , 1976 and Attewell and Ramana (1966). Because of this linear dependence with frequency, we can describe the attenuation process as
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