The classical method is to measure and correlate amplitudes from ray to ray along the earth 's surface utilizing information from many earthquakes and recording

The attenuation of seismic waves is a direct measure of the absorption due to nonelastic proc~ esses in the earth. The well known difficulties in obtaining body wave amplitude decrement data have been avoided by studying the spectral ratios of multiple ScS and sScS phases from two deep focus earthquakes recorded at near normal incidence. The average Q, for shear, in the mantle is about 600 for the frequency range 0.015 to 0.07 ups. Assuming that equal radiation occurs upwards and downwards from the source the average Q for the upper 600 km of the mantle is determined to be about 200 and about 2200 for the rest of the mantle. The value for Q at the base of the mantle is at least 5000 for shear waves. INTRODUCTION The at tenuat ion of seismic energy in the mantle is an important parameter in discussions of source mechanism, ear thquake magnitude and the range of detectabili ty of seismic signals. Attenuation, being a manifestat ion of anelasticity, also has a direct bearing on discussions of the phase, composition and tempera ture of the earth 's mantle. The main limitation in obtaining meaningful seismic wave a t tenuat ion data is tha t measurements are restricted to the surface of the earth. The classical method is to measure and correlate amplitudes from ray to ray along the earth 's surface utilizing information from many earthquakes and recording stations and a t tempt ing to infer the spatial decay rate of a pulse along a given ray. I t is well known tha t the differences between events, instruments and recording sites tend to obscure the ampli tude differences of the seismic phases. There are three possible ways to completely remove the effects of source and ins trument. One method is to measure the rate of decay of successive transits of surface waves past a single station. Since these waves are guided by the surface of the ear th we can obtain the spatial decay rate along the path. Another method is to determine the tinle rate of decay of peaks associated with the free oscillations of the earth. The complications due to the source are replaced by complexities of interpretat ion which, however, are now well in hand (Anderson and Archambeau, 1964). The third method is to consider seismic rays which have repeatedly traversed the same pa th and to compare amplitudes af ter successive passages. One such ray is the shear wave which travels between the surface and the core of the earth at near normal incidence. By studying spectral ratios of successive ScS and sScS phases at near normal incidence we are able to remove the effect of the source and extract meaningful ampli tude decrement da ta over a fairly wide frequency range. This is the method used in this paper. At tenuat ion effects for propagating waves can be represented by a factor exp (--/~D) where k is the coefficient of absorption and D is distance along the ray. For a propagating monochromatic shear wave k = ~/~TQ where f~ is the shear velocity, T is the period and Q-1 is the specific absorption coefficient of the material. 1855 1856 BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA There are several published estimates of the average Q of the mantle for shear waves. Press (1956) studied the amplitude decrement of shear waves reflected from the earth's core at near normal incidence but excessive reverberations and the low sensitivity of the seismographs used linfited the amount of useful data. A value of 500 was obtained for the dimensionless quality factor Q for the whole mantle for 11 second shear waves. Gutenberg (1958) determined a Q of 700 for 12 second shear waves and a Q of 400 for 24 second shear waves but his measurements were severely limited by corrections for source, instrument "and differences in path. Otsuka (1963) interpreted the spectra of ScS from two deep focus earthquakes with the assumption that the source was an impulse composed of equal amplitudes for all frequencies. With this assumption the slope of the spectrum, corrected for instrumental" response, yields the absorption coefficient. Otsuka assumed a solid friction mechanism and estimated an average Q of at least 340 for shear waves in the mantle. This method does not require an absolute measurement of amplitude but the assumption regarding the source is a severe limitation. A similar method was TABLE 1 EARTHQUAKES AND STATIONS SELECTED FOR STUDY