The anelasticity of the Earth

The attenuation of seismic waves is one manifestation of the earth's anelasticity and is not unrelated to the response of the earth to stresses of longer duration. The well-known difficulties involved in the extraction of meaningful amplitude information from body waves have prevented an accurate determination of attenuation of seismic energy versus depth. Most of these difficulties are not present in surface wave and free oscillation measurements, but there are complexities of interpretation. A method is developed for the analysis of the amplitudes of dispersed wave trains and free oscillations which yields the anelasticity (Q) as a function of depth in the earth just as the frequency spectrum yields the elasticity-density structure. The advantages and limitations of the method are essentially identical to those of the dispersion method. The amplitude decay versus period for toroidal oscillations and Love waves was computed for a variety of hypothetical Q distributions in the earth. Those models which satisfy the available attenuation measurements have a broad, highly attenuating zone in the upper mantle and a high-Q lower mantle. The range of Q for shear waves in these models is from about 80 in the upper mantle to about 2000 in the lower mantle. A rapid increase in Q beginning at about 400 km seems to be a required feature. This is probably the most direct evidence for inhomogeneity, possibly a phase change, beginning at this depth. The details of this transition zone must await more accurate data on surface wave attenuation. The high Q of the lower mantle seems to imply temperatures substantially below the melting point, and it probably precludes extensive lower mantle convection. There is no need to invoke a frequency-dependent Q in order to satisfy available body and surface wave data in the period range 10 seconds to 30 minutes, although a Q that is frequency dependent cannot be ruled out.