Dissipation in the earth's mantle and rigidity and viscosity in the earth's core determined from waves multiply reflected from the mantle-core boundary

Abstract

Spectral amplitude ratios of 33 shear waves multiply reflected from the core (from a deep-focus earthquake recorded in the epicentral distance range from 7° to 80°) are used to determine statistically the following quantities: (a) the quality factor, Q, of shear waves in the mantle, (b) the rigidity of the earth's core, and (c) the viscosity of the earth's core. The determined mean value of Q for the whole mantle, using eight stations in the epicentral range of 7° to 80°, is much lower than any mean Q value obtained previously. This Q value is called the mean apparent quality factor of shear waves in the earth's mantle. The mean lower bound value of Q determined from 13 observations when two close stations are used is 581 ± 33. In this case, when Q is assumed to depend upon period, its value decreases with increasing period, from 720 at 34 sec to 232 at 90 sec. When the recording stations are grouped according to epicentral distances, the mean apparent values of Q obtained from the combined series for each group show a tendency to decrease as the epicentral distance increases. An upper bound of the mean core rigidity is determined to be 5.45 × 10¹⁰ dynes/cm², shear velocity in the core = 0.73 km/sec, when the mantle is assumed to be a perfect elastic body (Q = ∞). When the core is assumed to be a viscous-liquid medium and the mantle is assumed to have an infinite Q, an upper bound for the viscosity of the upper part of the outer core is found to be 8.61 × 10¹¹ dynes-sec/cm². The computed values of the rigidity and viscosity of the earth's core are affected by the assumed Q distribution in the earth's mantle. Since there is insufficient data available on Q as a function of depth, various μ_c and v_c for 13 assumed Q distributions as a function of depth have been computed and tabulated.