Absorption band Q model for the Earth

Abstract

Body wave, su~ace wave, and .norm~! mode data are used to place constraints on the frequency depe_n.dence of Q m the mantle. With a simple absorption band model it is possible to satisfy the shear sensitive data over a broad frequency range. The quality factor Qs(w) is proportional to w" in the band and to ~ and w-1 at higher and lower frequencies, respectively, as appropriate for a relaxation mech~msm with a spectrum of relaxation times. The parameters of the band are Q(min) = 80, a= 0.15, and w1dt~, 5 decades. The center of the band varies from 10 1 seconds in the upper mantle, to 1.6 x 10 3 seconds m the lower mantle. The shift of the band with depth is consistent with the expected effects of temper~ture, pressure and stress. High Qs regions of the mantle are attributed to a shift of the absorptiOn band to longer periods. To satisfy the gravest fundamental spheroidal modes and the ScS data, the absorption band must shift back into the short-period seismic band at the base of the mantle This may be .due to a ~ig~ te.mp~rature gradient or high shear stresses. A preliminary attempt is als~ made to s~ec1fy bulk dissipation m the mantle and core. Specific features of the absorption band model are lo": Q m the body wave ~mnd at both the top and the base of the mantle, low Q for long-period body wave~ m the outer core, an mner.core ~s that increases with period, and low QP/Qs at short periods in the middle mantle. The short-penod Qs mcreases rapidly at 400 km and is relatively constant from this depth to 2400 km. The deformational Q of the earth at a period of 14 months is predicted to be 463.

The seismic attenuation structure of the East Pacific Rise

“…Sato and Sacks [1990] suggest that since the grain boundary mechanism is dependent upon the grain size, laboratory measurements at high frequencies and small grain sizes may scale to the lower frequencies and larger grain sizes typical of seismic observations. On the basis of the absence of a strong frequency dependence in their results they argue that their measurements fall within a regime that is equivalent to the region of weak frequency dependence in the absorption band model of Anderson and Given [1982]. By comparing oceanic geotherms derived from heat flow data in older oceanic crust with the temperatures their results predict for models of seismic Q, proceed to derive a small correction term to account for the differences between the laboratory and upper mantle conditions.…”

Shallow mantle temperatures under Europe from P and S wave tomography

“…In section 2.1 our forward modeling procedure is explained, and using simple one-dimensional models, the sensitivity of seismic velocities to variations in temperature, composition, and partial melt is estimated in section 2.2. [Chapman, 1986] (Table A2) with estimates of Q from seismic waves (dark shading, for active (A) and shield (S) regions [Mitchell, 1995]; light shading, global model ABM [Anderson and Given, 1982] Table 1). The equations used for calculating partial derivatives are given in the appendix.…”

Anomalous bulk viscosity of two‐phase fluids and implications for planetary interiors

“…Figure 3 and compared with the model suggested by Anderson and Given [1982] from their analysis of the normal mode data. This is not, of course a confirmation of the model (which fortuitously has a si~ilar functional form) but merely a demonstration of compatibility.…”

“…The present paper considers fluid media, including the earth's outer core. Analyses of the outer core by previous workers [Loper and Roberts, 1978;Gubbins, 1978;Anderson, 1980;Anderson and Given, 1982] are based entirely on the Vaisnys treatment.…”