Attenuation in the earth at low frequencies

Abstract
The introduction of global, digitally recording, seismic networks has provided the seismological community with a large quantity of high quality data. At low frequencies the IDA (International Deployment of Accelerometers) network provides the best available data and, in this report, over 500 IDA records have been carefully analysed giving nearly 4000 reliable measurements of centre frequency and apparent attenuation of fundamental spheroidal modes. The attenuation rate of a normal mode of free oscillation of the Earth is measured in terms of its or quality factor and mean Q values for the modes 0 S 8 - 0 S 46 are presented with standard deviations of 2-9% . Mean centre frequencies have relative standard deviation of 5 x 10- 5 to 5 x 10- 4 . The distribution of the centre frequencies reveals a large-scale aspherical structure in velocity and density but the distribution of the apparent attenuation measurements does not reveal a corresponding structure. A total of 26 new measurements of the mean Q of overtone modes with standard deviations of 5-30 % have also been obtained by using single-record and multiple-record techniques. Combining the new data with reliable Q measurements from the literature gives a total of 71 data with which we can infer the radial structure of attenuation inside the Earth. This structure is not well constrained in detail and very simple models are capable of fitting the data. Experiments with synthetic data show that an improvement of an order of magnitude in both the number and quality of the measurements is required to make detailed inferences about the structure of attenuation. The data do constrain the average shear Q- 1 in the inner core to be 1/3500 ( ± 60 %) and the average shear Q- 1 the mantle to be 1/250 ( ± 4 %). These values are appropriate for frequencies less than 5 mHz. Comparison with published values at higher frequencies indicates there is a measurable frequency dependence of attenuation between 3 and 30 mHz. Very little can be inferred about bulk dissipation in the Earth beyond that it must exist to satisfy the attenuation of the radial modes. Experiments show that the data can be satisfied if bulk attenuation is an average 1.3%, or more, of the shear attenuation. Constraining bulk attenuation to be no greater than 2 % of the shear attenuation, and constraining the outer core to have no attenuation, forces bulk attenuation to be concentrated in the upper mantle.