xv, 108 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / Studies on seismic attenuation are an important complement to those on seismic velocity, especially when interpreting results in terms of temperature. But estimation of attenuation (t*) is more computationally involved and prone to contamination by noise, especially signal-generated noise. We have examined the effects of various forms of synthetic noise on t* estimation using time and frequency domain methods with varying window lengths and data frames of reference. We find that for S-waves, error due to noise can be reduced by rotating the data into the estimated polarization direction of the signal, but unless the exact nature of the noise is known, no method or window size is clearly preferable. We recommend the use of multiple estimation methods including a careful assessment of the uncertainty associated with each estimate, which is used as a weight during inversion for 1/Q. Our synthetic tests demonstrate that the misfit between actual and estimate-predicted traces or spectra correlates with t* error, and a similar relationship is suggested for real data. Applying this approach to data from the Yellowstone Intermountain Seismic Array, we employ two important constraints during inversion. First, we scale the misfit values so that the resulting weights are comparable in magnitude to the squares of the eventual data residuals. Second, we smooth the model so that the maximum attenuation (1/Q) does not exceed a value which would totally explain the observed velocity anomaly. The tomographic models from all the estimation methods are similar, but in the vicinity of the Yellowstone mantle plume, S-wave models show greater attenuation than do P-wave models. We attribute this difference to greater focusing by the plume of S-waves. All models show relatively high attenuation for the plume at depth, but above 250 km attenuation in the plume drops rapidly to values less than those of the surrounding mantle. We attribute this drop to the onset of partial melting, which dehydrates the olivine crystals, suppressing dislocation mobility and thereby attenuation. These attenuation models suggest excess plume temperatures at depth which are too low to support a plume origin in the lower mantle. This dissertation includes unpublished co-authored material. / Committee in charge: Eugene Humphreys, Chairperson, Geological Sciences; Emilie Hooft Toomey, Member, Geological Sciences; Douglas Toomey, Member, Geological Sciences; James Isenberg, Outside Member, Mathematics