In the first of three projects, differential travel times of the seismic inner core phase PKP(DF) relative to the outer core phases PKP(BC) (BC-DF) and PKP(AB) (AB-DF) were measured by cross correlation to study the inner core velocity structure and rotation. Data from Novaya Zemlya nuclear tests to four Antarctica stations show that the inner core anisotropy is laterally and radially heterogeneous. The negative slopes of the differential time residuals versus calendar year provide support for inner core differential rotation relative to the mantle.; To observe the small PKP(DF) travel time change with higher precision, I used waveform comparison in the second project to search for doublets, which occurred essentially at the same spatial position but at different origin times, in the South Sandwich Islands region. Seventeen event pairs were determined to be doublets. One pair has clear PKP(DF) waveforms, and exhibits a PKP(DF) travel time decrease of 0.12 seconds over about eight years. This result strongly supports the inner core differential rotation. The derived rotation rate is 0.35° to 0.79°/year eastward. Analyses based on the seventeen doublets show that both the PDE and the ISC event locations have higher precision than had been expected.; In the third project, 73 French nuclear tests in the South Pacific were relocated by the double difference algorithm applied to teleseismic records. Results show large improvement over previously published locations. 56 doublets were determined among these events. The doublet event source separations are consistent with relocation errors. The relative BC-DF or AB-DF differential time changes between the two events of each doublet were measured by waveform cross correlation on the same phase. All of them are not larger than 0.03 seconds, the precision limit, with the maximum event origin time difference of five years. Unfortunately, this null result fails to distinguish between inner core anisotropy and inner core heterogeneity as the main contributor to the PKP(DF) travel time changes observed previously for high latitude sources and stations.
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