We have used the University of Texas LAGEOS series of pole positions to obtain a Chandler wooble data set that has then been deconvolved. The deconvolution filter used here can be derived from the ideas of Backus-Gilbert inverse theory. By trading off resolution against accuracy a model for the Chandler wobble's excitation function can be obtained that is able to reproduce all of the features of the input Chandler wobble data set except for the noise contained therein. Two observed features of this excitation function are discussed. First, a change of amplitude 0.04` in the direction -54°E longitude is observed to have taken place from August 14.0, 1977, to September 3.0, 1977. The only notable geophysical event known to us to have occurred in this time interal is the great Sumba, Indonesia, earthquake of August 19, 1977. However, elastic dislocation theory applied to a double-couple model of this event is unable to explain the observed pole shift. We speculate that if the observed shift is causally related to the Sumba event it could be due to motions of the subducted slab occurring within 20 days of the main shock.By deconvolving Chandler wobble data sets obtained by other independent methods we find that this shift is not evident in the excitation function derived from Bureau International de l'Heure data. Therefore we cannot conclusively determine whether or not the shift seen in the LAGEOS-derived excitation function is geophysically significant. Second, a study is conducted into the possible influence on the Chandler wobble of the extraordinarily strong 1982-1983 Southern Oscillation/El Niño event which has been observed to have had a great influence on the length of day. We find in the Chandler wobble's excitation function a very encouraging signature that can be explained by the 1982-1983 El Niño event. It is encouraging in the sense that the y component ψy(t) of the excitation function appears to be temporally correlated with the Southern Oscillation index and that the polarity and overall magnitude of the change in ψy as well as the quiescence of the excitation function's x component during this period are all consistent with observations of the 1982-1983 El Niño.