Comments on Paper by D. E. Smylie and L. Mansinha: 'The Elasticity Theory of Dislocations in Real Earth Models and Changes in the Rotation of the Earth'

Abstract

Smylie & Mansinha (1971) have attempted to utilize static elastic dislocation theory in order to compute the change in the inertia tensor of a realistic spherically symmetric Earth model produced by a point tangential displacement dislocation. The present author has performed similar computations and has combined this theory together with an empirical earthquake moment-magnitude relation in order to estimate the total excitation of the Chandler wobble by all observed large earthquakes since 1904 (Dahlen 1971). The purpose of this note is to point out that there is significant disagreement between the final numerical results of Smylie & Mansinha (1971) and those of Dahlen (1971) and to suggest a possible explanation for this disagreement. In order to investigate the effect of the earthquake focal depth on the shift of the Earth's mean pole of rotation, Smylie & Mansinha (1971) have considered two point tangential displacement dislocation models for the faulting associated with the 1964 Alaskan earthquake. One model is a realistic shallow focus (depth h = lskm), shallow dip angle, thrust faulting mechanism; the other model has the same mechanism, but the focal depth h is taken to be 637 km. Table 1 shows a direct comparison of the results obtained for these two models by Smylie & Mansinha (1971) and the results obtained from my own computations (Dahlen 1971). The fault parameters used in all cases were those considered by Smylie and Mansinha (epicentral colatitude O,, = 29.0°, epicentral longitude 4,, = 213-0°, fault strike N42E, fault dip 8W, mechanism pure dip slip thrust, fault slip area 1-54 x 1OI2 m3). These fault parameters for the 1964 Alaskan earthquake differ slightly from those considered by Dahlen (1971). It can be seen that the computations of Smylie & Mansinha (1971) predict that the change in the inertia tensor produced by a deep focus earthquake will be nearly an order of magnitude larger than that produced by a shallow focus earthquake with the same fault parameters; my own computations predict that a deep focus earthquake will have a slightly smaller effect than a similar shallow focus earthquake. The major differences in the theoretical treatments of Smylie & Mansinha (1971) and Dahlen (1971) arise in the method used to deal with the fluid core of the Earth model. The reason why the treatment of a fluid core is not straightforward is that in the absence of both inertia and viscosity, individual fluid particles in a non-rotating fluid core encounter no resistance to a tangential (non-radial) displacement, and because of this the particle displacement field within the fluid core produced by a static tangential displacement dislocation (or any other static force system) located within the solid elastic mantle becomes indeterminate. In discussing this problem I