Low Frequency Discriminants for Small Events.

The Cagniard-deHoop method in generalized ray theory is extended to spherically layered media. The theory is approximate and is asymptotic in reciprocal fractional powers of the frequency. For mantle body wave phases it is estimated that the theory can be used for P pulses with periods less than 40 superscript s and S pulses with periods less than 75 superscript s. An initial application of the theory to the study of LRSM recordings of NTS events shows: (1) models derived from travel time data alone may have synthetic seismograms that disagree with observations; (2) the structure of the upper mantle beneath North America has very significant lateral variations in the uppermost 700 km. Some classical results in normal mode theory have recently been uncovered. They permit one to study the residual static displacement field, caused by an earthquake or explosion, in terms of the normal mode eigenfunctions. The dynamical and statistical fields have the same expansion coefficients in the normal mode representation. Consequently, there is an indirect method for finding static fields. (Author)