Models of earthquake sources that have no volume change, no net force, and no net torque as criteria for the radiation of first motions, have five degrees of freedom in their spatial orientation. The usual double‐couple model has only three degrees of freedom. The most general source of high‐frequency seismic motions must be a linear combination of a double couple and another source called the compensated linear‐vector dipole. A radiation pattern of amplitudes of first motions on the focal sphere cannot be uniquely decomposed into the radiation patterns due to the two sources.

The arrest of a semi-infinite longitudinal shear crack is caused by either (1) the finiteness of available strain energy, or (2) an increase in fracture energy along the trajectory of the running crack. In the former case the following relationship may be used to evaluate the fracture energy:where yo is the fracture energy per unit length along the crack edge per unit extension of the cracktip (erg cm-2), R is the characteristic radius of the fault (cm), ACJ is the stress drop (dyne cm-2) and p is the rigidity (dyne cm-2). This leads to the following relationship:log Aa = -3 log R +f log (2ptny0) or from the Keylis-Borok relationship (1959):where M , is the seismic moment in dyne cm-'. These two relationships are statistically acceptable for Southern California faults and the Tonga-Kermadec Arc earthquakes. The fracture energy is found to vary from lo3 to lo9 erg cm-' with fresh fracture being associated with 10'-lQ9 erg cm-2 while frictional rupture with 103-107 erg cm-2. These values are in good agreement with other independent estimates.

The travel times of S waves have been revised using the same statistical methods and data from the same selection of earthquakes as for the 1968 Seismological Tables for P phases. Because of the large quantity of data used, significant departures are observed in the new travel times from those of Jeffreys. A corresponding velocity distribution is obtained and involves lower velocities in the upper mantle and higher velocities at depths from 700 to 1000 km.

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Amplitudes of long‐period pulses are used in an analysis of several intermediate and deep‐focus earthquakes to determine whether the mechanism is of the double‐couple or compensated linear vector dipole type. For most of the shocks, the double‐couple model dominates the linear dipole model, but not overwhelmingly so.