Present-day plate motions

A data set comprising 110 spreading rates, 78 transform fault azimuths and 142 earthquake slip vectors was inverted to yield a new instantaneous plate motion model, designated RM2. The mean averaging interval for the relative motion data was reduced to less than 3 My. A detailed comparison of RM2 with angular velocity vectors which best fit the data along individual plate boundaries indicates that RM2 performs close to optimally in most regions, with several notable exceptions. On the other hand, a previous estimate (RM1) failed to satisfy an extensive set of new data collected in the South Atlantic Ocean. It is shown that RM1 incorrectly predicts the plate kinematics in the South Atlantic because the presently available data are inconsistent with the plate geometry assumed in deriving RM1. It is demonstrated that this inconsistency can be remedied by postulating the existence of internal deformation with the Indian plate, although alternate explanations are possible

Transformation of multipolar source fields under a change of reference frame

Simple and convenient formulae are derived which describe the transformation of a multipolar expansion under an arbitrary proper rotation of the reference frame. When combined with the corresponding formulae for a translation, these results show how multipolar representations of source fields transform under any proper displacement of the reference frame. Particular emphasis is placed on the seismic source problem; however, these results find applications in many other physical problems

Transient and impulse responses of a one-dimensional linearly attenuating medium — II. A parametric study

We investigate one-dimensional waves in a standard linear solid for geophysically relevant ranges of the parameters. The critical parameters are shown to be T*= t_u/Q_m where t_u is the travel time and Q_m the quality factor in the absorption band, and τ^(-1)_m, the high-frequency cut-off of the relaxation spectrum. The visual onset time, rise time, peak time, and peak amplitude are studied as functions of T* and τ_m. For very small τ_m, this model is shown to be very similar to previously proposed attenuation models. As τ_m grows past a critical value which depends on T*, the character of the attenuated pulse changes. Seismological implications of this model may be inferred by comparing body wave travel times with a ‘one second’ earth model derived from long-period observations and corrected for attenuation effects assuming a frequency independent Q over the seismic band. From such a comparison we speculate that there may be a gap in the relaxation spectrum of the Earth's mantle for relaxation times shorter than about one second. However, observational constraints from the attenuation of body waves suggest that such a gap might in fact occur at higher frequencies. Such a hypothesis would imply a frequency dependence of Q in the Earth's mantle for short-period body waves

Near-field waveforms from an arbitrarily expanding, transparent spherical cavity in a prestressed medium

A simple, approximate (‘transparent’) solution is derived for the near-field radiation emitted by a spherical cavity expanding in an initial pure shear prestress field. Near-field terms, their propagation and decay are discussed for a variety of growth histories, and are shown to be rather insensitive to the detailed variations of rupture velocity. The transparency approximation is shown to be adequate in the near field as well as in the far field; the main effect is a slight narrowing of far-field pulses. Time domain moment estimators at close range are more reliable for the S wave than for the P wave since transverse pulses are not as strongly contaminated by near-field effects

Slipping interfaces: A possible source of S radiation from explosive sources

We consider the problem of reflection and refraction of purely compressional waves incident on an interface separating identical solid half-spaces in which the condition of continuity of shear displacement at the boundary is generalized to one that allows slippage. The problem is solved using the Cagniard-de Hoop technique. It is found that the generation of reflected P and S waves, as well as transmitted S waves, is most effective in the case of perfectly unbounded half-spaces. We discuss the implications of this model for the generation of S waves by block movement in the vicinity of an underground explosion