Rifting of stable continents is a key element of plate tectonic cycles. In spite of numerous studies, the mechanism responsible for the initiation and evolution of rift valleys such as the East African Rift System (EARS) is still poorly understood, partly because most previous investigations focused on rift segments that were in the mature stage. Geodynamic modeling [Huismans et al., 2001] suggests that upwelling of the asthenosphere ubiquitously observed beneath mature rifts can either originate from thermal or dynamic anomalies in the deep mantle (active rifting) or be induced by thinning of the lithosphere from far‐field stresses (passive rifting) [Sengor and Burke, 1978].

This paper presents a new approach to the analysis of three-component digital seismograms.Earlier approaches used techniques such as Principal Components to estimate particlemotion using models of P and S waves. In this paper the Maximum-Likelihood (ML) estimator is preferred because this allows the use of X2-probabilities to test whether energy of a specific wave type (P, S, Love or Rayleigh) is present. In addition, this analysis allows the joint estimation of azimuth of approach and in cases of P-and SV-waves also apparent angle of incidence (and, hence, information on apparent velocity). For a single three-component seismogram, the covariance matrix provides only six independent observations, thus restricting analysis to rather simple wave models. The technique works satisfactorily for P-waves whereas shear and surface-wave models sometimes prove cumbersome to handle due to correlation between radial and transverse components reflecting complex propagation characteristics in inhomogeneous media. This technique has been tested on synthetic data and in such cases works perfectly for all wave types.An important aspect of this work has been the visual display of the probability and velocity information as functions of time and azimuth. Displaying the data in this form provides information on the ray path in a manner similar to analysis performed by seismic arrays.Practical examples on a variety of siesmic data are given to illustrate the viability of the technique: the data cover a broad spectrum of frequencies and applications from broad-band teleseismic data (1 Hz), regional seismic data (10-40 Hz), seismic profiling data (125 Hz) and VSP (500 Hz) recordings.

In recent years the use of synthetic seismograms calculated for radially stratified models has gained increasing popularity as a means of placing further constraints on the velocity structure of the Earth's mantle. Such synthetics do, however, have a number of limitations. At short periods (-1 s) the amplitudes as well as the wave shapes of travel-time branches are affected by seismograph siting, the structure immediately beneath the seismograph and any laterally heterogeneous structure in the mantle. Later arrivals can also be masked by signal-generated noise and by extended source times. At longer periods (-20 s) the larger wavelengths reduce the sensitivity of amplitudes and waveforms to contarninating effects. As a result the use of long-period synthetics can only lead to the resolution of the gross features of the Earth's interior.

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A method for calculation of theoretical SH-waves in a laterally homogeneous layered medium is presented. The SH wave trains are complete, i.e. they include surface waves as well as body waves. The SH displacements are calculated for two point sources, a single horizontal force and a shear dislocation of arbitrary orientation, both buried in the layered half-space. Numerical problems are discussed. The correctness of the method is ascertained by its ability to reproduce complete synthetic SH seismograms published elsewhere in the literature. Several examples demonstrate that our method is well suited for crustal studies as well as for teleseismic studies of the upper and lower mantle.