we consider the semigroup $s$ of highest weights appearing in tensor powers $v^{otimes k}$ of a finite dimensional representation $v$ of a connected reductive group. we describe the cone generated by $s$ as the cone over the weight polytope of $v$ intersected with the positive weyl chamber. from this we get a description for the asymptotic of the number of highest weights appearing in $v^{otime...

Moment tensors are indefinite tensors derived from seismic measurements and encode important information about earthquakes and surface displacement in the earth’s mantle. Appropriate analysis of scattered moment tensor fields requires multi-scale visualization to identify related seismic events. For this matter we provide a visualization of the tensor field at different scales based on multivar...

S U M M A R Y We determine centroid-moment tensor (CMT) solutions by minimizing waveform differences between observed and simulated seismograms based on an adjoint method. Synthetic seismograms and Fréchet derivatives are calculated based on a spectral-element method. The non-linear adjoint CMT inversion algorithm requires three simulations for each iteration: one ‘forward’ simulation to obtain...

This paper presents an exact formula for calculating the fourth-moment tensor from the second-moment tensor for the three dimensional Jeffery’s equation. Although this approach falls within the category of a moment tensor closure, it does not rely upon an approximation, either analytic or curve fit, of the fourth-moment tensor as do previous closures. This closure is orthotropic in the sense of...

Waveform inversion to determine the seismic moment tensor is a standard approach in determining the source mechanism of natural and man-made seismicity. The moment tensor is a general representation that includes the double-couple (DC) and non-double-couple sources such as explosions, opening and closing cracks, and volume compensated linear vector dipoles (CLVD). Previous studies (Ford et al.,...

We consider a problem of reconstructing a cluster of small elastic inclusions which are located close to each other. We show that the location of the cluster and the elastic moment tensor associated with it can be reconstructed by the measurements of the displacement vectors on the boundary corresponding to the traction applied on the boundary. The detected elastic moment tensor represents the ...