S U M M A R Y We decompose a general seismic potency tensor into isotropic tensor, double-couple tensor and compensated linear vector dipole using the eigenvectors and eigenvalues of the full tensor. Two dimensionless parameters are used to quantify the size of the isotropic and compensated linear vector dipole components. The parameters have well-defined finite ranges and are suited for non-li...

where Mkk represents the trace components of the moment tensor,  and  are Lame constants. These results imply that the damage evolution and the accumulation of relative crack volume are also estimated from the moment tensor analysis. From moment tensors determined in bending tests of concrete specimens with a notch [Ohtsu & Ohtsuka 1998], the damage and the accumulation of crack volume were e...

Three commonly used methods to determine the principal moments of inertia of a plane area and their directions are based on: (i) the stationarity condition for the axial moment of inertia, (ii) the eigenvalue analysis, and (iii) Mohr’s circle. In this paper we provide two new derivations, which are based on: (a) the matrix diagonalization and the invariant tensor properties, and (b) the conjuga...

In 2 experiments, participants haptically estimated length and heaviness of handheld rods while wielding without seeing them. The sets of rods had been constructed such that variation of static moment and the 1st eigenvalue of the inertia tensor (I1) were separated. Consistent with previous findings, perceived rod length correlated strongly with I1. However, multiple regressions on current data...

Seismic moment tensor and finite-source analyses are performed for the 21 February 2008 Wells, Nevada earthquake. Using complete, intermediate period (10-50s), regional waveforms, and assuming the U. S. Geological Survey (USGS)-reported hypocenter, the best-fit moment tensor solution is a normal mechanism that strikes approximately northeast-southwest, consistent with the trend of Basin and Ran...

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated moment matrix problem and give a new criterion for flat extension of Quasi-Hankel matrices. We connect this criterion to the commutation characterisation of bor...

A generalization from 2D to 3D of the tensor method for derivation of both affine invariants and rotation, translation and scaling (TRS) invariants is described. The method for generation of the 3D TRS invariants of higher orders is automated and experimentally tested.

An earthquake on a fault separating two dissimilar materials does not have a well-defined moment density tensor. We present a complete characterization of this bimaterial ambiguity in the general case of slip on a fault in an anisotropic medium. The ambiguity can be eliminated by utilizing a potency density rather than a moment density representation of a bimaterial source.

We develop a theoretical and computational framework to perform guaranteed tensor decomposition, which also has the potential to accomplish other tensor tasks such as tensor completion and denoising. We formulate tensor decomposition as a problem of measure estimation from moments. By constructing a dual polynomial, we demonstrate that measure optimization returns the correct CP decomposition u...