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The homogeneous distribution of inelastic strain is equivalent to the homogeneous moment density in the volume.
The transition dipole moments are also analyzed on the basis of the transition dipole moment density (TDMD).
If only one large earthquake occurs in the volume, the high moment density tensor is distributed along the earthquake fault.
We consider the moment density tensor of a tensile crack with normal direction (Figure 3a): Figure 3 Source coordinates for (a) a crack and (b) a spherical source in a half-space.
Assuming a uniform distribution of earthquake point sources in the volume, we define the average moment density tensor in the volume as m_{ij} = mathop sum limits_{k}^{K} M_{ij}^{k} /Delta V (2 where the seismic moment tensor of the kth earthquake is (M_{ij}^{k}) and K is the number of earthquakes.
In Equation 8, which shall be referred to as the H - A model, this situation can occur when the magnetic ions are distributed as sparsely dispersed large clusters and the magnetic moment density associated with an ion is of short range [18]: M Brillouin - H - A model = M Brillouin + M H - A model.
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Fig. 7 a Target model used in the checkerboard resolution tests (moment densities of 0 Nm/m2 and 2.7 × 109 Nm/m2).
The basic concept is the idealization of the inclusions as 1-D-beams continuously distributed throughout the matrix, leading to a micropolar description which accounts for shear force and bending moment densities.
The distribution of [ u i ] on the surface can then be obtained, and the moment-density tensor calculated by (9).
and the moment-density tensor m pq is defined in terms of the displacement discontinuity as m_{pq}= c_{ijpq}[!u_{i}]n_{j}.
Finally, the moment tensor of the equivalent point source is obtained by integrating the moment-density tensor over the source surface as in (11).
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