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By Udias A., Madariaga R., Buforn E.

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The properties of the medium such as its density or elastic coefficients are considered to be piecewise-continuous functions of space. The displacement at a point of a deformable medium is given by the vector u(x, t). The deformation or strain within a deformable medium, if only infinitesimal deformations are considered, can be expressed by the Cauchy tensor eij, which, if u varies continuously and slowly with position, is given in component form by   1 ∂ui ∂uj 1 eij ¼ ¼ ðui , j þ uj , i Þ þ ð3:1Þ 2 ∂xj ∂xi 2 Thus, a comma between the sub-indices indicates a partial derivative with respect to a space coordinate.

19); by adding a zero to the instrumental response we can obtain directly the ground displacement u(t). The second option is more convenient because it implies fewer calculations. 2 show the amplitude response and the instrumental response for a BB seismograph. We observe that the instrument response is given in terms of its Laplace transform, in units of radians per second corresponding to the angular frequency ω. If the units are Hz/s, the values correspond to the frequency f. 19), we must add a factor (2π)a with a ¼ Nz – Np.

3. 7. The east–west (LHE), north–south (LHN) and vertical (LHZ) components recorded on the LH channel are shown. seismographs record the ground displacement u(t) while electromagnetic instruments record the ground velocity v(t). Records from a mechanical seismograph (a Wiechert model) and from an electromagnetic seismograph (a BB Streckeisen model) at the same site are shown in Fig. 4. Since all modern seismographs are electromagnetic, in order to obtain the ground displacement u(t) we have to integrate the velocity signal.

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