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The response is given in Cartesian coordinates; see Fig. 2. 7) u yy (r, t) = S 1 Graff, K. , 1975, Wave motion in elastic solids, Ohio State University Press, pp. 285, 288, eqs. 40. However, both formulas are missing a divisor 2πµ, and eq. 21 should be conjugated to conform to our sign convention. 1: Plane strain loads. 3 SH line load in an orthotropic space Consider an orthotropic elastic space with shear moduli µx , µz in the plane of wave propagation. 2a: Green’s function for anti-plane line load in full space.
30. 6, which facilitates comparisons. , 1962, The Fourier integral and its applications, McGraw-Hill. 3, Impulse response at r/r0 = 5 for pressure pπr02 = δ(t). Observe that the magnitude of the discontinuity in Fig. 58) This expression is obtained by multiplying the displacement scaling factor, the applied pressure, and the jump amplitude behind the wave front obtained previously from the asymptotic properties of Fourier transforms. 2 Point load (Stokes problem) Unit impulsive point sources act at the origin, in any coordinate direction, within an inﬁnite, homogeneous space.
Are tensor bases, or dyads. Now, here we have assumed the medium to be laterally homogeneous, so the dependence of the Green’s functions within a given plane is only a function of the relative horizontal position of the receiver and the source. Thus, except for the terms involving the vertical derivatives, the gradient with respect to the receiver is the negative of the gradient with respect to the source. It follows that in the computation of the Green’s functions for dipoles, it sufﬁces for us to reverse the signs of the terms other than those for the vertical derivatives.