Long-Wave Elastic Anisotropy Produced by Horizontal Layering
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...It is easy to show analytically (Backus, 1962), as verified numerically in the corresponding entries of Table 1, that assumption of constant Poisson's ratio leads to <3 = O....
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...This conclusion appears to disagree with a result by Backus (1965). Corresponding remarks apply to the shear polarization vectors; they are each transverse to the corresponding k, in the case of weak anisotropy....
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...Backus (1965) treats the case of weak anisotropy of arbitrary symmetry, defining anisotropy differently than is done here, without implementing criteria (1) and (2) which follows equation (7d)....
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..., the normal seismic exploration context), the wave propagates as though it were in a homogeneous, but anisotropic, medium (Backus, 1962)....
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"Long-Wave Elastic Anisotropy Produc..." refers background in this paper
...The problem of elastic wave propagation i finely layered media has been treated by a number of authors, all of whom except Thomson [1950], Helbig [1958], and Anderson [1961] have restricted themselves to what we shall call periodic, isotropic, two-layered (PITL) medium: a medium periodic in the vertical direction and consisting of alternating isotropic layers of thicknesses h•, h,., having constant Lam• parameters X,, tz,, and X,., •z,., and constant densities Riznichenko [1949] calculated, for long compression waves, the velocities of propagation i the vertical and horizontal directions, treating the medium as if it were locally static in order to get average stress-strain relations. Thomson [1950] gave the formal solution for waves of arbitrary wavelength in a medium consisting of any number of different homogeneous isotropic layers; he found the displacements and vertical stresses at any interface by multiplying the surface displacements and stresses by a product of propagator matrices, one matrix for each layer between the interface and the surface....
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...The problem of elastic wave propagation i finely layered media has been treated by a number of authors, all of whom except Thomson [1950], Helbig [1958], and Anderson [1961] have restricted themselves to what we shall call periodic, isotropic, two-layered (PITL) medium: a medium periodic in the vertical direction and consisting of alternating isotropic layers of thicknesses h•, h,., having constant Lam• parameters X,, tz,, and X,., •z,., and constant densities Riznichenko [1949] calculated, for long compression waves, the velocities of propagation i the vertical and horizontal directions, treating the medium as if it were locally static in order to get average stress-strain relations....
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...The problem of elastic wave propagation i finely layered media has been treated by a number of authors, all of whom except Thomson [1950], Helbig [1958], and Anderson [1961] have restricted themselves to what we shall call periodic, isotropic, two-layered (PITL) medium: a medium periodic in the vertical direction and consisting of alternating isotropic layers of thicknesses h•, h,....
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