### ASA 127th Meeting M.I.T. 1994 June 6-10

## 2pPA4. Nonlinear tube waves.

**D. L. Johnson
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S. Kostek
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*Schlumberger--Doll Res., Ridgefield, CT 06877-4108
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**A. N. Norris
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*Rutgers Univ., Piscataway, NJ 08855-0909
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The nonlinear characteristics of an acoustic tube wave propagating along
the axis of a fluid-filled circular borehole in an elastic solid which is
locally isotropic but whose properties may vary radially are considered. The
analysis is carried out in the quasistatic limit. All terms are considered
through quadratic in the amplitude of the wave and the amplitude of
2nd-harmonic generation is expressed as well as the pressure dependence of the
tube wave speed, dV[sub T]/dp, in terms of the fluid and formation of nonlinear
parameters. The results show that if there is no radial variation of the shear
modulus of the solid then both the amplitude of 2nd-harmonic generation and
dV[sub T]/dp are independent of the third-order elastic constants of the solid
and nearly equal to those of the fluid alone. If there is a radial variation of
the shear modulus then our numerical calculations indicate that both the
amplitude of 2nd-harmonic generation and dV[sub T]/dp can be completely
dominated by the nonlinear parameters of the solid. A perturbation theory is
derived that is valid for the case in which the shear modulus is nearly
constant, which demonstrates that the nonlinear response is scaled by the value
of the third-order parameters of the solid, leveraged by the degree and depth
of alteration of the shear modulus.