CiteULike: norris sdr

Nonlinear pulse propagation in arbitrarily dispersive media: Tube waves in permeable formations

David Johnson — 2007-02-16T19:14:10-00:00

The Journal of the Acoustical Society of America, Vol. 105, No. 6. (1999), pp. 3087-3096.

An approximate quasistatic equation, analogous to the Burgers equation, is derived to account for the combined effects on tube wave propagation of (a) dispersion/attenuation in permeable formations, and (b) quadratic nonlinearity of the fluid and of the formation. Numerical results for weak nonlinearity and narrow-band pulses indicate that pulse self-demodulation does occur, but over relatively large distances because of the relatively low-frequency band relevant for tube wave propagation in characteristic borehole geometries (f<10 kHz). The self-demodulated pulse shape can be very significantly distorted from that predicted by the conventional Burgers equation, depending upon the choice of relevant parameters such as the permeability, the carrier frequency, and the mudcake membrane stiffness. Numerically exact analytical formulas for the self-demodulated pulse shape, as well as for the energy in the second harmonic band, are derived for cases in which the pulse duration is long and the nonlinearity is relatively weak. These formulas are valid for any arbitrary dispersion/attenuation mechanism, and not just tube waves in permeable formations, as long as the propagation wave vector may be specified uniquely as a function of frequency. ©1999 Acoustical Society of America.

Nonlinear tube waves in permeable formations: Difference frequency generation

Yaroslav Tserkovnyak — 2007-02-16T18:57:05-00:00

The Journal of the Acoustical Society of America, Vol. 116, No. 1. (2004), pp. 209-216.

We extend earlier work on nonlinear tube wave propagation in permeable formations to study, analytically and numerically, the generation and propagation of a difference frequency, = 1–2, due to an initial pulse consisting of carrier frequencies 1 and 2. Tube waves in permeable formations have very significant linear dispersion/attenuation, which is specifically addressed here. We find that the difference frequency is predicted to be rather easily measurable with existing techniques and could yield useful information about formation nonlinear properties. ©2004 Acoustical Society of America.

Three wave mixing test of hyperelasticity in highly nonlinear solids: sedimentary rocks

RM D’angelo — 2007-02-15T15:18:57-00:00

JASA

Granular packings: Nonlinear elasticity, sound propagation, and collective relaxation dynamics

Hernan Makse — 2007-02-15T15:14:34-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 70, No. 6. (2004)

Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a long-standing question in the field of granular matter. Here we perform a test of the applicability of elasticity theory to granular materials. We perform sound propagation experiments, numerical simulations, and theoretical studies to understand the elastic response of a deforming granular assembly of soft spheres under isotropic loading. Our results for the behavior of the elastic moduli of the system agree very well with experiments. We show that the elasticity partially describes the experimental and numerical results for a system under compressional loads. However, it drastically fails for systems under shear perturbations, particularly for packings without tangential forces and friction. Our work indicates that a correct treatment should include not only the purely elastic response but also collective relaxation mechanisms related to structural disorder and nonaffine motion of grains.