Nonlinear Hysteresis in an Endochronic Solid
Abstract
Propagation of seismic waves in the nearfield where rock rheology is demonstrably nonlinear raises unique difficulties. Nonlinearity arises primarily in two forms at intermediate to large strains: (1) nonlinear elasticity, and (2) amplitude-dependent attenuation. The proper representation of nonlinear constitutive equations for rocks in the regime is a potentially important ingredient of quantitative source models. We have shown previously that nonlinear one-dimensional wave propagation can result in spectral distortions at all wavelengths. This effect is strongly pulse-shape dependent, and therefore calls for 3-D capability. More recently, we found that our approximate description of the phenomenology in the nonlinear regime was inadequate and unable to simulate new laboratory observations. We describe an intrinsically nonlinear rheological model, based on the endochronic framework of K. Valanis, which replicates the main features of observed hysteresis loops in the strain regime of interest and is easily reduced to differential form. The resulting differential equations can be readily solved numerically. Thus, this model is suitable for finite difference and finite element stress wave codes. Ultimately, a complete description of the rheology in terms of a thermodynamically valid constitutive equation is really what should be used in numerical simulations, if it can be developed and validate experimentally
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 04, 1994
- Accession Number
- ADA283142
Entities
People
- Jean-bernard Minster
Organizations
- Scripps Institution of Oceanography