LOCALIZED FOLDING OF VISCOELASTIC LAYERS

Naturally occurring fold systems are typically irregular. Although suc h systems may sometimes be approximated by a periodic geometry, in rea lity they are commonly aperiodic. Ord (1994) has proposed that natural ly occurring fold systems may display spatial chaos in their geometry. Previous work has indicated that linear theories for the formation of fold systems, such as those developed by Blot (1965), result in stric tly periodic geometries. In this paper the development of spatially ch aotic geometries is explored for a thin compressed elastic layer embed ded in a viscoelastic medium which shows elastic softening. In particu lar, it is shown that spatially localized forms of buckling can develo p and the evolution of these systems in the time domain is presented. A nonlinear partial differential equation, fourth order in a spatial v ariable and first order in time, is found to govern the evolution. A r elated nonlinear fourth-order ordinary differential equation governs a n initial elastic phase of folding. The latter equation belongs to a c lass with spatially chaotic solutions. The paper reviews the implicati ons of localization in the geological framework, and draws some tentat ive conclusions about the development of spatial chaos. Crudely arrive d-at, yet plausible, evolutionary time plots under the constraint of c onstant applied end displacement are presented. Emphasis throughout is on phenomenology, rather than underlying mathematics or numerics.