Development of folds within carmel formation, Arches National Monument, Utah

Abstract Crenulations of bedding within the Carmel Formation of southeastern Utah usually have been interpreted to be chaotic structures. In Arches National Monument, however, definite patterns can be recognized and the patterns can be understood in terms of multilayer-folding theory. In some places, interbedded sandstones and siltstones of the Carmel Formation were confined above and below by relatively massive and rigid Entrada and Navajo sandstones. As a result, the fold pattern within the Carmel is of the internal variety in which the fold amplitudes diminish upwards and downwards from a maximum near the center of the Carmel. The maximum amplitudes usually are not at the center of the Carmel as we would expect if the Carmel had uniform physical properties at the time of folding. Rather the maximum amplitudes are displaced towards the base of the Carmel, apparently indicating that the lower beds were softer than the upper beds. In other places, the folds within the Carmel Formation extend upwards into the lower part of the massive Entrada Sandstone, where their amplitudes gradually diminish. Two factors seem to control this type of folding and they can be understood in terms of an inequality of the form: B B o > (T) 2 2t 1 where B is the modulus of the stiff beds of the multilayer (Carmel), Bois the modulus of the confining medium (Entrada), T is the total thickness of the multilayer, and t1 is the thickness of each of the stiff beds of the multilayer. If this inequality is satisfied, according to theory, folding should be of the general buckling variety in which the folds extend into the overlying Entrada. If this inequality is not satisfied, folding should be of the internal variety. The inequality seems to account for the field observation that, where the Carmel is quite massive, that is where the number of beds, T/t, is quite small, the folds usually deflect the lower part of the Entrada. Where the Carmel is well-bedded, however, that is, where T/t, is quite large, the inequality apparently is not satisfied, because the folds are of the internal variety. The elastic analog of Biot's theory of the multilayer is derived and the assumptions that lead to the theory are emphasized and discussed so that the theory can be modified to account for field observations. There is field evidence that beds of the Carmel were somewhat irregular prior to folding, rather than being perfectly flat plates as is assumed in theory, so that effects of initial deflections within single layers and within multilayers are analyzed. The analysis indicates that the internal folding of an initially deflected multilayer is of the form: v = δ i (1 − P P mult ) sin πy T sin 2πx L where δi is the amplitude and L is the wavelength of the initial deflection, P is the axial load, and Pmult is the critical load for buckling of initially flat layers. This solution for the deflection helps us to realize the significance of initial deflections, even small ones, in the process of buckle folding. The solution indicates that as the magnitude of the initial deflection becomes smaller and smaller, the magnitude of the axial load required for significant deflection becomes larger and larger, until, in the limit, when the initial deflection has vanishing amplitude, the axial load equals the critical buckling load, Pmult. Thus the critical load is the maximum load required for significant folding or real layers, which are never perfectly flat. Analysis of folding of markedly irregular multilayers indicates that the resultant fold pattern usually will have a dominant wavelength of the Biot wavelength: L B = 2π T 2π B p I p tb B n 4 which is the dominant wavelength in initially flat beds, unless irregularities with other wavelengths have much greater initial deflections than the irregularities of the Biot wavelength. Here Bp is the modulus parallel to bedding, Ip is the moment of inertia of each stiff bed, and Bn is the modulus normal to bedding. The Biot wavelength becomes: L B = 2 Tπt 1 12 ≈ 1.90 Tt 1 where t1 is the thickness of each stiff bed, if the modulus or viscosity of the soft beds is much smaller than that of the stiff beds. This equation predicts remarkably well the wavelengths of the internal-buckling folds of the Carmel. The simplified theory of buckling of multilayered sequences does not account for all the factors recognized in the field but we can understand most of the factors in terms of the theory.