Microfolding in the Permian Castile Formation: an Example of Geometric Systems in Multilayer Folding, Texas and New Mexico

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Microfolding in the Permian Castile formation: An example of geometric systems in multilayer folding, Texas and New Mexico

J.I.D. ALEXANDER Center for Microgravity and Materials Research, University of Alabama, Huntsville, Alabama 35899 A. J. WATKINSON Washington State University, Department of Geology, Pullman, Washington 99164-2812

ABSTRACT

Outstanding examples of small-scale folds in the Castile forma- systems. Even more striking is that competent layers both thicker and tion are of considerable interest to structural geologists because, thinner than folded layers remain planar. We believe that current fold owing to the low-strain condition of the rock (-25% shortening), they theories for the onset of folding, which are based on the premise of afford a view of folds that have not yet formed pervasively throughout folding perturbations being identically unstable, cannot adequately the multilayer. Some folds have long, along-the-layer continuity in- explain this observation. A published theory is discussed that incorpo- volving few of the layers of the multilayer sequence. Others, predomi- rates both gravity and surface-tension effects and offers an explana- nantly in the hinge zone of larger folds (wavelength >1 m), have more tion for this observation. It suggests that folding in the Castile was predominant components of across-the-layer folding. Combinations likely a phenomenon akin to a Kelvin-Helmholtz instability, that is, a of these components result in dendriform patterns of distribution of critical rate of strain must be exceeded before folding occurs. folds and possible zones of interference between systems. One of the most striking features of the Castile folding is the INTRODUCTION presence of planar layers between folded layers, creating internal fold One of the outstanding descriptions of small-scale folds in the geologic literature is that of Kirkland and Anderson (1970). They described small-scale folds in a multilayered anhydrite-calcite formation, the Castile, in Texas and New Mexico. We believe that these folds are of considerable interest to structural geologists because, owing to the low-strain condition of the rocks, they afford a view of folds that have not yet formed pervasively throughout the multilayer. This gives us an unusual opportunity to examine the geometry of such isolated fold systems. The field observations stimulate potential ideas as to how such systems may interact with one another, leading to the complex geometries that are so typically observed in pervasively folded systems. Whereas the main analyses by Biot (1957, 1961,1964,1965a, 1965b), Ramberg (1963,1970a, 1970b, 1979), Smith (1975, 1977, 1979), Fletcher (1974, 1977, 1979), and Johnson (1977) of the onset of geologic folding may broadly explain some of the observed structures, certain other features in the folded Castile are difficult to explain by these analyses. We would like to bring to the attention of geologists an analysis with both gravity and layer-interfacial effects (surface tension) included, which has the advantage of giving an explanation of certain key observations (Wollkind and Alexander, 1982). The first part of this paper describes in more detail than in Kirkland and Anderson (1970) some of the fold geometries observed in the Castile formation. It promotes the idea of describing multilayer folds in terms of geometric systems (Watkinson and Alexander, 1979); that is, within the Figure 1. Locality of Castile outcrop, on the state line between total multilayer fold system, there are sets or groups of folds with geometric Texas and New Mexico. See Anderson and Kirkland (1987) for more features ( wavelengths and/or amplitudes and/or profile shapes) distinctive details. from other sets.

Geological Society of America Bulletin, v. 101, p. 742-750, 12 figs., 1 table, May 1989.

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Figure 2a. Example of an isolated fold system involving one ob- Figure 2b. Example of multilayer folds having predominant com- vious predominant anhydrite layer. ponents of along-the-layer folding, with a small component of across- the-Iayer folding in the top right-hand corner.

The second part draws attention to one or two specific fold geome- pecially when compared to those observed in modern-day sabkha envi- tries and outlines the elements of Wollkind and Alexander's analysis, in ronments (for example, Shinn, 1983, p. 195-196). In fact, these folds are the context of a discussion of previous analyses, which provide an attractive some of the most periodic and regular that we have observed anywhere in explanation for such features. We argue that the folding in the Castile the world. formation has occurred because a critical rate of strain has been locally A key observation made by Kirkland and Anderson was that the exceeded. The planar layers were thus no longer stable to small perturbations of a critical wavelength (defined by the critical rate of strain), and so these perturbations grew. The onset of folding in the Castile thus can be viewed as a stability problem in the same class as the Kelvin-Helmholtz instability (Chandrasekhar, 1961; Yih, 1965). The Kelvin-Helmholtz instability is a shear instability which arises in parallel flows of stratified fluids. The essential mechanism of the instability can be described as follows. The available kinetic energy of the relative motion of layers of the basic flow is converted kinetic energy of the basic disturbance. For layers separated by an interface, instability will occur, provided the kinetic energy of the disturbance is sufficient to overcome both the potential energy needed to raise and lower the fluid (whenever the density decreases with height) and the increase in surface free energy consequent to a deformation of the initially planar interface.

ORIGIN OF THE CASTILE MICROFOLDING— "SEDIMENTARY" OR TECTONIC?

We preface our discussion of the observations on the folding with a brief review of ideas concerning the origin of the folds. There is still lively debate, concerning both the origin of the forces that formed the Castile folds and the exact state of the layers at the time of folding. Kirkland and Anderson (1970) carefully considered and recently reiterated (Anderson and Kirkland, 1987) the various ideas concerning the origin of the folds, that is, slump triggered by earthquake activity, ripple marks, crystal growth, or tectonics. They considered that because the folds are polyharmonically associated with larger-wavelength folds, and have reasonably consistent fold axial directions parallel to regional structural trends (but oblique to the projected basin paleoslope), the folding was most likely of tectonic origin. As we shall illustrate further, these Castile folds are strikingly periodic and regular (although locally developed), es-

Figure 3. An example of one of the few chevron/kink-like folds observed in the Castile outcrop.

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unfolded portions of the layers have thickened in comparison to the folded portions, consistent with the idea that lateral compression of the layers led to either layer thickening or buckling. Also, the field evidence for a contrast in layer behavior between the anhydrite and the calcite layers seems consistent and unequivocal. It is, however, a notoriously difficult task to ascertain the exact state of the layers at the time of folding, that is, whether the folds are "soft sediment" or tectonic (see detailed discussions in Elliott and Williams, 1988; Maltman, 1984). In terms of the mathematical modeling, the field observations are the basis for establishing two of the major boundary conditions or constraints for the model—layer-parallel shortening and "viscosity" contrast between the anhydrite and calcite-rich layers. Although we cannot be dogmatic about the exact rheological state of the layers at the time of folding, we consider the modeling to be appropriate as long as the layers have short- ened and were in a "viscous" state at the time of folding. Furthermore, as we shall illustrate, we believe that the modeling can explain the intermit- tently developed nature of the folds. As structural geologists, we would challenge the sedimentologists to prove that the layers were unconsoli- dated at the time of folding! As modelers, it is not crucial to the model. Indeed, if the system was "fluidized" at the time of folding, the inclusion of surface tension may be particularly appropriate for modeling this particular fold system (see later discussion also).

FIELD OBSERVATIONS

The field observations of the folding of the Castile formation are based on our own observations of the Eddy County state-line outcrop, New Mexico (Fig. 1), coupled with observations on core samples very

Figure 5. Dendriform patterns of combinations of across-the-layer and along-the-layer components. These patterns typically occur in the hinge zone of larger-scale folds. The insert (b) shows Figure 4. An exam- blocked-out areas of ple of multilayer folding. folds. The folds tend toward a similar fold geometry. Note the change in sym- metry of the folds from the lower to the upper folds.

kindly made available to us by Anderson, and on observations made by Kirkland and Anderson (1970). The formation consists of alternating laminae of brown calcite and gray-white anhydrite. The anhydrite layers are as much as 5 mm thick with a mean thickness of 1.1 mm. The brown calcite-rich layers, containing some organic material plus some intermit- tently distributed anhydrite crystals, are on average 0.4 mm thick and as

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Figure 6. Examples of styles of multilayer folds. 6a shows internal systems bounded by planar interfaces (arrows). 6b shows more pervasive folding, with some dis- harmony across thicker incompetent layers (the dark layers high- lighted by arrows).

much as 1.2 mm thick. All structural indications are that the anhydrite "pods." The pods are located predominantly in the hinge zones of larger- layers were the more competent layers during the folding deformation. scale folds (wavelengths approximately 1 m), in both the synclinal and The anhydrite layers frequently have a cuspate-lobate fold form (Ramsay anticlinal hinges. The outline shapes of these concentrated zones of micro- and Huber, 1987, p. 403). We see no evidence of interlayer slip such as folds are typically either elongate along the layering or elongate in a bedding-plane slickensides or striae and thus assume that the layer contacts direction parallel to the axial-plane trace of the folds, at a high angle to the remained bonded during deformation. layering. This observation provides the motivation for a useful way of One of the most striking features of the state-line outcrop, described communicating the details of the distribution of the minor folds— by Kirkland and Anderson (1970, Figs. 8 and 9; Anderson and Kirkland, continuity of folds in terms of components of along-the-layer and across- 1987), is the occurrence of the small-scale folds in concentrated zone or the-layer systems (Watkinson and Alexander, 1979).

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An extremely important detail is that even within the pods of micro- folds, not all of the anhydrite layers are folded. As we shall illustrate later, there are examples where both thicker layers (—4-5 mm) and thinner layers (< 1 mm) remain essentially unfolded adjacent to folded layers. This creates systems of folds that have a long lateral continuity compared to the across-the-layer component. Figure 2 illustrates typical examples of fold systems with many folds laterally but involving only one or two competent layers. In some examples, these lateral systems are quite isolated (Fig. 2a). The folds die out in a variety of ways; some decrease in both amplitude and wavelength, and others die out with an increased wavelength (or, more correctly, span, if only one fold exists of one size) and decreased amplitude. In contrast to the systems with obvious lateral continuity compared to the "across-the-layer" continuity, other systems noticeably involve harmonic folding of many layers, in many cases with short lateral extent, and in most cases in the hinge zone of the larger folds. The obvious end member of this type of system is a kink fold, which only rarely occurs in the Castile sequence (Fig. 3). The tendency for extensive "across-layer" systems to develop is where all layer thicknesses or layer-couplet (anhydrite/calcite laminae) ratio thicknesses remain constant, that is, there are no obvious markedly thick or thinner beds. As expected in these more homogeneous multilayer sequences, the folding tends to be a chevron to sinusoidal type (Figs. 3 and 4), rather than the typical rounded, cuspate inner arc, buckle type seen in the "single" layer folds. In detail, many of the zones of microfolding show multilayer folds with several layers folding out laterally, farther "along the layer" than others; this creates dendriform patterns of fold distribution (Fig. 5). Some zones occur where the folding is totally pervasive, that is, all of the layers are folded. More frequently, the folds occur harmonically within multilayer packets, with some folds harmonic across several multilayer packets. In general, the multilayer folds will be disharmonic across either anomalously thick layers (either anhydrite or calcite) or thin layers that remain unfolded. Figures 6 and 7 show some typical examples of fold patterns. Notice that compared to the folded layer(s), the adjacent unfolded layer or layers may be both thicker or thinner (Fig. 7). There are examples where one interface of a thicker layer may be perturbed as a cusp interface, but not the other. If we assume that the Castile formation represents an arrested, low- strain stage of multilayer folding, we can speculate as to possible effects that may occur, were the folding to continue. Physical-analogue models (Cobbold, 1975) and numerical modeling using the finite-element tech- nique (Williams and others, 1978; Wickham, 1980) for single competent layers suggest lateral, serial propagation of the folds from the early-formed zones. Therefore, we may expect the "along-the-layer" systems to extend farther laterally. Presumably, amplification of the early folds may lead to finite-strain perturbations across the layers (that is, involve more layers). The successive involvement of more layers will lead to further-developed components of across-the-layer systems, perhaps leading to interference between systems. This kind of effect is born out by analogue modeling of propagating multilayer folds (Cobbold, 1976; Watkinson, 1976; Watkin- son and Cobbold, 1978), which suggests the formation of interference zones where systems interact, leading to localized asymmetry of folds, Figure 7. Examples wherein anhydrite layers both "thicker" and "dead" zones, and final fold "saturation" of the layers. The multilayer folds "thinner" remain essentially planar (arrows), whereas layers of "in- shown in Figure 8 show a zone of change of fold geometry perhaps termediate" thickness buckle. indicative of interference between fold systems.

DISCUSSION OF PREVIOUS FOLDING ANALYSES IN RELATION TO THE CASTILE FOLDS the Castile multilayer folding sequence can be qualitatively explained in the light of Ramberg's conclusions, the most obvious being the generation One of the outstanding analyses of multilayer folding, including the of several orders of wavelengths and varying amplitudes of folds across the effects of gravity, is that of Ramberg (1970a, 1970b). Several features of layers (Ramberg, 1970b, p. 94). Ramberg's analysis emphasizes the cou-

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Figure 9a. An example traced from a natural sample where out-of- phase folds could lead to interference of their "contact strain" zones, result- ing in an unfolded layer between them.

Figure 9b. Other examples, however, demon- strate the existence of planar layers even where the folded layers on either side are in phase.

Ramberg (1964) has shown how in a multilayer where there is a very low competence contrast between competent and incompetent layers, folds may not significantly amplify in low-strain conditions. One could argue perhaps for the Castile that the contrast between the anhydrite and calcite layers was not constant (due to slight variations in grain size and composition) and therefore that some layers remain essentially planar owing to low competence contrasts. If this is the case, however, it is neither obvious nor systematic. Biot's analysis (1965a, 1965b) of internal systems for fold geometries shows internal boundaries of planar layers; the problem is, still, why do particular layers act as internal boundaries? In the Castile folds, the occurrence of internal boundaries separating systems of folds is clearly not periodic, neither is there any obvious periodicity in the manner in which fold amplitudes die out in the "across-layer" direction. In fact, the termina- tion of a system can be quite abrupt (see Fig. 7). Biot's analysis for anisotropic systems does show critical behavior Figure 8. Multilayer folds showing a zone wherein the fold (Biot, 1965a, 1965b; Cobbold and others, 1971; Latham, 1985a); that is, a geometry changes. Perhaps an example of interference between fold critical-stress difference and/or degree of anisotropy is required to initiate "systems." significant folding instabilities, both in elastic and viscous media (assuming the principle of correspondence). One might imagine that such a multilayer system as the Castile would be an attractive one to analyze in terms pling effects of closely spaced competent layers and the prediction that as of bulk anisotropic properties, as it is composed of a large stack of two competent layers become more and more widely spaced, less and less alternating units. Many other bilaminate-type sequences (for example, coupling occurs, and the competent layers fold independent of each other. shale/chert, spaced cleavage in phyllites) typically show large "across-the- For the Castile folds, however, we frequently observe closely spaced com- layer" multilayer fold systems of kink/chevron-style folds. Somewhat petent layers that appear to be uncoupled, that is, planar layers adjacent to surprisingly, the Castile appears to be unusually sensitive to changes in folded layers. thickness of the layers, with frequent planar boundary layers, making it If we examine explanations that have been offered in the geologic difficult to assess the bulk layer properties as an aggregate, multilayer literature for such uncoupling effects and maintenance of essentially planar anisotropic system. There are examples in the Castile of layers that are layers, it appears to us that none of them are entirely satisfactory to explain regularly alternating, forming uniform multilayer stacks. Some of these the Castile geometries. uniform multilayers remain planar, whereas others fold in harmonic multi- For a single layer, Wickham (1980) has shown that if the upper- and layer folds (for example, see Fig. 4). Biot's analysis may explain why some lower-interface perturbation flows are symmetric about an axis parallel to of the uniform multilayers fold, whereas others remain planar. The varia- the length of the layer, and the layer is not so wide such that decoupling of tion in position within the major folds may lead to a variation in stress the perturbation flow occurs, the layer may remain essentially planar for difference and therefore critical/subcritical behavior. Another important finite-strain deformations. This may well explain localized areas where the variable is that both the couplet thickness and the ratio of the anhydrite to contact-strain zones of out-of-phase folds either side of a planar layer result calcite-rich layer in a couplet varies. This will affect the degree of aniso- in interference and cancellation of any folding perturbation on the planar tropy of the bulk properties (Casey and Huggenberger, 1985) and has a layer (Fig. 9a). This argument will not hold in general, however, because profound effect on conditions of instability (Fig. 5 in Latham, 1985a) and frequently folds are "harmonic" across the planar layer, and yet the rein- therefore on whether the multilayers fold. forced, contact-strain, perturbation effect does not result in folding the At low temperatures and fast strain rates (for anhydrite tested by sandwiched layer (Fig. 9b). Miiller and Briegel, 1978), anhydrite may experience work-hardening

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Figure 10. A kink-like fold passing into a fault discontinuity (arrow). This fold appears to fold the multilayer folds and may therefore be later.

rheological behavior1 and, as pointed out by Latham (1985a), in such perturbation growth rate. Initiation of the folds by an elastic component materials after significant shortening, the material may build up a signifi- (for example, Johnson, 1977) cannot explain the thinner layers remaining cant induced anisotropy leading to instability. Latham, however, predicted stable, because the critical buckling stress is a function of layer thickness, kink-like folding or faulting under such conditions (Latham, 1985b), and, that is, predicting that thinner elastic struts buckle before thicker ones of as pointed out previously, kinks only rarely occur; there are a few exam- similar composition. ples of kink-like folds or asymmetric box folds associated with faults (Fig. The analysis of Wollkind and Alexander (1982) is based on a two- 10)—perhaps an expression of the above effect. dimensional mathematical model of the initiation of folding in a single It appears, then, that the amplification of perturbations and initial growth of the folds, and particularly how many layers are initially involved in the folding, must be a particularly sensitive parameter, determining whether the multilayer folds as a unit or as sets of "single" layers. Kirkland and Anderson (1970, Fig. 18) gave an outstanding example of correlation of deformed layers over several kilometers, which illustrates perfectly how, at similar bulk-strain conditions (-25% shortening), the folds involve dif- fering numbers of layers from core to core. This strongly suggests that as it is assumed that all layers must be susceptible to initial folding perturbations, some layers resist the initial perturbations or are stabilized against such perturbations. As mentioned in the observations, typically it is slightly thicker layers that remain planar, but also thinner layers remain planar whilst adjacent layers fold. It is this observation that is hard to reconcile with the well-known analyses on the onset of viscous-layer folding. Im- plicit in these analyses is that the fold-type perturbations are identically unstable, that is, all existing perturbations are inherently unstable and grow. The subsequent characterization of the wave train is by the predominant wavelength associated with that disturbance having the maximum Figure 11. Graph of dimensionless thickness, H, versus strain rate, e, adapted from Wollkind and Alexander (1982). It shows the critical stability phenomenon, whereby folding commences at a critical 'To our knowledge, no rheological tests have been carried out on the Castile strain rate, ec. Notice that at strain rates e > ec, a band of layers anhydrite. becomes unstable, with thin and thick layers remaining stable.

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Figure 12. An example of soft-sediment deformation dominated by strongly cuspate, lower interfaces of silt layers. The upper interface of the silt layers remains stable. This characteristic fold shape (type 1A, Ramsay, 1967) is seldom observed in the Castile folds (see Figs. 5 and 6). This specimen is from the Bedford shale-Berea sandstone in Ohio (specimen courtesy of J. Wilson).

rock layer embedded in a less competent matrix. The model employed a model can be argued from two points of view, both equally valid. First, it represents this situation in terms of a layered heterogeneous Newtonian is commonly the case in the field of materials science that the excess fluid, and the effects of gravity and surface tension were assumed to be internal energy associated with a surface between two solids is character- important. (The validity of both assumptions will be discussed later in this ized as a surface energy. The existence of a surface stress associated with paper.) The basic state of this layered system was assumed to correspond the surface energy of solids has been demonstrated theoretically (Herring, to a uniform parallel-layer thickening at a constant rate of compressive 1953; Shuttleworth, 1950; Johnson and Alexander, 1986) and examined strain. Owing to the vanishingly small Reynolds number corresponding to experimentally (Alexander and others, 1951). The simplest form of surface the conditions under investigation, inertial effects were neglected, and the stress between two solids is a surface tension (Shuttleworth, 1950; Herring, quasi-static approximation (Präger, 1961) of the governing equations of 1953; Murdoch, 1976; Gurtin and Murdoch, 1975). Unlike the case in motion was invoked. The stability (to infinitesimal fold-like disturbances) simple fluids (Gibbs, 1928), the surface tension is not simply equal to the of the uniform layer-thickening solution to these equations was then exam- surface free-energy density. Indeed, for elastic surfaces, Murdoch (1976) ined by means of a linear stability analysis. has shown that the surface tension is equal to The main result of the analysis was that for a given set of physical d>h properties (viscosity, density difference between the layers, surface ten- + (1) oj sion), the onset of folding occurred at a critical value of the imposed rate of strain. At this critical rate of strain, only one wavelength was unstable. At where ij> is the surface free-energy density and J is the determinant of the higher rates of strain, a finite bandwidth of unstable wavelengths is present surface-deformation gradient. If the deformation involves no change in (Fig. 11). This is in contrast to earlier analyses which predicted that the surface area, or if the surface free energy is independent of J, then the layer would be unstable to all disturbances. The reason for this difference is surface free energy is equal to the surface tension. The second argument is that both capillarity and gravity were included in the analysis. Thus, both that surface properties may be used as convenient modeling tools and has long- and short-wavelength disturbances to the basic flow could be been advanced by Murdoch (1976) concerning the application of a surface stabilized. thermodynamic theory to engineering problems involving thin metal skins. The inclusion of capillarity, or surface tension, in models of rock The assumption made by Wollkind and Alexander (1982) is equiva- deformation at small-length scales is certainly not "standard" and thus lent to assuming that at sufficiently small-length scales, the excess energy merits further discussion. The justification for including capillarity in such associated with the interface between two rock layers is associated with a surface tension. The difficulty in interpreting the validity of the model arises when considering the nature of the fluid model employed to describe

TABLE 1. CUTOFF WAVELENGTHS AND WAVELENGTHS the deformation process. The nature of surface tension is well defined for ASSOCIATED WITH FASTEST-GROWING DISTURBANCE fluids. Surface stress and surface tension are well defined for solid surfaces. It is not clear how the concept of a surface stress should be treated when Viscosity é H Ap 4> 0 hc (1 matrix using a viscous-fluid model to treat a body that on shorter time scales we (dyne-s-cm"') (s1) (cm) (gem 3) (cm) (cm) yi layer treat as a solid. If surface effects are retained, however, then the appro-

10" 10 16 1 0.1 0.98 4.7 3.0 0.1 priate model would include viscous surface stresses (Scriven, 1960). The 10" 10" 2 0.2 0.4 135 11.0 0.1 10" 10 15 0.5 0.1 0.49 3.8 2.2 0.1 Wollkind-Alexander analysis corresponds to an approximation which re- tains surface effects only through the surface tension and which effects are Note-, the value of the cutoff wavelength, depends on the ratio, r, of the viscosities of the matrix and the layer. manifested only when there is a curvature to the surface. Whether surface n matrix//* layer, and on a parameter tension or some analogous quantity actually plays a role in the onset of ApgH„ = ~ folding is not certain; however, its effects cannot be discounted.

where Ap is the density difference, g is the gravitational acceleration, H0 is the initial layer thickness, and é is the basic rate Gravity has not been considered to date to be an important effect as a of strain. The value of Xc decreases with decreasing values of the basic strain rate. It appears that gravitational effects stabilizing force for small-length scales of folding. Ramberg (1970a, become important even at small-length scales. Kà is the wavelength associated with the fastest-growing disturbance. 1970b) in fact dismisses the stabilizing effects of gravity on folds with

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wavelengths less than 100 m. The Wollkind-Alexander analysis, however, REFERENCES CITED shows that for layers with significant density contrasts (for the Castile, that Alexander, B. H„ Kuczynski, G. C., and Dawson, M. H., 1951, Relations between diffusion and viscous flow in metals, in 3 Kingston, W. E., ed., Physics of powder metallurgy (Chapter 11): New York, McGraw-Hill, p. 202-213. is, anhydrite in a calcite matrix, A p may range from 0.2-0.8 gm/cm ), the Alexander, J.I.D.. 1981, Folds and folding in single and multilayered rocks: Mathematical models and field observations (Ph.D. thesis]: Pullman, Washington. Washington State University. 145 p. slower the rate of strain, the more important are the gravitational effects. Anderson, R. Y., and Kirkland, D. W., 1987, Banded Castile evaporites, Delaware basin, New Mexico, in Beus, S. S., ed.. Alexander (1981) showed for a single layer (Table 1) that there is an upper Rocky Mountain Section of the Geological Society of America: Boulder, Colorado, Geological Society of Amer- ica, Ce ntennial Field Guide, v. 2, p. 455-458. limit to the wavelength of instabilities, Xc (the amplitudes of small distur- Biot, M. A., 1957, Folding instability of a layered viscoelastic medium under compression: Royal Society of London Proceedings, ser. A, v. 242, p. 444-454. bances with wavelengths greater than kc will decay exponentially with 1961, Theory of folding of stratified viscoelastic media and its implications in tectonics and orogenesis: Geological time), and that this value decreases with decreasing values of the basic Societ) of America Bulletin, v. 72, p. 1595-1620. 1964, Theory of viscous buckling of multilayered fluids undergoing finite strain: Physics of Fluids, v. 7, strain rate. p. 855 -859. 1965a, Mechanics of incremental deformations: New York, John Wiley and Sons, 504 p. Finally, two other important aspects should be mentioned, which are 1965b, Further development of the theory of internal buckling of multilayers: Geological Society of America the effect of nonlinear rheologies on the stability analyses and the tectonic Bulletin, v. 76, p. 833-840. Casey, M., and Huggenberger, P., 1985, Numerical modelling of finite-amplitude similar folds developing under general origin of the Castile folds. deformation histories: Journal of Structural Geology, v. 7, p. 103-114. Chandrasekhar, S., 1961, Hydrodynamic and hydromagnetic stability: Oxford, United Kingdom, Clarendon Press, 652 p. Rheological tests on polycrystalline anhydrite (Miiller and Briegel, Cobbold, P. 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C., 1974, Wavelength selection in the folding of a single layer with power-law rheology: American Journal of of the stability behavior. Scienoi, v. 274, p. 1029-1043. 1977, Folding of a single viscous layer: Exact infinitesimal-amplitude solution: Tectonophysics, v. 39, p. 593-606. Smith (1979) and Fletcher (1974) have examined nonlinear rheolo- 1979, The shape of single-layer folds at small but finite amplitude: Tectonophysics, v. 60, p. 77-87. Gibbs, J. W., 1928, On the equilibrium of heterogeneous substances, in J. W. Gibbs: Collected works (Volume 1): New gies in their identically unstable models and, indeed, Smith rationalizes a York, Longmans, p. 33-353. choice of strongly nonlinear rheology in order to explain the appearance of Gurtin, M., and Murdoch, A. I., 1975, Elastic material surfaces: Archives for Rational Mechanics and Analysis, v. 57, p. 291-323. small-scale folds of X/H ratios of 4-6. Wollkind and Alexander's analysis Herring, C., 1953, The use of classical macroscopic concepts in surface energy problems, in Gomer, R., and Smith, C. S., eds.. Structure and properties of solid surfaces: Chicago, Illinois, University of Chicago Press. (1982) can also accommodate this observation without recourse to a Johnson, A. M., 1977, Styles of folding: Amsterdam, the Netherlands, Elsevier, 406 p. nonlinear rheology. Johnson, W. C., and Alexander, J.I.D., 1986, Interfacial conditions for thermomechanical equilibrium in two-phase crystals: Journal of Applied Physics, v. 59, p. 2735-2746. We find nothing to contradict Kirkland and Anderson's assertion that Kirkland, D. W., and Anderson, R. Y., 1970, Microfolding in the Castile and Todilto evaporites, Texas and New Mexico: Geological Society of America Bulletin, v. 81, p. 3259-3282. the folds in the Castile are of tectonic origin rather than "enterolithic" Latham, J.-P., 1985a, The influence of nonlinear material properties and resistance to bending on the development of origin (Fig. 12). Hydration structures of anhydrite to gypsum do occur in internal structures: Journal of Structural Geology, v. 7, p. 225-236. 1985b, A numerical investigation and geological discussion of the relationship between folding, kinking and the outcrop but are readily distinguishable from the orderly folding. An faulting: Journal of Structural Geology, v. 7, p. 237-250. Maltman, A., 1984, On the term "soft-sediment deformation": Journal of Structural Geology, v. 6, p. 589-592. attractive feature of Wollkind and Alexander's analysis is that it offers a Miiller, W. H., and Briegel, U., 1978, The rheological behavior of polycrystalline anhydrite: Eclogae Geologicae Helvetiae, rational argument to explain the main feature that is often used to appeal v. 71, no. 2, p. 397-407. Murdoch, A. I., 1976, A thermodynamical theory of elastic material interfaces: Quarterly Journal of Mechanics and to the diagenetic/sedimentary origin of the folds—the presence of planar Applied Mathematics, v. 29, p. 246-275. Präger, W., 1961, Introduction to mechanics of continua: Boston, Massachusetts, Ginn, 230 p. layers between folded layers. Ramberg, H., 1963, Fluid dynamics of viscous buckling applicable to folding of layered rocks: American Association of Petroleum Geologists Bulletin, v. 47, p. 484-505. In conclusion, we envisage the tectonic scenario for the Castile folds 1964, Selective buckling of composite layers with contrasted physical properties: A theory of simultaneous as multilayer buckling with stress concentrations in the hinge zones of the formation of several orders of folds: Tectonophysics, v. 1, p. 307-341. 1970a, Folding of laterally compressed multilayers in the field of gravity, I: Physics of the Earth and Planetary larger-scale folds causing increased strain rates and initiation of buckle- Interiors, v. 2, p. 202-232. 1970b, Folding of laterally compressed multilayers in the field of gravity, II: Physics of the Earth and Planetary folded layers between stabilized layers, both thicker and thinner than the Interiors, v. 4, p. 83-120. folded layers. This phenomenon would then be a truly critical form of Ramsay, J. G., 1967, Folding and fracturing of rocks: New York, McGraw-Hill, 568 p. Ramsay, J. G., and Huber, M. I., 1987, The techniques of modern structural geology (Volume 2): New York, Academic instability rather than the identically unstable form implicit in most anal- Press. Scriven, L. E., I960, Dynamics of a fluid interface: Chemical Engineering Science, v. 12, p. 98-108. yses. The more homogeneous layer-couplet zones behave more as Shinn, E. A., 1983, Tidal flat, in Scholle, P. A., Bebout, D. G., and Moore, C. H., eds., Carbonate deposition^ multilayer fold packets forming sinusoidal-to-chevron fold zones. Were environments: American Association of Petroleum Geologists Memoir 33, p. 171-210. Shuttleworth, R., 1950, The surface tension of solids: Physics Society Proceedings, v. A63, p. 444 457. folding to continue, we would expect increased lateral extent of along-the- Smith, R. B., 1975, Unified theory of the onset of folding, boudinage, and mullion structure: Geological Society of America Bulletin, v. 86, p. 1601-1609. layer systems. Increased amplification of folds would produce finite-strain 1977, Formation of folds, boudinage, and mullion in non-Newtonian materials: Geological Society of America perturbation across layers, including some previously unfolded layers, re- Bulletin, v. 88, p. 312-320. 1979, The folding of a strongly non-Newtonian layer: American Journal of Science, v. 274, p. 1029-1043. sulting in interference between systems. Watkinson, A. J., 1976, Fold propagation and interference in a single multilayer unit: Tectonophysics, v. 34, p. T37-T42. Watkinson, A. J., and Alexander, J.I.D., 1979, The importance of geometric systems in multilayer folding, in Cobbold, P. R., and Ferguson, C. C., eds., Conference report on spatial periodicity in geologic structures: Journal of Structural Geology, v. 1, p. 95. ACKNOWLEDGMENTS Watkinson, A. J., and Cobbold, P. R., 1978, Localization of minor folds by major folds: Geological Society of America Bulletin, v. 89, p. 448-450. Wickham, J. S., 1980, The effects of deformation in rocks: Tectonic Studies Group Conference Report, Göttingen, We would like to thank Roger Anderson for giving us access to the Germany, April. Williams, J. R., Lewis, R. W., and Zienkiewicz, O. C., 1978, A finite-element analysis of the role of initial perturbations in Castile cores and for his enthusiastic support for our study. Joe Wilson the folding of a single viscous layer: Tectonophysics, v. 45, p. 187-200. kindly sent us the superb example of "soft" sediment deformation. We Wollkind, D. J., and Alexander, J.I.D., 1982, Kelvin-Helmholtz instability in a layered Newtonian fluid model of the geological phenomenon of rock folding: SIAM Journal of Applied Mathematics, v. 42, p. 1276-1295. appreciate the careful and thoughtful reviews of the earlier version of this Yih, C. S., 1965, Dynamics of nonhomogeneous fluids: New York, Macmillan, 306 p. paper. We would like to thank Franz Rosenberger for his support through MANUSCRIPT RECEIVED BY THE SOCIETY OCTOBER 29,1987 REVISED MANUSCRIPT RECEIVED SEPTEMBER 21,1988 the Center for Microgravity and Materials Research. MANUSCRIPT ACCEPTED OCTOBER 3, 1988

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