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Discussion

Locally exposed in one to two wavelength sections, the interbedded sandstone and shale of this study area are folded into concentric-like, kink-like, and chevron-like folds. Apart from the kink-like fold, wavelength and amplitude increase from north to south. Asymmetry, with a top-to-the-south sense of layer-parallel shear, is strong from the south end of Section II to the south end of the outcrop. Lenticular beds and pinch outs are more common in Section I than in other sections. Faults in the outcrop are dominantly thrusts consistent with layer-parallel shortening. Thrusts in the concentric-like fold occur on both limbs, in the chevron-like folds they are mainly on the long limbs. Ramp faults repeat beds the length of a limb in Sections I and VI, on both north and south-dipping limbs. Each section also has an anticline with a thrust fault on the long north-dipping limb that extends through the hinge and across the south-dipping limb. Deeply weathered brecciated shale layers occur on the short steep limbs of the chevron-like folds. Calcareous layers with localized boudinage, are found throughout the outcrop, with closer spacing in Section I than in Section VI, though beds are also thinner in Section I.

Outcrop Fold Package

The variations in asymmetry and wavelength, and shortness of the exposed fold trains (beds could not be traced through the entire outcrop), lead to modeling of the outcrop as a stack of multilayers. These multilayer folds can be described genetically by a folding mechanism, and geometrically by fold form. Since fold form is not unique to a specific folding mechanism, mechanisms of folding will be examined before fold form.

Folding Mechanism

In a fold and thrust belt, the types of folding and corresponding mechanisms of folding that might be found include a) buckle folding: layer-parallel shortening, b) ramp folding: duplication of strata by faulting, c) drape folding: flexure of strata caused by slip on a buried fault, and d) drag folding: layer-parallel shear on the limb of a higher order fold. As a mechanism for shortening, layer-parallel shortening produces maximum shortening and buckling. Layer parallel shortening is consistent with the most of the faults in the outcrop and for this study, is considered the dominant folding mechanism.

Fold Form

The geometric form of multilayer folds formed in layer-parallel shortening depends on the material properties of the layers and the confining media. Essential properties are a) relative strength of the layers and confining media, b) relative thickness of the layers and confining media, and c) whether contacts are bonded, free slip, or stick slip. Asymmetry of folds is a function of layer contacts and the sense of layer-parallel shear. Though the properties at the time of folding are not known, some assumptions can be made and models applied based on these assumptions.

The layers in the outcrop can be modeled as a multilayer of units with respective relative strength and thickness (Figure 30). Having a thickness greater than the wavelengths of other units, Section III can act as an infinite half-space to units above and below. It is likely a relatively stiff medium since it has greater sandstone to shale ratio and greater bed thickness than other units (Table 3). The upper and lower relatively soft media represent the muddier sections to the north and south of the outcrop.

Table 3. A summary of bed thickness and sandstone to shale ratios by folding unit. Section IV is split into two units with the layers of fold 18, Section IV-north, stratigraphicallly above Section VI.

All the layer, media, and contact properties are pertinent to the fold forms of this study. Relative strength of the confining media determines whether a multilayer will be constrained or concentric in form; ideal concentric folds form in relatively soft media and constrained folds form in relatively stiff media (Figure 31). Whether contacts have linear or nonlinear slip in layer-parallel shear determines whether kink or drag fold asymmetry develops. Relative strength and spacing of layers determines whether layers will fold independently forming a similar multilayer, and at high amplitude, chevron-like folds.

The sharp hinges in the chevron-like folds of the outcrop have not been reproduced in linear-viscous theoretical multilayers even to high amplitude , and may require nonlinear material behavior for their formation. Nonlinear material behavior of layers in the outcrop is evident by the presence of boudins that do not form in linear-viscous material. Distinguishing between linear and nonlinear material behavior, though, is not critical to essential fold form since the behaviors produce comparable fold form and wavelength. Similar folds in the interior of a theoretical multilayer may be used as a precursor of the ideal chevron form. The final fold form is also not affected by whether contacts are bonded or free slip, though folds with free slip grow faster.

Figure 31. Theoretical multilayer folds. Layers have linear slip or no slip on the layer interfaces. Viscosity contrasts are: m _stiff/m _soft = 10 and m _{very stiff}/m _soft = 10. A. and B. Constrained folds confined in stiff media and concentric folds formed in soft confining media. C. and D. An infinitely thick, similar multilayer of chevron-like folds in layer-parallel shortening, then subjected to layer-parallel shearing deformation. E., F., and G. Multilayer fold form varies from concentric (E), to similar (G), as stiff layers have greater spacing and a greater degree of independence .

Ideal multilayer fold forms are constrained, concentric, and similar incorporating the basic sinusoidal or chevron fold forms (Figure 31A, B, C). Constrained folds have amplitudes diminishing to zero at upper and lower media contacts. Wide crests and narrow troughs at the upper media interface, and narrow crests and wide troughs at the lower interface characterize concentric-like folds. Similar folds are sinusoidal at low amplitudes and chevron at high amplitudes. Hybrids of ideal multilayers develop if properties are intermediate between end member forms.

Concentric-like Fold

The concentric-like fold of Section I (Figure 32), flattened crest bounded by narrow troughs, is characteristic of the upper layers of theoretical concentric multilayers or layers slightly lower in theoretical constrained multilayers (Figure 31B, A). Crests of layers in the concentric-like fold in Section I are broad above, narrow in the middle, and slightly rounded in the core. Sections II and III provide a relatively stiff medium above Section I (Figure 30). The concentric-like fold in the outcrop is similar to the upper part of the ideal constrained multilayer (Figure 31A).

Figure 32. Fold form of Section I.

Chevron-like Folds

Development of a similar multilayer of chevron-like folds is dependent on the relative thickness of stiff and soft interbeds, and the multilayer thickness. Theoretically, chevron-like folds will develop in a multilayer if the stiff to soft thickness ratio is small, allowing the stiff beds to fold independently (Figure 31G). Johnson and Fletcher define the degree of independence, d, as

where m _n is the normal viscosity of the multilayer,

L is the wavelength of the folds, h is bed thickness, m is viscosity, and 1 and 2 refer to stiff and soft respectively (Figure 33). If d is near zero, the beds behave strongly as an ensemble. If d is significantly greater than zero, on the order of 0.5 or greater, the beds fold weakly as an ensemble and the stiff layers will fold independently (Figure 31G) .

Figure 33. Parameters for multilayer folding models. T is multilayer thickness, L: wavelength, L_p: preferred wavelength, h₁ and h₂: thickness of stiff and soft layers, respectively.

Assuming viscosity contrast, m ₂/m ₁ = 0.1, and h₂/h₁ = 1, a generous estimate for the outcrop, then m _n/m ₁ = 0.5. For the layers to be relatively independent, d ³ 0.5, the thickness of soft layers would need to be close to the wavelength of the folds. An increase in the viscosity contrast does not significantly affect the results. With no indication of sufficiently thick soft layers within the multilayers of the outcrop, the stiff layers must fold dependently. The theoretical similar multilayer of independent stiff layers is not a suitable model for the chevron-like folds.

Chevron-like folds also form in the interior of theoretical concentric or constrained multilayers having a small wavelength to multilayer thickness ratio. Johnson and Pfaff use a ratio of 0.06 as an example of a confined multilayer in which chevron-like folds will form. Pfaff refers to the required wavelength to thickness ratio as being much less than one.

For a 28 m wavelength as in Section VI, the multilayer thickness needs to be 466 m to obtain a wavelength to thickness ratio of 0.06. Assuming a multilayer thickness of even 60 to 100 m, with folds of wavelength 12 to 28 m, yields a wavelength to multilayer thickness ratio of 0.2 to 0.28. Even if this is sufficiently less than one, there is still the problem of no visible bounding concentric-like folds above and below the chevron-like folds to match a theoretical multilayer. The chevron-like folds as exposed do not have an equivalent theoretical multilayer in form.

Asymmetry

The properties of the layer interface determine whether drag or kink fold asymmetry develops for a given sense of layer-parallel shear. With nonlinear slip on the interface, the rate of slip during folding is a nonlinear function of contact stress, and the sense of asymmetry of monoclinal kink folds is produced. Linear slip, the rate of slip is a linear function of the contact stress, produces the sense of asymmetry of drag folds. Concentric and chevron folds are products of linear slip.

Given the sense of layer-parallel shear, orientation of the short limb distinguishes a monoclinal kink fold from a drag fold (Figure 34). The orientation of the short limb, or the vergence, cannot be used as an indicator for the sense of shear. Krabbendam and Leslie discuss folds in the Dalradian of southeast Scotland arguing there is widespread evidence of vergence opposite to the sense of shear. Likewise, Pfaff describes monoclinal kink folds in the Huasna Syncline, California, and the Wills Mountain Anticline, West Virginia, having vergence opposite to the sense of shear.

Figure 34. Opposite sense of asymmetry of monoclinal kink and drag folds. The sense of shear responsible for asymmetry of folds is indicated by arrows and implied by position in the larger fold. In right-lateral layer-parallel shear, the short limb faces left in a monoclinal kink fold, and faces right in a drag fold. Traces of axial planes (a) are shown for major and minor folds.

In top-to-the-right sense of layer-parallel shear, the short limb of a monoclinal kink fold faces left and layers are offset to the left, the short limb of a drag fold faces right and layers are offset to the right (Figure 34). With the short limbs facing south, the asymmetry of the chevron-like folds in the study outcrop is consistent with drag folds formed in a top-to-the-south sense of layer-parallel shear (Figure 34). This sense of shear is evident in the top-to-the-south thrust faults on long limbs of the chevron-like folds and in the duplex-like structure between Sections I and II. The sense of offset in the kink-like fold is opposite that of the chevron-like folds, but is consistent with top-to-the-south sense of layer-parallel shear (Figure 34).

The top-to-the-south sense of layer-parallel shear of the outcrop indicates that, with the folds on the south-dipping slope of the Oakland anticline, thrust sheet stresses override any simple shear local to the south limb of the anticline (Figure 35). A principal compressive stress oblique to layering and mean top-to-the-south layer–parallel shear is consistent with the geologic setting in a thrust sheet verging NNW.

The alternative to folds forming on a south-dipping slope is for the layers to pass through a trough at the north end of the outcrop. A syncline on the order of the Oakland anticline or even intermediate between it and the study area folds is not evident near the north end of the folds, or on maps of the areas to the east and west. This option also requires a locally developed companion anticline since past geologic mapping shows no area wide evidence of north-dipping beds immediately south of the outcrop. The syncline-anticline option would need more evidence from the field.

Kink-Like Fold

The asymmetry of the kink-like fold, short limb facing north, is consistent with the top-to-the-south layer-parallel shear evident in the outcrop. The localized tan siltstone and calcareous layers within the kink-like fold (Figure 20) are possible evidence of nonlinear slip, required for the formation of theoretical monoclinal kink folds. Calcareous layers in the outcrop tend to have boudinage, evidence of nonlinear material behavior. The soft tan siltstone may be an indication of diagenesis in response to a local increased resistance to slip. Limited exposure of the layers bordering the siltstone prevents examination of the interface beyond the fold.

Unit Thickness

In mechanical and theoretical models of folded multilayers, thickness of a folded unit is directly proportional to wavelength. The folding unit can consist of more than one layer if soft interbeds are thin allowing the stiff layers to fold as an ensemble. This applies to the outcrop where stiff layers do not fold independently. The outcrop multilayers can thus be modeled as stiff layers with bonded or free slip.

Bonded layers

For a multilayer of bonded stiff layers or an equivalent single layer, approximate analysis of folding of viscous material shows that the dominant wavelength, L_d, the wavelength that grows most rapidly, is related to the initial thickness of the stiff layer or bonded multilayer, T₀, by

where m is viscosity. This approximation is best for greater viscosity contrast. An approximate relation between the dominant wavelength and the preferred wavelength, L_p, (wavelength that attains the greatest amplitude) is

where S_x is the stretch (estimated as the ratio of observed wavelength to arclength). The stretch is about 0.6 and 0.65 in Sections I and VI respectively. In this analysis the preferred wavelength is taken to be equivalent to the observed wavelength.

Because Sections I and VI have relatively stiff and soft media, the media viscosity is an average. The layer to media viscosity ratio may be written as

where m _upper is viscosity of the upper medium and m _lower is viscosity of the lower medium. Figure 36 shows the range of layer to average media viscosity ratios for Section I and VI based on the viscosity contrast assumptions of the model outcrop multilayer (Figure 30).

Figure 36. Chart of layer to average media viscosity. In Section I, layer to lower media ratios of 2 to 10, and 0.3 to 1 for the upper media result in a layer to average media viscosity ratio of 0.5 to 1.8. In Section VI, layer to upper media ratios of 1 to 5, and 0.7 to 1 for the lower media, result in a layer to average media viscosity ratio of 0.8 to 1.7.

Applying the above equations to Section I with layer to average media viscosity ratio of 0.5 to 1.8 (Figure 36), yields initial multilayer thickness of 6 to 8 m (Figure 37). An initial thickness of 8 m allows for layer thickening of 25 percent to achieve the final thickness of 10 m (Figure 9). Within the constraints of the initial viscosity assumptions, an 8 m initial thickness corresponds to m_layer/m_{avg. media} of 0.5.

In Section VI, assuming m_layer/m_{lower media} is 1 to 5 and m_layer/m_{upper media} is 0.7 to 1, m_layer/m_{avg. media} is 0.8 to 1.7 (Figure 36). A layer to average media viscosity contrast of 0.8 to 1.7 yields initial thickness of 12 to 15 m (Figure 37) compared with a measured thickness of 20 m. An initial thickness of 15 m implies thickening of 33 percent in layer-parallel shortening. Within the constraints of the initial viscosity assumptions, the 15 m initial thickness corresponds to m_layer/m_{avg. media} of 0.8.

Stiff Layers with Free Slip

Equations for approximating the wavelength to thickness ratio incorporating the number of structural units are presented by Johnson and Pfaff. The equations work best for multilayers of four or more units. For a multilayer in rigid media composed of N structural layers having free slip, the ratio of dominant wavelength, L_d, to multilayer thickness, T, is

For multilayers in soft media, Johnson and Pfaff present a graphical solution for (L_d/T)_Soft as related to (L_d/T)_Rigid (Figure 38).

Table 4. Results of applying the model relating multilayer thickness, number of structural units, and viscosity contrast in a multilayer with free slip. For both Section I and VI, a model of two structural layers produces a viscosity contrast consistent with the range used in the bonded layer model.

The relations are applied to yield preferred wavelengths, L_p = L_d * S_x, similar to the observed wavelengths in Sections I and VI (Table 4) with a multilayer thickness approximated by total bed thickness plus the amplitude. Section I result for a multilayer thickness of 16 m shows two structural units are required to produce a layer to average media viscosity ratio of 0.7. Evidence in the outcrop may be the relatively thick brecciated shale layer adjoining the lenticular bed in fold 4. Section VI result for a multilayer of 26 m also requires two structural units though there is no comparable field evidence as in Section I. These results may just indicate the folds formed in layers that were more bonded than free slip since the model is best for four or more structural units.

Comparing results of the two models for the concentric-like fold of Section I, show consistency in thickness for an average media to layer viscosity ratio of 1.5. The ratio yields initial thickness of 8 m in the model of bonded layers and final thickness of 16 m in the free slip model, for a vertical stretch of 1.8. Considering the minimum measured shortening is 40 percent, or horizontal stretch of 0.6, the results are reasonable.

Section VI has a similar correspondence between the two models for an average media to layer viscosity ratio of 1.7. The initial thickness of 15 m and final multilayer thickness of 26 m is a vertical stretch of 1.7, slightly less than Section I and similar to the difference in horizontal stretch.

Outcrop Setting

The setting of the folds stratigraphically above the mudstone unit, Tum (Figure 6), provides a contrast in viscosity and possible detachment surface for the initiation of folding or faulting. The abrupt change in bedding orientation observed north of the outcrop at the lower mudstone contact indicates the lower turbidite unit may be in fault contact with the mudstone at this location. This places the outcrop near the base of a splay thrust within the main thrust sheet that extends north 1.7 km to the Cooper Creek Reservoir fault. If the chevron folds in the calcareous concretionary siltstone near the Cooper Creek Reservoir fault are related to the layers in the outcrop, then the possible splay fault at the base of the mudstone unit becomes more significant. The symmetry of the folds in Section I may be due to their position in this splay thrust.

There are three recognized channel fill deposits within the Tenmile Formation, at least one of which, the Rasler Creek tongue, has rounded, white calcareous concretions. The turbidites of the study area may be a relatively thin turbidite unit related to another channel fill in the Tenmile Formation or the channel conglomerate of the Bushnell Rock Formation located south of Woodruff Mountain. As a small unit, it would provide greater contrast in material properties with less thickness, enabling shorter wavelength folds to develop.

Previous work in the study area by Perttu and Benson describe the folds as having formed in beds considerably lithified and at shallow depth due to the continuity of bedding and constant thickness of sandstone beds, even in hinges. It does appear that folding in the study area was not syndepositional. Fluid escape structures and secondary mineralization are absent and faulting and boudinage occurred early in the deformation process. However, the style of folding does not necessitate formation at shallow depths.

The style and extent of deformation in the overburden depends on the distance to major thrust faults and the relative material properties of the overburden. The relative material properties determine how the overburden responds to layer-parallel shortening. Response in the overburden may be of longer wavelength with the appearance of less deformation, such as in the White Tail Ridge Formation. Ryberg’s constraint on folding due to the different style of deformation in the White Tail Ridge Formation may not be justified. A variation in the amplitude of folds does not exclude the folds from forming at the same time.

Extent of the overburden in the study area at the time of folding depends on the thickness of the turbidite units and the overlying White Tail Ridge Formation, and the relative position of the folds in the turbidites. The overburden does not include the Camas Valley Formation since it appears the principal period of deformation occurred prior to its deposition. The White Tail Ridge Formation crops out north of the study area and southwest of Woodruff Mountain (Figure 1). Intermediate to these locations, including the study area, the White Tail Ridge appears to have been uplifted and subsequently eroded. Uplift was likely associated with movement on the Cooper Creek Reservoir fault and possibly the Bonanza fault. Assuming the layers of the folds are intermediate within the turbidite unit, an estimate of the overburden at the time of folding is 700 to 800 m and a maximum of 1700 m (Figure 7). A reasonable compromise based on lateral variation in the subbasin is about 1300 m (Figure 4). The White Tail Ridge Formation makes up about 500 m of the total, and undifferentiated Umpqua Group turbidites and mudstone the remainder.

Constraining the beginning of folding is the lithification of sediments some time after deposition in early Eocene. The end of folding is constrained by the end of major N-S shortening. Assuming the shortening subsided coincident with the end of significant offset on the NNW verging Bonanza fault yields an upper time limit of 52 Ma, prior to deposition of the Camas Valley Formation in earliest middle Eocene.

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