INTRODUCTION

The purpose of this note is to emphasize the relative importance of antithetic faults in upthrusting and to show that knowledge of their behavior can result in more reasonable subsurface interpretations. The mechanics of upthrusting have received considerable attention since the early 1950s (see Prucha, et al., 1965, for excellent discussion, summary, and references). Faults antithetic to the synthetic upthrust faults have played an integral role in these mechanics; clay models show that antithetic faults are present in the upthrusting process, and stress analyses combined with shear-fracture criteria predict their presence. Being distinctly subordinate to the upthrusts in both magnitude and displacement, antithetic faults commonly have been ignored in outcrop, but they are significan for an overall understanding of upthrusting.

For antithetic faults (Dennis, 1967) in upthrusting, King's treatment of antithetic and synthetic faults is especially useful: "(The faults) ^hellip have moved ^hellip in opposition to the general uplift; such faults have been termed antithetic^hellip For the opposite kind, faults that have moved in harmony with the general uplift, the term synthetic has been used" (King, 1948, p. 112). This relation is demonstrated clearly in Figure 1.

The term "antithetic faults" as first used in the literature by H. Cloos in 1928 cannot be applied universally to antithetic faults related to upthrusting for two reasons: (1) the antithetic faults originally were specified as being nearly parallel normal faults, whereas in the present case the antithetic faults can be both normal and reverse; (2) in the original definition antithetic faults were described as dipping in a direction opposite to the dip of bedding, but this is not uniformly true in the present case.

MODEL AND ANALYTIC EVIDENCE

Numerous small faults antithetic to the main upthrust faults developed in the clay model of an upthrust block (Fig. 1); this experiment can be consistently reproduced. In an analytic study by Hafner (1951), potential fault surfaces have a position antithetic to the upthrusts (Fig. 2). In the clay the antithetic faults maintain an angle of about 60° to the upthrust faults as predicted by shear-fracture criteria; the same angle was selected by Hafner in the stress analysis.

As an upthrust curves and flattens progressively upward in response to the rotation of maximum principal compressive stress, so too does the orientation of the antithetic faults change along the cross-sectional trace of the upthrust (Figs. 1, 2). Depending on its position along the upthrust, an antithetic fault can have displacement of either normal or reverse sense.

The clay model and the analytic study both show graphically the relation of faults antithetic to upthrusts. No mechanical analogy between model and analysis is either intended or implied, as the clay exhibits some plastic deformation before shearing and the stress analysis assumes purely elastic behavior.

FIELD EVIDENCE

Surface

In Wyoming I have observed numerous antithetic faults which offset beds by amounts ranging from a fraction of an inch to about 20 ft. Low-angle reverse faults, including those of very small displacement, are antithetic to the synthetic upthrust at Rattlesnake Mountain in northwest Wyoming (Fig. 3). Figure 4 shows

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Click to view image in GIF format. Fig. 1. [Grey Scale] A. Clay-model experiment. B. Annotation showing faults antithetic to upthrusting. Antithetic faults are commonly sigmoidal, range from horizontal to low dip, and show very small displacement of both normal and reverse sense. Note rotation of maximum principal compressive stress (^sgr_I) and hence change in orientation of antithetic faults along upthrust zone from lower part to upper part of clay. Ellipses are deformed circles.

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Fig. 2. Stress field, due to superimposed vertical pressure of sinusoidal form applied to bottom of block, yields potential faults marked by A (= antithetic) which vary in attitude in such a way as always to be antithetic to upthrusts marked by S (= synthetic). Note that antithetic faults can be of either normal- or reverse-sense displacement. (From Prucha et al., 1965, after Hafner, 1951, pl. 1, D.)

Click to view image in GIF format. Fig. 3. [Grey Scale] Antithetic faults at Rattlesnake Mountain, northwest Wyoming. In all cases upthrust block is at right. A. View toward northwest of antithetic faults offsetting contact between Bighorn Dolomite (Ob-Ordovician) and Grove Creek Formation (^egrg-Cambrian) at west end of parking plaza for Buffalo Bill Dam, Highway 14-16-20, 6 mi west of Cody (Sec. 12, T52N, R103W). Note: faults vary somewhat in trend; fault surface marked by X has slickensides; blowup has eraser for scale. B. View toward northwest of antithetic fault offsetting massive unit in Madison Limestone (Mississippian) about 1 mi north of Mooncrest Ranch, 9.5 mi northwest of Highway 14-16-20, in Rattlesnake Cany n (T54N, R104W). Madison is involved in large, sharp monoclinal flexure bending down from right to left with almost vertical dips just off photograph on left.

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an antithetic reverse fault dipping about 45° south above Boysen Reservoir on the upthrust south flank of the Owl Creek Mountains.

In principle the attitude of the antithetic fault could be used to gain a rough idea of the curvature of the upthrust, if the value of the dihedral angle at the time it originated were known and if the angle remained reasonably constant after it was formed. For example, if the dihedral angle is assumed to be 60° at Boysen Reservoir, along the 45° south-dipping antithetic fault, a conjugate synthetic fault (upthrust), if developed, should dip 15° north. Even in this example, where there is no actual synthetic fault conjugate to the antithetic fault at the level of observation, knowledge of the attitude of the potential synthetic fault would help to determine the overall curvature of the upthrust zone, which in turn would aid in deciphering the frontal structure of the ra ge.

Subsurface

Figure 5a shows the interpretation of the Golden thrust by Berg (1962). Note that one fault (the third fault from the top in the Johnson 1 well) is a normal fault, whereas all the others are reverse faults--yet all of these faults are in essentially the same orientation. This interpretation carries the unlikely implication that the normal fault was the product of a deformation different in both stress orientation and time from that which created the reverse (upthrust) faults. A more reasonable interpretation is that the normal fault developed at the same time and by the same stresses that caused

Fig. 3. See caption on page 1948.

Click to view image in GIF format. Fig. 4. [Grey Scale] View toward west of antithetic fault with reverse movement offsetting color change (indicated by dashed line) in Bighorn Dolomite above Boysen Reservoir on south flank of Owl Creek Mountains (T40N, R6E), Wyoming. Displacement is estimated to be 20 ft. Owl Creek Mountains are at right.

Fig. 5. A. Interpretation of Golden thrust (Soda Lakes area, Jefferson County, Colorado) from Berg (1962). B. Interpretation showing third fault from top in Johnson 1 well as an antithetic fault. Dihedral angle of 60° is assumed. Section penetrated by well remains same; only attitude of fault is changed.

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the upthrusts, but that it is a very low-angle reverse fault antithetic to the upthrusts, as shown in Figure 5b.

Thus, realization of the role of antithetic faults in upthrusting can result in more credible subsurface interpretations. Antithetic faults should be taken into account in unraveling the structure of producing fields having complex upthrust flanks on which wells indicate many fault cuts.