Half-graben structures: Balanced models of extensional fault-bend folds RICHARD H. GROSHONG, JR. Department of Geology, University of Alabama, Tuscaloosa, Alabama 35487-1945 ABSTRACT The models proposed by Eyidogan and Jackson (1985) and Jackson (1987) for seismically active normal faults in Turkey have the same One common structural style in extensional regimes is a half general form. They found earthquakes on the horizontal to gently dipping graben bounded on one side by a master normal fault and on the other lower detachments, as well as on the ramps. A half graben is considered by side by a domain of beds dipping toward the master fault. This geome- Rosendahl (1987) to be the fundamental cross-sectional geometry in the try is modeled as being caused by a bend in the master fault. The East African rifts. The most basic geometries shown on seismic lines 206 hanging-wall beds dipping toward the master fault are bounded by and 212 of Rosendahl (1987) resemble those in Figure 1. axial surfaces formed as the hanging wall moves past the bend, result- There is more than one style of extensional faulting. A tilted—fault- ing in an extensional fault-bend fold. The footwall beds remain unde- block or domino style was proposed by Morton and Black (1975) for fault formed and unrotated. The major assumptions used in the derivation blocks in the Afar depression. In this style, both the faults and the fault are that the geometry is area balanced and that the axial surfaces in the blocks rotate during extension, a result that has been produced experimen- hanging wall have dips equal and opposite to the dip of the master tally by McClay and Ellis (1987) and Vendeville and others (1987). Listric fault above the bend. Important consequences of the model include a faults (Gibbs, 1983) and low-angle planar normal faults (Wernicke and relationship between master-fault dip above and below a bend and the Burchfiel, 1982) are other important styles that can be treated as generali- amount of hanging-wall dip. The horizontal width of the dipping beds zations of the model to be presented herein. in the hanging wall is twice the heave on the master fault above the In another type of geometric model, the geometry of a single hanging- bend. The asymmetry of the axial surfaces in the hanging wall requires wall bed is used to predict the shape of the underlying fault (Verrall, 1981; that the rotated beds be strained. Hanging-wall beds dipping toward Gibbs, 1983; Davison, 1986; White and others, 1986; Wheeler, 1987; the master fault are predicted for a fault bend wherein the dip de- Williams and Vann, 1987). Different fault shapes are predicted, depending creases downward. Hanging-wall beds dipping away from the master upon the assumptions of the model (Williams and Vann, 1987). The fault are predicted for a bend wherein the dip increases downward. geometry of a hanging-wall bed can be defined by the location and dip The model fits measurements taken from a published ramp-and-flat change at a sequence of hinges along the bed. Hinges in successive beds clay model by E. Cloos and is used to develop a balanced and restor- generate an axial surface. None of the models has explicitly used the able cross section of the Schell Creek fault, a Basin and Range axial-surface geometry in the hanging wall, which is, in fact, a critical structure in Nevada. aspect of the structure. The model developed herein relates the axial- surface geometry to the fault geometry and in this respect is analogous to INTRODUCTION the balanced kinematic models of reverse faults by Suppe (1983) and Jamison (1987). The model of Suppe (1983) also applies to normal faults, The basic balanced geometric and kinematic model for extensional but the axial-surface geometry is quite different from that in Figure 1 or the faulting and related bending of the half-graben style developed in this clay model of Cloos (1968) because the axial surfaces in the Suppe model paper is shown in Figure 1A. The essential elements are a flat-bottomed dip in the same direction as the master fault. The hanging-wall hinges are graben bounded by a normal fault on one side and by a continuous sequence of dipping beds on the other. The purpose of the model is to provide a set of mathematical relations that allow an interpreter to create a section that is balanced and restorable without going through a long proc- ess of trial and error. The relations developed herein are tested on a clay model for which the geometry is known and are used to develop a bal- anced cross section for the Schell Creek fault, a young Basin and Range structure in Nevada. In the extensional style treated herein, the footwall does not deform or rotate during deformation, and rotation in the hanging wall is related to a bend in the fault (Fig. 1). A clay model of this style was produced by Cloos (1968) by extending a clay cake above a horizontal detachment. Several authors have commented upon the resemblance between the clay c I model of Cloos and the younger structures in the Basin and Range prov- ince. Stewart (1971) may have been the first to note the similarity, and Anderson and others (1983) made a point of it. The review by Anderson and others (1983) shows several Basin and Range structures having a form Figure 1. Kinematic model of extension above a horizontal de- similar to that in Figure 1; Diamond Valley seems to be the most similar. tachment, showing the result of increasing displacement. Geological Society of America Bulletin, v. 101, p. 96-105, 11 figs., 1 table, January 1989. 96 Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/101/1/96/3380507/i0016-7606-101-1-96.pdf by guest on 30 September 2021 HALF-GRABEN STRUCTURES 97 directly related to bends in the fault, and so they are "fault-bend folds" in therefore, the terminology of Suppe (1983). A balanced cross section is defined as one in which volume remains Area AIJE = (d sin (180 - 0) = id sin 0. (2) constant during deformation (Dahlstrom, 1969). The model developed herein is area balanced, which means that the cross-sectional area is con- Equations 1 and 2 are identical, showing that the assumed geometry is area stant. It is based on the geometry of a planar normal fault that joins a balanced. The total displacement on the flat to the right of H2 is 2d = W, planar detachment at depth (Fig. 1A). As a result of extension, a half the standard width of the antithetic dip domain. graben develops, bounded on one side by the master fault and on the other The relationship between the antithetic dip, a, and the dip of the fault by a zone of dipping beds, causing the total structure to be asymmetric. is found by using the law of sines on triangle IJE. The side opposite a is I "Reverse drag" (Hamblin, 1965) is a commonly used term for hanging- = d/cos 0, angle IJE = 0 - a, and the side opposite, IE, = 2d; therefore, wall beds that dip toward a normal fault. The dip is not related to the d _ 2d mechanics of "drag" on the fault but rather is interpreted as the conse- quence of rotation above a bent or curved fault; consequently, this term sino cos0 sin (0 - a) will not be used. Hanging-wall dips opposite in direction to that of the Using the relationship sin (x - y) = sin x cos y - cos x sin y, the previous master fault are herein termed "antithetic dips," and dips in the same expression can be reduced to direction as the master fault are termed "synthetic dips." Regions of uni- form dip between axial surfaces or faults are referred to as "dip domains" tana = (tan 0)/3. (3) (Groshong and Usdansky, 1988). As displacement increases on the master fault (Figs. IB and 1C), the flat bottom of the graben gradually disappears The antithetic dip is related to the dip of the master-fault ramp by equation as it drops down and shifts laterally into the domain of antithetic dip. The 3, plotted in Figure 3. The width of the domain is W = 2d, or if h, rather antithetic dip domain is bounded by two parallel axial surfaces that dip at than d, is known (Fig. 2), defining a length D equal to 2d, an angle equal and opposite to that of the master fault. First, it will be 2h demonstrated that the geometry of Figure 1 is area balanced. The model D = W = . (4) will then be extended by considering a finite initial width at the base of the tan 0 graben and by deriving the relationships for a dipping lower detachment. The model is quantitatively tested against the clay model of Cloos (1968) WIDE ZONE OF ANTITHETIC DIP and is then applied to the Schell Creek fault as an example of the method. The antithetic-dip domain may be wider than the standard-width domain from the first instant of displacement. This will be seen in the clay STANDARD-WIDTH DOMAIN OF ANTITHETIC DIP model and is presumably related to the difficulty of bending a thick single layer and to the extension that occurred prior to formation of the through- going master fault. This is treated as an initial offset, W , between axial What is herein termed the "standard-width domain of antithetic dip" 0 surfaces HI and H2 (Fig. 4A). After displacement on the master fault, the has a width W equal to the displacement on the lower detachment C-G as antithetic dip, a', will be less than the dip within the standard-width zone shown in Figure 2 for a horizontal lower detachment.