Interaction Between Normal Faults and Fractures and Fault Scarp Morphology
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GEOPHYSICAL RESEARCH LETTERS, VOL. 28, NO. 19, PAGES 3777-3780, OCTOBER 1, 2001 Interaction between normal faults and fractures and fault scarp morphology George E. Hilley1,JRam´on Arrowsmith, and Lee Amoroso Department of Geological Sciences, Arizona State University, Tempe, Arizo na Abstract. Fault slip and geomorphic surface processes cre- opening along the fractures; the presence of fractures in the ate and modify bedrock normal fault scarps. Our field stud- near surface results in larger total offset for a constant stress iesand numerical modelsshow that mechanical interaction drop than a fault in isolation. between near-surface fracturesand active faultsmay dimin- To illustrate the mechanical analysis, we studied active ish scarp slopes and broaden deformation near the surface. fault scarps along low slip rate graben-bounding faults of In our models, increasing fracture density and depth reduces the southern Colorado Plateau that expose pervasively frac- and complicates the scarp’s topographic expression. Frac- tured rocks of the Permian Kaibab Formation and Triassic ture depth and density, and orientation of the structures Moenkopi Formation. Our field observations show irregu- control the location and magnitude of zonesof positive and lar topography resulting from distributed deformation along negative shear displacements along the fractures. Our field near-surface fractures. Thus, irregular fault scarp morpholo- studies of the interaction of active graben bounding normal gies do not require surface transport processes to redis- faultsand fracturesin Northern Arizona illustrate the me- tribute material and instead may result from near-surface chanical analysis. Reduction in scarp slopes and broadening distributed deformation. of the deformation field may cause incorrect interpretations of shallow bedrock scarp morphologies as old, rather than Fractures in the vicinity of a slipping as the result of slip along fractures around the fault. fault Introduction We constructed a boundary element model to compute slip and opening along fractures in the vicinity of a slipping Numerous detailed studies of seismically generated fault fault. The crust was idealized as a homogeneous, linear scarps have resulted in models that determine age of fault- elastic half-space subject to plane-strain [e.g.; Jaeger and ing events, rates of movement along faults, and recurrence Cook, 1969; Segall and Pollard, 1980; Segall, 1984]. Faults time between earthquakesfrom scarptopographic form [ e.g.; and fractureswere modeled by introducing a set of confined Nash, 1980; Hanks et al., 1984; Bucknam and Anderson, frictionless displacement discontinuities in the crust [Segall 1979; Avouac, 1993; Arrowsmith et al., 1996, 1999]. These and Pollard, 1980; Crouch and Starfield, 1983]. We allow studies were conducted on regolith mantled scarps; however, the fault to slip in response to a shear stress drop along scarps within fractured bedrock are common throughout the itsdowndip length [ e.g.; Willemse, 1997; Crider and Pol- world and occur at a variety of scales [e.g.; Stewart and Han- lard, 1998], which results in the loading of the surrounding cock, 1990; Strecker et al., 1990; Cannon and B¨urgmann, medium and fractures. The fractures then slip solely in re- 1999; Villemin et al., 1994]. In such areas, an additional sponse to this stress transfer. By neglecting the effect of set of complex geomorphic and tectonic processes are intro- remote stresses along the fractures, we implicitly assume duced [Altunel and Hancock, 1993]. For example, extension that induced stresses near the fault are large compared to may be accommodated by both slip along normal faults and remote stresses. Although friction, lithostatic loading, and opening of fissures in the area around the fault. In these the associated Poisson stresses are neglected in our simple cases, shallow topographic slopes around fault scarps may model, previouswork hasshown that first-order featuresof be produced and maintained by near-surface structural com- the stress and deformation fields are captured by this ap- plexity. proach [Segall and Pollard, 1980; Willemse, 1997; Thomas, We used mechanical models and field observations to in- 1993]. vestigate how slip along fractures near the earth’s surface leads to distributed surficial deformation and irregular scarp Models of Interacting Faults and morphologies. We used mechanical models to explore how Fractures surface displacements changed with fracture depth, density, dip, and fault dip. Increasing fracture depth and density In our models, we varied fault dip (β), fracture dip (γ), cause scarp morphology to become more irregular, as in- fracture length (λ), and fracture density (1/ξ). The hori- teraction between fracturesand the fault becomesmore im- zontal position, fracture length, and fracture density were portant. Fracture orientation controls the sense of shear and normalized by the fault length (L). Therefore, surface dis- placement at a point is controlled by six variables: stress 1 Now at Institut f¨ur Geowissenschaften, Universit¨at Potsdam, drop (ts), normalized position (x/L), β, normalized fracture Potsdam, Germany length (λ/L), γ, and normalized fracture density (L/ξ). We Copyright 2001 by the American Geophysical Union. considered a normal fault undergoing an uniform 4.33 MPa stress drop along its length. Elastic parameters typical of Paper number 2001GL012876. rock (i.e., shear modulus of 30 GPa and Poisson’s ratio of 0094-8276/01/2001GL012876$05.00 0.25) were used. 3777 3778 HILLEY ET AL.: INTERACTION BETWEEN NORMAL FAULTS AND FRACTURES (a) (b) (c) -4 4 x 10 0 -4 -8 no fractures λ -12 /L = 0.025 λ/L = 0.05 -16 (d) (e) (f) Elevation (H/L) -5 4 x 10 0 -4 -8 -12 -0.08 0 0.08 -0.08 0 0.08 -0.08 0 0.08 Distance (x/L) Figure 1. Scarp profiles produced by a stress drop along a 60◦ dipping normal fault. (a)–(c) Surface displacements for a fault that reaches the surface. (d)–(f) Displacements for a fault with the upper tip buried 0.1L below the surface. (a) and (d), (b) and (e), and (c) and (f) Displacements resulting from 60◦,90◦, and 120◦ dipping fractures, respectively. The heaviest line shows the case in which fractures are not present, and progressively lighter lines show the case of deeper fractures (0.025L and 0.05L). Fracture density is fixed to 0.01L. H is elevation. Cartoon depicts general fracture and fault geometry relative to surface. We first examined the effect of fracture length on surface Finally, the effect of normal fault dip wasinvestigated displacements surrounding the fault scarp. Progressive in- (Figure 2b and d). In all cases, fractures were vertical, ex- crease in fracture length relative to fault length increased tended to a depth of 0.05L, and had a density of L/ξ =0.4. mechanical interaction of fractures, modifying the surface The fault dip did not greatly influence the sense of motion displacement field (Figure 1). Long fractures slipped more along the fractures; however, the offset magnitude along the than short fractures, causing scarp morphology to be jagged and slopes to decrease. We found that fracture dip also has an important influence on scarp morphology. In cases where (a) (b) -4 the fault reached the surface (Figure 1a–c), fractures in the x 10-4 x 10 ◦ 0 footwall dipping at 60 slipped only moderately, while those 0 in the hangingwall showed large displacement reverse mo- ◦ -2 tion. With a 90 dip, both postive and negative shear dis- β = 45o -2 no fractures β o placementsresulted from movement along the fault. Where L/ξ = 0.1 -4 = 60 o the fault did not reach the surface (Figure 1d–f), a stepped L/ξ = 0.05 β = 90 -4 L/ξ = 0.01 -6 flexure resulting from movement along the underlying fault wasproduced. Fracturesdipping parallel to the fault caused reverse shear in the hangingwall and normal shear in the footwall (Figure 1d). When fracturesdipped into the fault, Elevation (H/L) (c) (d) -5 reverse motion along the fractures was often resolved. x 10 Figure 2a and 2c show the effects of fracture density on 0 surface deformation. Figure 2a demonstrates surface defor- -4 mation resulting from the interaction of a 60◦ dipping fault that reachesthe surface with 90 ◦ dipping fracturesextend- -8 ing to a depth of 0.05L. Thisset of modelsshowsthat me- -12 chanical interaction between fracturesincreaseswith frac- -0.08 0 0.08 -0.08 0 0.08 ture density, and that complex surface displacement distri- butions result from increased fracture density. When the Distance (x/L) fault did not reach the surface (Figure 2c; upper fault tip is buried 0.1L), increased fracture density magnified the steps Figure 2. Scarp profiles produced by variations in fracture den- sity and fault geometry. (a) and (c) Effects of changes in fracture of the monoclinal flexure. With higher fracture density, to- density for surface rupturing and blind faults, respectively. (b) tal relief across the structure increased while slip on each and (d) Effects of changes in fault dip for surface rupturing and fracture decreased simultaneously. blind faults, respectively. HILLEY ET AL.: INTERACTION BETWEEN NORMAL FAULTS AND FRACTURES 3779 (a) Colorado Plateau TRm TR Tension m P fissure Qya k Arrowhead Flagstaff Graben Lineament Scarp 3 Basin and Range Qyf 2 Bedding strike and dip 5 Arizona Monocline Qbb Fault, ball on 3 A' downthrown side 3 Fault, approximate 20 B' location Qmb Pk 8 Fault, concealed 6 B 3 TRm Q , younger alluvium yc Pk Qya, young alluvium A Alluvial fans Qyf, mid alluvium Qyo, oldest alluvium P 2 Qbb, mid Pleistocene basalt ? k 9 TRm 8 Qmb, lower Pleistocene basalt N ? TRm TR m, Triassic Moenkopi Formation 500 Meters Qyo ? Pk, Permian Kaibab Formation Qyc AA' Qyo 25 2 (b) Fracture Orientations 5x vertical exag. 0 BB' 25 20% 10 10 20 Elevation (m) Elevation n = 169 5x vertical exag. 0 125 Meters Figure 3. (a) Geologic map and cross-sections of Arrowhead graben illustrating relationships among faults, fractures, and monoclines exemplifying aspects of the preceding mechanical analysis.