12
Morphologic Dating and Modeling Degradation of Fault Scarps

DAVID B.NASH

University of Cincinnati

ABSTRACT

The pattern of degradation observed on some scarps formed by normal, range-front faulting of alluvial fan surfaces may be accurately modeled, and, when properly calibrated, these models provide a means for determining the ages of some scarps (morphologic dating). Two different degradation patterns are observed: some scarps recline, becoming more rounded with time, whereas others retreat with little or no decrease in gradient. Scarps that recline are generally covered with soil or loosened debris and are termed transport-limited because more loosened debris is produced than the transport processes are capable of removing. Retreating scarps are generally stripped bare of debris and are termed loosening-limited because debris is carried away as rapidly as it is loosened from the surface. These two different modes of degradation require two fundamentally different models.

Morphologic dating matches the observed morphology of a degraded scarp with that predicted by the appropriate calibrated model. The accuracy of the age calculated for a fault scarp is dependent on the accuracy of the calibration and the accuracy of the initial morphology assumed for the scarp prior to degradation (potentially complex for fault scarps). Despite some limitations, morphologic dating provides a means for dating fault scarps and other scarps resulting from active tectonism.

INTRODUCTION

Most geologists have their first, and generally last, exposure to the subject of hillslope degradation in a discussion of landscape evolution during their introductory physical geology course. In that discussion, it is questioned whether hillslopes slowly progress through a series of evolutionary forms as they degrade as suggested by Davis (1899) or fairly rapidly reach an equilibrium form dependent on underlying structure as suggested by Hack (1960). It is further questioned, if hillslopes do in fact evolve slowly with time, what is that pattern of evolution? Do hillslopes retreat retaining a steep gradient as suggested by Bryan (1922) and King (1953) or progressively decrease in gradient, becoming more rounded as suggested by Davis (1899) and, to some extent, by Penck (1953)? Unfortunately, these diametrically opposed theories of hillslope degradation and the often acrimonious debates over the relative merits of each have convinced many geologists that little is known about the degradation of hillslopes.

Within the past 15 years, great progress has been made in our understanding of hillslopes. Much of this progress resulted from careful study of the degradation



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Active Tectonics: Studies in Geophysics 12 Morphologic Dating and Modeling Degradation of Fault Scarps DAVID B.NASH University of Cincinnati ABSTRACT The pattern of degradation observed on some scarps formed by normal, range-front faulting of alluvial fan surfaces may be accurately modeled, and, when properly calibrated, these models provide a means for determining the ages of some scarps (morphologic dating). Two different degradation patterns are observed: some scarps recline, becoming more rounded with time, whereas others retreat with little or no decrease in gradient. Scarps that recline are generally covered with soil or loosened debris and are termed transport-limited because more loosened debris is produced than the transport processes are capable of removing. Retreating scarps are generally stripped bare of debris and are termed loosening-limited because debris is carried away as rapidly as it is loosened from the surface. These two different modes of degradation require two fundamentally different models. Morphologic dating matches the observed morphology of a degraded scarp with that predicted by the appropriate calibrated model. The accuracy of the age calculated for a fault scarp is dependent on the accuracy of the calibration and the accuracy of the initial morphology assumed for the scarp prior to degradation (potentially complex for fault scarps). Despite some limitations, morphologic dating provides a means for dating fault scarps and other scarps resulting from active tectonism. INTRODUCTION Most geologists have their first, and generally last, exposure to the subject of hillslope degradation in a discussion of landscape evolution during their introductory physical geology course. In that discussion, it is questioned whether hillslopes slowly progress through a series of evolutionary forms as they degrade as suggested by Davis (1899) or fairly rapidly reach an equilibrium form dependent on underlying structure as suggested by Hack (1960). It is further questioned, if hillslopes do in fact evolve slowly with time, what is that pattern of evolution? Do hillslopes retreat retaining a steep gradient as suggested by Bryan (1922) and King (1953) or progressively decrease in gradient, becoming more rounded as suggested by Davis (1899) and, to some extent, by Penck (1953)? Unfortunately, these diametrically opposed theories of hillslope degradation and the often acrimonious debates over the relative merits of each have convinced many geologists that little is known about the degradation of hillslopes. Within the past 15 years, great progress has been made in our understanding of hillslopes. Much of this progress resulted from careful study of the degradation

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Active Tectonics: Studies in Geophysics processes active on hillslopes summarized in several excellent books, including those by Brunsden (1971), Carson and Kirkby (1972), and Young (1972), as well as by the rediscovery and popularization by Schumm and Mosley (1973) of several classic but generally forgotten works. Enough is now known about these processes that analytical modeling of the degradation of hillslopes has become possible. Two of these models have been tested and found to be sufficiently accurate for some hillslopes to be dated (morphologic dating) by matching their observed profile with that predicted by the properly calibrated model. The hillslopes that will be modeled here are assumed to be closed systems, isolated from the surrounding landscape. Although this assumption is not valid for all hillslopes, it is appropriate for some. Scarps bounded by horizontal or gently inclined bases and crests, such as fault scarps produced by normal faulting, of alluvial fans, abandoned fluvial cutbanks (terrace scarps), and abandoned wave-cut bluffs, on which debris derived from the scarp face accumulates at its base (i.e., debris is not removed by fluvial or wave undercutting) and where degradation is by soil creep or by the raveling of sand and gravel may be modeled as a closed system. OBSERVED PATTERNS OF HILLSLOPE DEGRADATION The degradation of most natural, vegetated hillslopes is extremely slow and difficult to observe directly, and the pattern of degradation observed on more rapidly eroding, man-made slopes, such as slag heaps and tailing piles, is not necessarily the same as on natural hillslopes. The degradation of natural hillslopes, however, may be observed indirectly by comparing the morphology of a series of different aged hillslopes assumed to have had the same initial morphology. This approach was probably first used by Savigear (1952), who studied differences in morphology among a series of coastal cliffs isolated from wave undercutting by the progressive lateral growth of a protective beach. In similar studies, Welch (1970) documented the change in scarp morphology with time from observations of active and abandoned wave-cut bluffs along the north shore of Lake Erie, and Brunsden and Kesel (1973) presented differences between active and abandoned cut-banks along the Mississippi River. Nash (1980b) compared the morphology of wave-cut bluffs abandoned 10,500 yr before present (BP) and 4000 yr BP along the shore of Lake Michigan with that of nearby, actively forming wave-cut bluffs underlain by the same material (Figure 12.1). A pattern of degradation similar to that observed by Savigear (1952), Welch (1970), and FIGURE 12.1 Profiles of modern, wave-cut bluffs similar to bluffs abandoned 4000 and 10,500 yr BP along the shores of Lake Michigan. All bluffs are underlain by a similar sandy morainal material. Brunsden and Kesel (1973) is observed on the Lake Michigan bluffs—modern bluffs have a nearly horizontal crest and base separated from a straight, steeply inclined midsection by a sharp crestal convexity and basal concavity (Figure 12.2a). The midsection gradient of the 4000-yr-old bluff has decreased slightly from that of the modern bluff, and the crestal convexity and basal concavity of the profile have become more rounded. This pattern of degradation is more pronounced on the 10,500-yr-old bluffs. These hillslopes appear to have reclined with age, but did they also retreat? Some fault scarps near the town of West Yellowstone in southwest Montana apparently did not retreat. In 1959 the Yellowstone earthquake occurred close to the town of West Yellowstone, Montana, forming numerous scarps in the overlying obsidian sand and gravel deposit. These scarps have a morphology similar to the

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Active Tectonics: Studies in Geophysics FIGURE 12.2 a, Profile of a scarp with a simple initial morphology: a straight base and crest inclined at the same angle, θ, and a straight midsection at the angle of repose of the underlying debris, α, the initial excess midsection slope angle is defined as the angle by which the initial midsection exceeds θ. The scarp offset, H, is the perpendicular distance separating the parallel crest and base, b, With time, the curvature of the crestal convexity and basal concavity decrease on transport-limited hillslopes. The degraded excess midsection slope angle, β, is defined as the angle by which the degraded midsection exceeds θ. The initial angle of the crest and base, θ, and H may be determined by analysis of the profile beyond the limits of the basal concavity and crestal convexity. From Nash (1984), reprinted from the Bulletin of the Geological Society of America, with permission. modern wave-cut bluffs along the shores of Lake Michigan—straight midsections separated from gently inclined crests and bases by sharp crestal convexities and basal concavities (Figure 12.2a). Many of the 1959 scarps are superimposed on much older scarps produced by prehistoric earthquakes. These older scarps have a more rounded crestal convexity and basal concavity and lower midsection gradient than the modern scarps, indicating a pattern of degradation similar to that of the abandoned wave-cut bluffs along the shores of Lake Michigan (Figure 12.1). The 1959 scarps are generally located near the center of the midsection of the prehistoric scarp (Figure 12.3), suggesting that little retreat of the older scarp has occurred. Scarp recline and rounding without significant retreat is fundamentally different from the pattern of scarp degradation reported by King (1953), Hamblin (1976), and Anderson (1977). King (1953) observed that the maximum gradient on hillslopes underlain by the same material is frequently the same on large, and presumably young, as on small, and presumably old, hillslopes and suggested that this demonstrates that once a stable angle has been reached, hillslopes no longer recline but retreat parallel to themselves. He further observed that the Drakensberg escarpment in Natal, South Africa, has “retreated back over 100 miles since the late Mesozoic and is still wall-like and over 4000 feet high.” Hamblin (1976) and Anderson (1977) found evidence for scarp retreat in their investigations of a flight of faceted spurs above the Wasatch Fault near Salt Lake City, Utah. They suggested that the accordance in the elevations of these facets (Figure 12.4) indicates that the facets are remnants of once continuous scarps formed by past movements of the Wasatch Fault and concluded that the scarps have retreated significantly [Hamblin (1976) suggested that modest recline of the scarp face also occurred]. On a much smaller scale, a similar pattern of nearly parallel retreat may be observed on rapidly degrading, natural and man-made scarps underlain by cohesionless sands and gravels. Oversteepened walls of borrow pits in the obsidian sand and gravel deposit overlying the West Yellowstone area are observed to retreat back at a high angle, progressively burying their base with loosened debris (Figure 12.5). Similarly, scarps produced by normal faulting of the same material during the 1959 earthquake were observed by Wallace (1980) to have retreated, progressively burying their base with an accumulation of debris loosened from the scarp face. Following the usage of Wallace (1980), these retreating, oversteepened scarp faces underlain by cohesionless material will be referred to as free faces. It is no wonder then that a controversy exists as to whether degrading hillslopes retreat or recline; there can be little doubt that both patterns of degradation may be observed. Why do some hillslopes recline with progressive rounding of their crestal convexity and basal concavity while others are apparently able to retreat considerable distances with little change in the morphology of their profiles? LOOSENING-LIMITED AND TRANSPORT-LIMITED HILLSLOPES In his classic study of the geology of the Henry Mountains, Gilbert (1877) offered an explanation for why the summit of Mount Ellen is gently rounded while the summit of nearby Mount Holmes is precipitously steep and jagged despite the fact each is underlain by similar trachyte dikes. He observed that the summit of Mount Ellen is sufficiently high to be vegetated while the 2500

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Active Tectonics: Studies in Geophysics feet lower summit of Mount Holmes is too hot and dry to support continuous vegetation and thus has bare rock slopes. He further observed: …vegetation favors the disintegration of rocks and retards the transportation of disintegrated material. Where vegetation is profuse there is always an excess of material awaiting transportation, and the limit to the rate of erosion comes to be merely the limit to the rate of transportation. And since the diversity of rock texture, such as hardness and softness, affect only the rate of disintegration (weathering and corraision) and not rate of transportation, these diversities do not affect the rate of erosion in regions of profuse vegetation and do not produce corresponding diversities of form. On the other hand, where vegetation is scant or absent, transportation and corraision are favored while weathering is retarded. There is no accumulation of disintegrated material. The rate of erosion is limited by the rate of weathering, and that varies with the diversity of rock texture. The soft are eaten away faster than the hard; and the structure is embodied in the topographic forms. This basic dichotomy between bare and debris mantled hillslopes has been largely overlooked by subsequent hillslope researchers until it was noted by Schumm (1956) in his study of the degradation of badland slopes. Schumm observed that creep-dominated slopes, those with a continuous cover of loosened debris, recline and become more rounded with time, whereas wash-dominated hillslopes, those on which wash processes sweep the surface bare of loosened debris, retreat with time. More recently Carson and Kirkby (1972) termed these two fundamentally different hillslope types transport-limited (hillslopes on which more loosened debris is available for removal than the transport processes are capable of removing) and weathering-limited (hillslopes on which the transport processes remove all debris as rapidly as it is loosened). Debris need not necessarily be loosened from the hillslope surface by weathering; sand and gravel are detached from the surface of the free face (Figure 12.5) by evaporation of pore water and by raveling. Because these are not weathering processes, the term loosening-limited will be used here instead of weathering-limited for hillslopes on which debris is removed as rapidly as it is loosened from the slope surface. Both loosening-limited and transport-limited hillslopes can occur in all climates; transport-limited hillslopes, however, are more common on unconsolidated or weakly consolidated materials in humid-temperate climates with continuous vegetative cover, whereas loosening-limited hillslopes are more common on FIGURE 12.3 The scarps formed during the 1959 West Yellowstone earthquake (indicated by the arrow) are generally found superimposed on the center of much older scarps indicating that little or no retreat of the older scarps has occurred (photo by J.R.Stacey, U.S. Geological Survey).

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Active Tectonics: Studies in Geophysics FIGURE 12.4 Flights of faceted spurs along the western front of the Wasatch Range. These facets are thought by Hamblin (1976) and Anderson (1977) to have formed by retreat of scarps produced by multiple movements of the Wasatch Fault (photo courtesy of W.K.Hamblin, Brigham Young University). weathering-resistant rocks and in arid to semiarid regions with insufficient moisture to support a continuous vegetative cover. As will be discussed, loosening-limited hillslopes degrade by retreat, whereas transport-limited hillslopes degrade by recline and rounding. It is interesting to note that the advocates of parallel retreat, such as Bryan (1922) and King (1953), worked primarily in arid and semiarid regions, whereas the most notable proponent of hillslope recline, Davis (1899), worked primarily in temperate-humid regions. MODELING THE DEGRADATION OF TRANSPORT-LIMITED HILLSLOPES The following model for describing the degradation of transport-limited hillslopes is not new; it has been proposed by many researchers including Culling (1960), Souchez (1964), Hirano (1968, 1975), and Pollack (1968). The model, sometimes termed the diffusion model of hillslope degradation, is based on the assumption that the volumetric rate at which debris moves downslope at a particular point on a hillslope profile is proportional to the gradient of the profile at that point. Although several transport mechanisms have been proposed for such debris transport, the most probable is soil creep (Culling 1963, 1965; Nash, 1980a). Debris Transport by Creep The slow, steady downslope creep of material on transport-limited hillslopes is thought by many to result from alternate expansion and contraction within the de-

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Active Tectonics: Studies in Geophysics FIGURE 12.5 Walls of borrow pit in the obsidian sand and gravel deposit overlying the West Yellowstone Basin, Montana. The loosening-limited free face of the wall is observed to retreat, progressively burying its base with debris. From Nash (1984), reprinted from the Bulletin of the Geological Society of America, with permission. bris mantle. This expansion and contraction may be the result of heating and cooling (Davison, 1888) or hydration and dehydration (Fleming, 1972) or freezing and thawing of pore water. If expansion occurs by heaving perpendicular to the slope surface and contraction by vertical dropping of the surface, a net downslope displacement of the debris cover results, which is proportional to the sine of the slope angle of the surface (Figure 12.6a). If the amount of expansion and contraction of the debris mantle is uniform throughout its thickness, the upward and downward displacement of debris decreases linearly with depth, and, therefore, the downslope movement of debris resulting from a single expansion and contraction episode will also decrease linearly with depth (Figure 12.6b). The depth to which an expansion and contraction cycle penetrates into the debris mantle, however, is highly variable. A light rain or light freeze may penetrate a few centimeters beneath the surface, but it will take the rarer, heavier rain or severe freeze to penetrate to greater depths. Thus we would expect the actual displacement profile within the debris mantle to reflect both the linear decrease in displacement with depth resulting from a single expansion- FIGURE 12.6 a, Downslope creep caused by expansion of the debris mantle perpendicular to the surface followed by vertical contraction. Alternate heating and cooling, freezing and thawing, or wetting and drying are thought to produce such creep, b, For a single episode of expansion and contraction, the displacement of soil downslope decreases linearly with depth (no displacement will occur beyond the depth of penetration of the expansion-contraction cycle). c, The frequency with which an expansion-contraction episode penetrates into the surface decreases rapidly with depth. When the linear downslope displacement of debris resulting from a single expansion-contraction episode is combined with the decreasing frequency of occurrence of penetration with depth, it produces a concave-downslope displacement profile after many episodes. This displacement profile has been observed in several field studies.

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Active Tectonics: Studies in Geophysics contraction episode and the decreasing frequency of penetration at greater depths to produce a concave-downslope displacement profile (Figure 12.6c). This prediction is verified by several field studies of creep displacement summarized by Carson and Kirkby (1972). If the depth of penetration is uniform over the hillslope surface during a single expansion-contraction event then the volumetric, downslope flux of debris, q, per unit length of contour at a point on a transport-limited hillslope will be proportional to the sine of the slope angle (ψ) at that point, or (12.1) where c is the coefficient of proportionality. Debris will seldom remain on slopes steeper than 30°, so little error is introduced by assuming that q at a point on a transport-limited hillslope is proportional to the tangent of the local slope angle, or (12.2) in two spatial dimensions, where x is the horizontal and y is the vertical coordinate of the point. Field studies by Schumm (1967) and others verify that the observed creep rate may be described by Eq. (12.2). Downslope Conservation of the Debris Flux A hillslope profile may be thought of as a series of linear segments each receiving debris at its upslope end and discharging debris at its downslope end. If more debris enters a segment than leaves, conservation of mass requires that the debris within the segment must increase, resulting in an increase in the elevation of the segment (Figure 12.7a). Conversely, if more debris leaves than enters a segment, its elevation must decrease (Figure 12.7b). Thus the downslope change in the debris flux, q, determines the change in elevation at a point on a hillslope. Debris will accumulate and the elevation will increase where q decreases downslope, such as at basal concavities. Debris will be depleted and the elevation will decrease where q increases downslope. In spatial dimension, x, the change in elevation, y, with time, t, on a hillslope profile is therefore equal to the downslope divergence of the debris flux, or (12.3) This equation predicts the pattern of degradation shown in Figure 12.8; the gradient of the midsection decreases and the curvatures of the basal concavity and crestal convexity decrease (become more rounded) with time. Equation (12.3) is not appropriate for loosening-lim FIGURE 12.7 Conservation of debris on a transport-limited hillslope, a, If the debris flux entering a hillslope segment, qu, exceeds the flux leaving q1, there will be a net accumulation of debris within the segment and its elevation will increase with time. b, If ql exceeds qu, there will be a net depletion of debris within the segment and its elevation will decrease with time. ited slopes because the transportational processes are capable of sweeping the slope surface completely clear of debris, nor is it appropriate for all transport-limited hillslopes. Although Eq. (12.2) is probably appropriate for describing raindrop-induced, surficial creep on bare sand (e.g., Savat and DePloey, 1968), it is probably not appropriate for wash erosion on transport-limited hillslopes (such erosion is rarely effective on continuously vegetated hillslopes underlain by cohesionless sands and gravels). Nash (1980b, 1984) demonstrated that Eq. (12.3) fits the pattern of degradation observed on abandoned wave-cut bluffs along the shore of Lake Michigan (Figure 12.1) and on fluvial terrace scarps along the Madison River near West Yellowstone (Figure 12.9). Hanks et al. (1984) fit the pattern of degradation observed on Lake Bonneville scarps and a fault scarps near Drum Mountain, Utah, abandoned sea cliffs along the Califor-

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Active Tectonics: Studies in Geophysics FIGURE 12.8 Model for the degradation of a transport-limited hillslope. The crestal convexity and basal concavity become more rounded and the midsection reclines. nia coast near Santa Cruz, and fault scarps near the Fish Spring Range, the Oquirrh Mountains, and the Sheeprock Mountains, Utah, with the pattern of degradation predicted by Eq. (12.3). Hanks and Wallace (in press) demonstrate that the degradation pattern observed on shoreline scarps formed by Lake Lahontan in western Nevada may be closely modeled with Eq. (12.3). The model also predicts that the degradation of a transport-limited scarp is not accompanied by retreat, which would explain why the scarps formed during the 1959 West Yellowstone earthquake are generally located near the center of much older scarps formed by previous offsets of the same fault (Figure 12.3). The model also successfully predicts the inverse relationship between scarp height and the slope angle documented by Bucknam and Anderson (1979) in a study of a degraded fault scarp near Drum Mountain, Utah (Nash, 1980b; Colman and Watson, 1983; Hanks et al., 1984; Hanks and Wallace, in press). MODELING THE DEGRADATION OF LOOSENING-LIMITED HILLSLOPES Loosening of Debris from a Bare Scarp Face Numerous researchers believe that a uniform thickness of material is loosened from the surface of a uniformly inclined scarp face underlain by homogeneous material during a given unit of time. Penck (1953) suggested the following: …On a slope of uniform gradient and equal exposure, a profile of reduction is formed which shows everywhere the same development and the same thickness. In the same time that the uppermost horizon of that profile has taken to acquire the mobility necessary for migration, a rock layer of the same thickness throughout has become reduced. At the close of a further equal interval of time, a further layer of rock, again of the same thickness and of equal thickness at every part of the slope, passes over into the reduced form. Removal of a uniform thickness of loosened debris from the scarp face results in parallel retreat with no rounding of the crestal convexity or basal concavity. The pattern of degradation, however, is dependent on whether the loosened debris accumulates at the base of the scarp or is removed. Accumulation of a Basal Debris Apron As long as debris is swept clear of the base of a scarp, the scarp retreats parallel to itself. This process may be observed on active fluvial cut-banks and wave-cut bluffs. When undercutting ceases and debris is no longer removed, an apron of debris inclined at a characteristic angle of repose will progressively grow, ultimately burying the retreating scarp face. The first analytical model of parallel retreat with accumulation of a basal debris apron was formulated by Fisher (1866) to describe the degradation of coastal chalk cliffs. Fisher’s model assumed a vertical scarp face and a horizontal crest and base. Lehmann (1933) modified the model to permit the treatment of nonvertical scarp faces and to allow for changes in volume of the debris as it moves from the scarp face to the debris apron. The model was further modified by Nash (1981a) to permit the treatment of scarps with nonhorizontal crests and bases. The pattern of degradation predicted by this model is shown in Figure 12.10. Note that the model predicts the development of an uneroded, parabolic core of debris beneath the debris apron. Immediately adjacent to the base of the retreating scarp face, the surface of the uneroded core of material is thinly buried and nearly parallel to the overlying surface of the debris apron. The predicted pattern of degradation of the scarp face is nearly identical to that documented by Wallace (1980) for scarps formed during the 1959 Yellowstone earthquake (Figure 12.11). It can also be used to explain the origin of the flight of faceted spurs along along the Wasatch Front above the Wasatch Fault noted by Hamblin (1976) and Anderson (1977) (Figures 12.4 and 12.12) and to provide a possible explanation for the origin of pediment surfaces. Pediments are bare or thinly veneered bedrock surfaces frequently found at the bases of loosening-limited ranges (Cooke and Warren, 1973). In numerous areas where the retreating face has been completely or extensively removed and the alluvial cover has been completely stripped away, the pediment

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Active Tectonics: Studies in Geophysics FIGURE 12.9 Comparison of the profiles measured on terrace scarps above the Madison river near West Yellowstone, Montana (solid lines), with the profiles predicted by the degradation model for transport-limited hillslopes (crosses). From Nash (1984), reprinted from the Bulletin of the Geological Society of America, with permission. surface is observed to have a parabolic shape. In fact, Fisher (1866) proposed the model to explain the origin of what he terms “parabolic noses” of chalk at the base of the chalk cliffs along the English coast. He suggested that the noses formed beneath a debris apron that was able to accumulate at the base of the retreating cliff during a prehistoric period of lower sea level. The subsequent rise of the sea to its present level removed the basal debris apron, exposing the uneroded chalk nose. USING THE HILLSLOPE DEGRADATION MODELS TO DATE SIMPLE FAULT SCARPS Both the transport-limited and the weathering-limited hillslope models offer a means for morphologic dating of some prehistoric fault scarps. Before this can be done, the initial morphology of a scarp must be accurately estimated and the models must be calibrated. Neither of these tasks is simple, nor are they even possi-

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Active Tectonics: Studies in Geophysics FIGURE 12.10 Model for retreating, loosening-limited scarp. The retreating free face is progressively buried by a basal apron of debris shed from its surface. ble in many cases. Although dating can be performed on several different types of scarp underlain by different kinds of materials, the following discussion of fault scarp dating is limited primarily to scarps produced by normal faulting of relatively cohesionless alluvium such as those produced by range-front faulting of alluvial fans in the Basin and Range region of the western United States. The initial morphology of such scarps can be quite complex. Frequently the fault surface will splay close to the ground surface to produce an assemblage of smaller scarps rather than producing a single scarp. Repeated faulting often superimposes younger scarps on FIGURE 12.11 Comparison of the profile of a scarp produced by the 1959 West Yellowstone earthquake with its profile observed 20 years later. The free face of the retreating scarp is nearly buried (compare with Figure 12.10). (Photo courtesy of R.E.Wallace, U.S. Geological Survey.) FIGURE 12.12 If a basal debris apron is not allowed to accumulate, the free face can retreat great distances. Subsequent movements of the fault may produce a new scarp before the older scarp is eliminated (compare with Figure 12.4). much older ones. The initial morphology of these complex scarps is difficult or impossible to determine with an accuracy sufficient to permit morphologic dating. Nash (1984) suggested that independent geologic evidence (e.g., from trenching) be used to determine whether a scarp had a complex initial morphology and, if so, to reject it for morphologic dating. The analysis below is for simple scarps. Recently, however, Hanks et al. (1984) have proposed a method for dating more complex scarps produced by repeated fault movements. Initial Morphology of Fault Scarps It is assumed here that the initial morphology consists of a single scarp that offsets a straight crest and base inclined at the prefaulting slope of the fan surface (Figure 12.2a). Scarps formed by normal faulting of cohesionless sands and gravels result from active Rankine failure producing failure planes inclined at 45+Φ/2 to the horizontal. Φ, the angle of internal friction, generally varies from 30° to 35° so initial scarp angles range from 60° to 62°. Theoretically, for a purely cohesionless material, a slope cannot exceed Φ (Carson, 1977), therefore, the initial fault scarp should rapidly recline to Φ. A rapid recline to Φ, however, is frequently not observed on normal fault scarps underlain by “cohesionless” sands and gravels, probably because of a weak, ephemeral cohesion among grains resulting from pore water in capillary tension and from minute amounts of cementing at contact points between grains. Instead, a loosening-limited free face is produced that retreats, progressively burying its base with debris. The time necessary for the retreating free face to be completely buried, producing a continuous debris apron that at Φ, varies with

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Active Tectonics: Studies in Geophysics FIGURE 12.13 Scarps produced by normal faulting of alluvial fans degrade in two stages. In the first, the loosening-limited free face retreats. After the free face has been buried, the second, transport-limited stage of degradation begins. the height of the scarp, the type of material, and the climate. Wallace (1980) found that the free face of most of the fault scarps produced by the 1959 earthquake in West Yellowstone are now nearly buried. On the other hand, the free face of the scarp produced by faulting during the 1915 Pleasant Valley, Nevada, earthquake is still clearly visible, and Wallace (1977) estimated that 300 yr will be required for it to be completely buried. The time necessary for the complete burial of the retreating free face may be from seconds to centuries but is probably most often on the order of decades. Degradation thus proceeds in two stages. During the first stage, the retreating free face may be described with the loosening-limited model. The second stage begins when the free face has been completely buried by the debris apron. Subsequent degradation of this apron may be described with the transport-limited model (Figure 12.13). Although the scarp retreats during the first stage, the center of the initial free face and the center of the debris apron that it produces are nearly the same, so that future movements of the fault will nearly bisect the debris apron (Figures 12.10 and 12.3). Morphologic Dating of Loosening-Limited Scarps Dating of fault scarps in the initial loosening-limited stage of degradation is simple in principle but difficult in practice: the distance that the free face has retreated from the fault is divided by the rate of scarp retreat. The accuracy of the calculated age is dependent on the accuracy of the retreat rate used, which varies not only from scarp to scarp but also along a given scarp face. The average retreat rate of the free faces resulting from the 1959 Yellowstone earthquake derived from data presented by Wallace (1980) is about 7–8 cm/yr, which is intermediate to the values derived from Wallace’s (1977) study of scarps in north central Nevada: a slower, 2 cm/yr for the 1915 Pleasant Valley scarp and a faster 10 cm/yr for the nearby scarp produced by the 1954 Dixie Valley earthquake. A large variation in the retreat rate along the Pleasant Valley scarp is quite evident; in some locations the free face is still standing immediately adjacent to a fresh-appearing basal graben, while nearby it has been completely buried. Retreat rates are probably a function of variations in the cohesion of the alluvium and of the climate. It is also likely that rate of retreat varies over relatively short periods of time (a great deal of retreat may occur during a particularly severe storm). Despite these limitations, when the effects that underlying material and climate have on retreat rates are understood well enough to permit accurate calibration of the loosening-limited model, it is likely that relatively accurate dates may be derived for some fault scarps in the first, retreating stage of degradation. Morphologic Dating of Transport-Limited Scarps With the burial of the free face by the basal debris apron, the scarp becomes transport-limited and dating must be based on Eq. (12.3). The first technique proposed for such dating (Nash, 1980a) uses the relationship between scarp height and rate of degradation to date the Drum Mountain, Utah, fault scarp observed by Bucknam and Anderson (1979). The method requires that a scarp of known age be located nearby and that both are underlain by the same material and show a continuous range of heights along their length. These requirements greatly limit the applicability of the technique. More flexible methods have subsequently been proposed by Nash (1981b), Colman and Watson (1983), and Hanks et al. (1984). The Nash (1981b) method is presented here, but all techniques based on Eq. (12.3) will yield similar ages for a given scarp. As it enters the second, rounding stage of degradation, the scarp is assumed to have a straight midsection at the angle of repose of the underlying debris, Φ, separating a straight base and crest equally inclined at an angle of θ, the original slope of the faulted fan surface (Figure 12.2a). The scarp offset, H, is defined as the perpendicular distance separating the crest, and base and the initial excess midsection slope angle, α, is defined as the angle by which the midsection slope angle exceeds θ (so Φ=α+θ). As it degrades, the crestal convexity and basal concavity of the scarp become more rounded but θ may still be observed beyond the extent of this rounding

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Active Tectonics: Studies in Geophysics and thus H may still be measured from the degraded profile (Figure 12.2b). The midsection of the degraded profile is defined as the straight inflection segment separating the basal concavity from the crestal convexity. The degraded excess midsection slope angle, β, is defined as the angle by which the inclination of the degraded midsection exceeds θ. For hillslopes with horizontal crests and bases (i.e., θ=0, a definite relationship exists among H, c, α, β, and t, the elapsed time since the initiation of the second stage of scarp degradation. A single value of tan α/tan β is the unique result of a single value of (tc/H2) tan2 α: (Nash, 1984). This relationship (Figure 12.14) may be used as the basis for morphologic dating. Although the relationship breaks down for hillslopes with steeply inlined crests and bases (θ>20°), negligible errors (less than 2 percent in the calculated value of t) result from using the following dating procedure on scarps on which θ<10° and where α+θ<35°. According to Figure 12.14, one-quarter as much time is required for a scarp to degrade from α to β if c is quadrupled or if H is halved. To date a scarp, H, β+θ, and θ are measured from a profile of the scarp, and α+θ is found indirectly by measuring the angle of repose, Φ, of the underlying debris, tan α/tan β is calculated and the corresponding value of (tc/H2) tan2 α is taken from Figure 12.14. This value of (tc/H2) tan2 α is multiplied by H2 and divided by tan2 α to yield tc. If t is known then c may be calculated. If c has been calculated for a nearby scarp of known age or has been derived by some other means, t may be calculated. Because the time required for completion of the first, loosening-limited stage of degradation is relatively short (rarely more than a few centuries), t is generally assumed to be equal to the total age of the scarp. The accuracy of t is dependent on the validity of assuming that a scarp had an initial morphology similar to that shown in Figure 12.2a and on the accuracy of c. Calculated values of c vary widely: 12×10−3 m2/yr for wave-cut bluffs underlain by sandy morainal material in Michigan (Nash, 1980b); 2×10−3 m2/yr for fluvial terrace scarps underlain by cohesionless obsidian sand and gravel near West Yellowstone, Montana; to a minimum of (0.9–1.0)×10−3 m2/yr calculated for the Lake Bonneville scarps by Colman and Watson (1983) and Hanks et al. (1984). [Hanks et al. (1984) also proposed that 1 m2/1000 yr be termed a G.K.G. in recognition of G.K.Gilbert’s contribution to the study of hillslopes.] Pierce and Colman (in press) observe a correlation between scarp aspect and c and also find a disturbing relationship between c and scarp height. It is likely that c is a function of underlying material, climate, and scarp aspect and thus is highly site specific. The identical values for c determined by Hanks and Wallace (in press) for the FIGURE 12.14 The relationship among initial excess midsection slope angle,; degraded excess midsection slope angle, β; scarp offset, H; c; and elapsed time since the start of the second stage of scarp degradation, t. This relationship forms the basis of the morphologic dating technique used here for dating transport-limited scarps. From Nash (1984), reprinted from the Bulletin of the Geological Society of America, with permission. Lake Bonneville and Lake Lahontan shoreline scarps, however, suggest that a value of c=(1.0–1.1)×10−3 m2/yr may be appropriate for many scarps underlain by alluvium in the Basin and Range province. Ideally, the value used for c should be derived from a nearby scarp of known age, underlain by the same material, and having the same aspect as the scarp to be dated. It is assumed that c does not change with time—questionable given the extent to which Holocene climatic conditions differed from those of the Pleistocene. Pre-Holocene dates are thus suspect, and it is possible that the moderation of climate during the xerotherm 4000 yr BP may have been sufficient to have changed c significantly.

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Active Tectonics: Studies in Geophysics Given the simple initial scarp morphology shown in Figure 12.2a, Eq. (12.3) predicts that curvature of the crestal convexity and basal concavity should be identical at any future time. If a significant asymmetry of the crestal convexity and basal concavity is observed, dating should be attempted with great caution [slope wash processes probably cannot be modeled with Eq. (12.3) and are likely to produce a profile with a more rounded basal concavity than crestal convexity]. RECOMMENDATIONS FOR FUTURE RESEARCH Although the validity of the models for loosening-limited and transport-limited hillslopes is fairly well established and accepted, widespread application of the models for morphologic dating of fault scarps is hampered by the lack of a means for accurately calibrating either model for a particular site. Both c and the rate of retreat of a free face are probably a function of factors such as climate, underlying material, and scarp aspect and therefore are highly site specific. Currently, both parameters must be determined from a nearby scarp having the same aspect and underlain by the same material as the scarp to be dated (generally such a scarp will not be available). If the effects of climate, material, and aspect on the retreat rate and c could be determined accurately, however, appropriate values for either parameter could be estimated by measurement of these factors. To determine these effects, retreat and rounding rates must be found for a large number of dated transport- and loosening-limited hillslopes in various climates, with a variety of aspects and underlying materials. The study of initial scarp morphology and rates of retreat of the free face would be helped considerably if a continuous set of photogrammetric quality stereo images were taken at ground level along each scarp immediately after faulting and at 10-yr intervals thereafter. This set of imagery would also permit future investigators to make measurements of morphologic parameters not considered by the initial investigators. CONCLUSIONS Degradation of scarps formed by normal faulting of alluvial fan surfaces occurs in two stages. In the first, the steep, loosening-limited free face retreats back, progressively burying itself with a basal apron of debris. The second stage of degradation begins when the free face is completely buried by debris to yield a midsection uniformly inclined at the angle of repose of the debris. Degradation of this transport-limited scarp proceeds by progressive rounding of the basal concavity and crestal convexity and recline of the midsection gradient. Both the parallel retreat of the free face in the first stage and the rounding of the scarp in the second stage can be described by two simple models. If the initial morphology of the scarp can be accurately estimated and if the models are properly calibrated, they can be used to date a scarp in either stage of degradation. The applicability of morphologic dating is limited by the need to recalibrate the models for each scarp to be dated, currently only possible by analysis of a nearby similar scarp of known age. With additional investigation, it is likely that the influence that climate, underlying material, and aspect have on c and on the rate of retreat will be known with sufficient accuracy that the models can be calibrated directly from measurements of these factors. Morphologic dating is not applicable to all scarps formed by normal faulting of alluvial fans. Degradation by slope wash cannot be described with either model, so dating of wash eroded scarps should probably be avoided (such scarps will often have a more rounded basal concavity than crestal convexity). It is also likely that the pre-Holocene climate was sufficiently different from the present that c was also different, making pre-Holocene dates suspect. Morphologic dating should not be applied to fault scarps that cannot be assumed to have had a simple initial morphology comprising an equally inclined crest and base separated by a straight midsection. Despite these limitations, morphologic dating, when used with considerable care, should prove itself to be a valuable tool for determining the deformational history of areas of active tectonism. ACKNOWLEDGMENTS My research in the area of morphologic dating of fault scarps was sponsored by the U.S. Geological Survey, Earthquake Hazards Reduction Program, under Contract 14–03–0001–19109. Arvid M.Johnson and Thomas C.Hanks are thanked for their critical reviews of this manuscript. Rebecca Chavlot-Talmon is thanked for her assistance with the drafting. REFERENCES Anderson, T.C. (1977). Compound faceted spurs and recurrent movement in the Wasatch Fault zone, north central Utah, Brigham Young Univ. Geol Stud. 24, 83–101. Brunsden, D., ed. (1971). Slopes Form and Process, Institute of British Geographers, Special Publ. No. 3, 178 pp. Brunsden, D., and R.H.Kesel (1973). Slope development on a Mississippi River bluff in historic time, J. Geol. 81, 576–597. Bryan, K. (1922). Erosion and sedimentation in the Papago Country, Arizona, U.S. Geol. Surv. Bull. 730-B, 19–90.

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Active Tectonics: Studies in Geophysics Bucknam, R.C., and R.E.Anderson (1979). Estimation of fault-scarp ages from a scarp-height-slope-angle relationship, Geology 7, 11–14. Carson, M.A. (1977). Angles of repose, angles of shearing resistance and angles of talus slopes, Earth Surface Processes 2, 363–380. Carson, M.A., and M.J.Kirkby (1972). Hillslope Form and Processes, Cambridge Univ. Press, Cambridge, 475 pp. Colman, S.M., and K.Watson (1983). Ages estimated from a diffusion equation model for scarp degradation, Science 221, 263–265. Cooke, A.V., and A.Warren (1973). Geomorphology in Deserts, University of California Press, Berkeley, 394 pp. Culling, W.E.H. (1960). Analytical theory of erosion, J. Geol. 68, 336–344. Culling, W.E.H. (1963). Soil creep and the development of hillside slopes, J. Geol. 71, 127–161. Culling, W.E.H. (1965). Theory of erosion on soil-covered slopes, J. Geol. 73, 230–254. Davis, W.M. (1899). The geographical cycle, Geogr. J. 14, 481–504. Davison, C. (1888). Note on the movement of scree-material, Q. J. Geol. Soc. Lond. 44, 232–238. Fisher, O. (1866). On the disintegration of a chalk cliff, Geol. Mag. 3, 354–356. Fleming, R.C. (1972). Soil creep in the vicinity of Stanford University, Ph.D. dissertation, Stanford Univ., 148 pp. Gilbert, G.K. (1877). Geology of the Henry Mountains, U.S. Geographical and Geological Survey, 160 pp. Hack, J.T. (1960). Interpretation of erosional topography in humid regions, Am. J. Sci. 258A, 80–97. Hamblin, W.K. (1976). Patterns of displacement along the Wasatch Fault, Geology 4, 619–622. Hanks, T.C., and R.E.Wallace (in press). Morphological analysis of Lake Lahontan shoreline and beachfront fault scarps, Pershing County, Nevada. Hanks, T.C., R.C.Bucknam, K.R.Lajoie, and R.E.Wallace (1984). Modification of wave-cut and fault-controlled landforms, J. Geophys. Res. 89, 5771–5790. Hirano, M. (1968). A mathematical model of slope development—an approach to the analytical theory of erosional topography, J. Geosci. Osaka City Univ. 11, 13–52. Hirano, M. (1975). Simulation of development process of interfluvial slopes with reference to graded form, J. Geol. 83, 113–123. King, L.C. (1953). Canons of landscape evolution, Geol. Soc. Am. Bull. 64, 721–751. Lehmann, O. (1933). Morphologische Theorie der Verwitterung von Steinschlagwanden, Vierteljahresschr. Naturforsch. Ges. Zurich 78, 83–126. Nash, D.B. (1980a). Forms of bluffs degraded for different lengths of time in Emmet County, Michigan, U.S.A, Earth Surface Processes 5, 331–345. Nash, D.B. (1980b). Morphologic dating of degraded normal fault scarps, J. Geol. 88, 353–360. Nash, D.B. (1981a). FAULT: A FORTRAN program for modeling the degradation of active normal fault scarps, Comput. Geosci. 7, 249–266. Nash, D.B. (1981b). Fault scarp morphology: Indicator of paleoseismic chronology, Final Tech. Rep., U.S. Geol. Surv. Contract Number 14–08–0001–19109, 132 pp. Nash, D.B. (1984). Morphologic dating of fluvial terraces scarps and fault scarps near West Yellowstone, Montana, Geol. Soc. Am. Bull. 95, 1413–1424. Penck, W. (1953). Morphological Analysis of Land Forms, H.Czeck and K.C.Boswell, translators, Macmillan, London, 429 pp. Pierce, K.L., and S.M.Colman (in press). Effect of orientation and height rates of scarp degradation, central Idaho. Pollack, H.N. (1968). On the interpretation of state vectors and local transformation operators, State Geol. Surv. of Kansas Computer Contrib. 22, 43–46. Savat, J., and J.DePloey (1968). Contribution à l’étude de l’érosion par le splash, Z. Geomorphol. 12, 174–192. Savigear, R.A.G. (1952). Some observations on slope development in South Wales, Trans. Inst. Brit. Geogr. 18, 31–51. Schumm, S.A. (1956). The role of creep and rainwash on the retreat of badland slopes, Am. J. Sci. 254, 693–706. Schumm, S.A. (1967). Rates of surficial creep on hillslopes in western Colorado, Science 155, 560–561. Schumm, S.A., and M.P.Mosley, eds. (1973). Slope Morphology, Dowden, Hutchinson and Ross, Inc., Stroudsburg, Pa., 454 pp. Souchez, R. (1964). Viscosité, plasticité et rupture dans l’evolution des ver sants, Ciel Terre 80, 3–24. Wallace, R.E. (1977). Profiles and ages of young fault scarps, north-central Nevada, Geol. Soc. Am. Bull. 88, 1267–1281. Wallace, R.E. (1980). Degradation of the Hebgen Lake Fault scarps of 1959, Geology 8, 225–229. Welch, D.M. (1970). Slope Analysis and Evolution on Protected Lacustrine Bluffs, Ph.D. dissertation, Univ. of Western Ontario, 184 pp. Young, A. (1963). Slopes, Oliver and Boyd, Edinburgh, 288 pp. NOTE: A BASIC language computer program (for an IBM PC) has been developed by the author for the morphologic dating of transport-limited scarps. Copies of the program are available without cost. Send the author a self-addressed, stamped envelope for details (Department of Geology, University of Cincinnati, Cincinnati, OH 45221).