Clement G. Chase

Fluvial landsculpting and the fractal dimension of topography

Abstract Quantitative models of landform development can help us to understand the evolution of mountains and regional topography, and the effects of tectonic motions and climate on landscape, including its fractal geometry. This paper presents a general and powerful three-dimensional model of fluvial erosion and deposition at hill- to mountain-range scale. The model works by accumulating the effects of randomly seeded storms or floods (precipitons) that cause diffusional smoothing then move downslope on digital topography grids, that erode portions of elevation differences, that transport a slope-limited amount of eroded material, and that deposit alluvium when their sediment-carrying capacity is exceeded. The iteration of these simple and almost linear rules produce very complicated simulated landscapes, demonstrating that complex landscapes do not require complex laws. Each process implemented in the model is affected differently by changes in horizontal scale. Erosion, a scale-free process, roughens topography at all wavelengths. This roughening is balanced by diffusive processes (scaling as 1 L 2 ) at short wavelengths and deposition (scaling (scaling as 1 L 2 ) at long wavelenghts. Such a mixture of scale-free and scale-dependent processes can produce multifractal behavior in the models. The fractal dimension of the model topography is much more sensitive to climatic variables than to tectonic uplift. Landscape evolution may be fractal, but it does not seem to be chaotic. Analysis of topography of areas in southern Arizona using variograms shows approximately fractal behavior, with mean fractal dimension around 2.2–2.3. Departures from an exact fractal relatioship imply that the topography is in detail multifractal. The fractal dimension at short wavelengths is less than that at long wavelengths. This variation could either be caused by the relative strengths of diffusive and erosional processes shaping the topography, or a result of changes in climatic or tectonic conditions still preserved in the landscape.

Stored mafic/ultramafic crust and early Archean mantle depletion

Abstract Both early and late Archean rocks from greenstone belts and felsic gneiss complexes exhibit positive eNd values of +1 to +5 by 3.5 Ga, demonstrating that a depleted mantle reservoir existed very early. The amount of preserved pre-3.0 Ga continental crust cannot explain such high e values in the depleted residue unless the volume of residual mantle was very small: a layer less than 70 km thick by 3.0 Ga. Repeated and exclusive sampling of such a thin layer, especially in forming the felsic gneiss complexes, is implausible. Extraction of enough continental crust to deplete the early mantle and its destructive recycling before 3.0 Ga ago requires another implausibility, that the sites of crustal generation and of recycling were substantially distinct. In contrast, formation of mafic or ultramafic crust analogous to present-day oceanic crust was continuous from very early times. Recycled subducted oceanic lithosphere is a likely contributor to present-day hotspot magmas, and forms a reservoir at least comparable in volume to continental crust. Subduction of an early mafic/ultramafic “oceanic” crust and temporary storage rather than immediate mixing back into undifferentiated mantle may be responsible for the depletion and high eNd values of the Archean upper mantle. Using oceanic crustal production proportional to heat productivity, we show that temporary storage in the mantle of that crust, whether basaltic as formed by 5–20% partial melting, or partly komatiitic and formed by higher extents of melting is sufficient to balance an early depleted mantle of significant volume with eNd at least +3.0.

Tectonic, climatic and lithologic influences on landscape fractal dimension and hypsometry: implications for landscape evolution in the San Gabriel Mountains, California

East-west variation in tectonic activity and strong north-south climatic gradients provide a unique opportunity to study tectonic, climatic and lithologic influences on landscape evolution in the San Gabriel Mountains, California. The competing tendencies of constructive tectonic and degradational climatic effects act against lithologic resistance to influence fluvial systems, and thus the nature of adjacent and nested drainage basins. Landscape fractal dimension (D), a measure of surface roughness over a variety of scales, and the hypsometric integral (I), a measure of the distribution of landmass volume above a reference plane are useful measures of altitudinal variation with scale. As such, they may provide clues as to the relative influences of tectonism, climate and rock type. Topographic analyses of the San Gabriel Mountains clearly indicate that tectonism strongly influences D at range-wavelength scales, while rock-type variation apparently influences D and I at smaller scales. Tectonism is also shown to influence I across the mountain-piedmont junction at all scales investigated. Tectonic activity shows strong negative correlation with both I and D because tectonically active portions of the mountain front do not allow time for much landscape dissection by lower-order streams. Three-dimensional topographic modeling suggests climatic parameters exert a stronger influence on D than does tectonism. This modeling also suggests an inverse correlation between range-scale D and I with varying climate and uplift rate; a positive correlation is observed in the San Gabriel Mountains. We suggest this difference results from (1) differences in uplift style between the San Gabriel Mountains and the models, and/or (2) variation in rock-type erodibility present in the San Gabriel Mountains but which was not modeled. We postulate that the interaction of tectonic, climatic and lithologic parameters influences the stable I and D to which a landscape evolves. Key questions remaining include: (1) the time required to reach a stable I or D after a climatic or tectonic change; (2) what does the fractal nature of topography tell us about the scaling characteristics of major landforming processes; (3) how does climate influence range-scale I and both range- and small-scale D; and (4) what are the effects on I and D of range-scale lithologic variation, both in the models and in real landscapes?

Raising the Colorado Plateau

Shallow-marine rocks exposed on the 2-km-high, 45-km-thick Colorado Plateau in the western United States indicate that it was near sea level during much of the Phanerozoic. Isostatic calculations, however, illuminate the difficulty in maintaining a 45-km-thick crust at or near sea level. We propose that an isostatically balanced, 30-km-thick, proto‐Colorado Plateau crust was thickened during the Late Cretaceous to early Tertiary by intracrustal flow out of an overthickened Sevier orogenic hinterland. This plateau would have been supported by a thick (>70 km) crustal root, which is proposed to have been the source region for hot and weak mid-crustal material that flowed eastward from the plateau toward the low-elevation proto‐Colorado Plateau.

Tectonic and climatic significance of a late Eocene low‐relief, high‐level geomorphic surface, Colorado

New paleobotanical data suggest that in the late Eocene the erosion surface which capped the Front Range, Colorado was 2.2–3.3 km in elevation, which is similar to the 2.5-km present elevation of surface remnants. This estimated elevation casts doubt on the conventional belief that the low-relief geomorphic surface was formed by lateral planation of streams to a base level not much higher than sea level and that the present deeply incised canyons must represent Neogene uplift of Colorado. Description of the surface, calculations of sediment volume, and isostatic balance and fluvial landsculpting models demonstrate that while the high elevation of the erosion surface was due to tectonic forces, its smoothness was mostly a result of climatic factors. A sediment balance calculated for the Front Range suggests that from 2 to 4 km of material were eroded by the late Eocene, consistent with fission track ages. This amount of erosion would remove a significant portion of the 7 km of Laramide upper crustal thickening. Isostatic modeling implies that the 2.2–3.3 km elevation was most likely created by lower crustal thickening during the Laramide. A numerical model of fluvial erosion and deposition suggests a way that a late Eocene surface could have formed at this high elevation without incision. A humid climate with a preponderance of small storm events will diffusively smooth topography and is a possible mechanism for formation of low-relief, high-level surfaces. Paleoclimate models suggest a lack of large storm events in the late Eocene because of cool sea surface temperatures in the equatorial region. Return to a drier but stormier climate post-Eocene could have caused the incision of the surface by young canyons. By this interpretation, regional erosion surfaces may represent regional climatic rather than tectonic conditions.

Cenozoic exhumation of the northern Sierra Nevada, California, from (U-Th)/He thermochronology

Apatite and zircon (U-Th)/He ages from a 100-km-long range-perpendicular transect in the northern Sierra Nevada, California, are used to constrain the exhumation history of the range since ca. 90 Ma. (U-Th)/He ages in apatite decrease from 80 Ma along the low western range flanks to 46 Ma in the higher elevations to the east. (U-Th)/He ages in zircon also show a weak inverse correlation with elevation, decreasing from 91 Ma in the west to 66 Ma in the east. Rocks near the range crest, sampled at elevations of 2200–2500 m, yield the youngest apatite helium ages (46–55 Ma), whereas zircon helium ages are more uniform across the divide. These data reveal relatively rapid cooling rates between ca. 90 and 60 Ma, which are consistent with relatively rapid exhumation rates of 0.2–0.8 km/m.y., followed by a long period of slower exhumation (0.02–0.04 km/m.y.) from the early Paleogene to today. This is reflected in the low-relief morphology of the northern Sierra Nevada, where an Eocene erosional surface has long been identified. A long period of slow exhumation is also consistent with well-documented, widespread lateritic paleosols at the base of Eocene depositional units. Laterites preserved in the northern Sierra Nevada are the product of intense weathering in a subtropical environment and suggest an enduring, soil-mantled topography. We interpret this exhumation history as recording a Late Cretaceous to early Cenozoic period of relatively rapid uplift and unroofing followed by tectonic quiescence and erosional smoothing of Sierran topography through the Neogene. Well-documented recent incision appears to have had little effect on (U-Th)/He ages, suggesting that less than ∼3 km has been eroded from the Sierra Nevada since the early Cenozoic.

Role of transform continental margins in major crustal growth episodes

Mantle plumes are often invoked as the ultimate cause of major episodes of continent generation. In this paper we explore the potential of normal plate-tectonic processes to generate intense crustal growth. The central problem is localization of rapid crustal growth into small regions. This can be achieved by transport of terranes parallel to the continental edge in orogenic zones, which we deduce from an analysis of the proportion of present-day continental margins that are dominated by strike-slip motion, together with the proportion of subduction zones showing obliquity >30°. There is a 16% probability of margin-parallel terrane transport on a scale >400 km, and a few margins show transport on a scale >1000 km. The results suggest that concentration of juvenile arc materials into restricted locations can explain both the apparent episodicity and rapid genesis of Precambrian juvenile provinces.

Evolution of Hawaiian basalts: a hotspot melting model

Melt generation and extraction along the Hawaiian volcanic chain should be largely controlled by the thermal structure of the Hawaiian swell and the heat source underneath it. We simulate numerically the time- and space-dependent evolution of Hawaiian volcanism in the framework of thermal evolution of the Hawaiian swell, constrained by residual topography, geoid anomalies, and anomalous heat flow along the Hawaiian volcanic chain. The transient heat transfer problem with melting relationships and variable boundary conditions is solved in cylindrical coordinates using a finite difference method. The model requires the lithosphere to be thinned mechanically by mantle plume flow. Melting starts quickly near the base of the plate when the hotspot is encountered. Thermal perturbation and partial melting are largely concentrated in the region where the original lithosphere is thinned and replaced by the mantle flow. The pre-shield Loihi alkalic and tholeiitic basalts are from similar sources, which are a mixture of at least three mantle components: the mantle plume, asthenosphere, and the lower lithosphere. The degree of partial melting averages 10–20%, with a peak value of 30% near the plume center. As a result of continuous compaction, melts are extracted from an active partial melting zone of about 10–20 km thickness, which moves upwards and laterally as the heating and compaction proceed. The rate of melt extraction from the swell increases rapidly to a maximum value of ∼ 1 × 105 km3/m.y. over the center of the heat source, corresponding to eruption of large amounts of tholeiitic lavas during the shield-building stage. This volume rate is adequate to account for the observed thickness of the Hawaiian volcanic ridge. Melts from direct partial melting of the mantle plume at depth may be important or even dominant at this stage, although the amount is uncertain. At the waning stage, mixing of melts from the mantle flow pattern with those from low-degree partial melting of the lithosphere may produce postshield alkalic basalts. After the plate moves off the heat source, continuous conductive heating can cause very low degree partial melting (less than 1%) of the lithosphere at shallow depths for about one million years. This process may be responsible for producing post-erosional alkalic basalts. The extraction time for removing such small amount of melts is about 0.4–2 m.y., similar to the time gap between the eruption of post-erosional alkalic lavas and the shield-building stage. Our results show that multi-stage Hawaiian volcanism and the general geochemical characteristics of Hawaiian basalts can be explained by a model of plume-plate interaction.

Uplift of the Sierra Nevada of California

Gravity and most seismic interpretations agree that the Sierra Nevada is at present isostatically compensated by a crustal root. The most reasonable timing for emplacement of the root was during Mesozoic batholithic intrusions. This is difficult to reconcile with the evidence that major uplift of the mountains occurred in the past 10 m.y. A simple quantitative model for flexural isostasy of an elastic plate before and after breaking resolves this problem and explains the tilt of the Sierra Nevada block and variations in topography along the range. We postulate that cooling and elastic strengthening of the Mesozoic magmatic arc prevented its reaching local isostatic equilibrium during erosion in the Cenozoic. Thus, an overcompensated residual mountain range was held down elastically until Basin and Range extension broke the elastic plate along the Owens Valley and allowed rapid uplift. The Moho density contrast that best models the amplitude of both late Cenozoic uplift and prior topography is slightly larger than seismic and gravity models suggest; this implies that up to 20% of the uplift may be driven by density contrasts in the upper mantle. The idea of overcompensated erosional remnants and their release upon lithospheric faulting has a more general application to “anorogenic” uplift of mountain blocks.

Crustal structure from three-dimensional gravity modeling of a metamorphic core complex: A model for uplift, Santa Catalina–Rincon mountains, Arizona

Gravity modeling shows that the observed fluctuations in gravity over the Catalina-Rincon metamorphic core complex of southeastern Arizona are caused primarily by shallow crustal density contrasts. The Wilderness suite granites, the probable source of a 20-mgal low over the central part of the core complex, may extend to depths of 7–12 km below the surface. Seismic refraction information is consistent with the existence of a deep crustal root under the Catalina-Rincon core complex. We hypothesize that the voluminous Wilderness suite granites are related to a crustal thickening event that built the root in early Tertiary time. Modeling of flexural isostatic uplift, resulting from an excess crustal root, predicts two episodes of uplift for the Catalina-Rincon metamorphic core complex: (1) low-relief flexural uplift in the middle Tertiary and (2) complete uplift precipitated by high-angle Basin and Range faulting at 10–15 Ma. The uplift and exposure of core complexes, therefore, can be an isostatically driven process that occurs in regions of locally thickened crust.