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A methodology for determining long-term denudation rates from morphologic markers in a Digital Elevation Model DEM is checked by a comparative study of two drainage basins in the PrecordiUera of the Central Andes. In both cases the initial configuration of an incised pediment surface has been restored by using two different methods: Where vertical incision and hillslope erosion are recorded, the IDW appears to be the most gellogia to reconstitute the pediment surfaces.
Conversely, where only vertical incision is observed, the BTH describes more precisely the former pediment surfaces and it is easier to solve. These estimations are largely in agreement with other reported estimates of long-term denudation rates in the Atacama Desert.
Comparison with long-term denudation rates reported in a wide range of climatic regimes suggests that our estimates cannot be explained by the current rainfall in the PrecordiUera. However they could be explained by a rainfall similar to that reported 40 km to the east in the Puna.
This suggests that during the time span concerned the geomorphologic evolution of the study area, this evolution is dominated by an orographically controlled rainfall pattern. The preserved pediment surface and the small long term denudation rates determined in this study also indicate that the PrecordiUera was never reached by humid tropical air masses and precipitation as currently observed in the Altiplano during the summer months.
Denudation rates result from the interaction between the relative effects of erosion, tectonics and climate on landscape evolution.
Knowledge of long-term denudation rates ky to 10 Ma and understanding the factors that control them are important for a number of reasons. They allow the description of the nature and rates of geomorphic processes that control landscape evolution. Realistic estimations of long-term denudation rates must be considered when interaction between tectonic and subaerial processes is geloogia, for instance, by using quantitative landscape evolution models Ahnert, ; Beaumont stahler al.
Comparison of long-term denudation and uplift rates can also be used to establish the degree of equilibrium reached by the landscape e. Long-term denudation rates are a vital component of mass balances studies aimed at understanding the factors that perturb the global carbon budget and consequently influence global climate Raymo et al. A knowledge of the long-term denudation rate and its comparison with the current sediment and solute yields of rivers, would allow discussion, for instance, of the relative impact of paraglacial sediment reworking i.
In order to quantify long-term denudation rates different methods have geologiz applied, including: These methods require arduous and expensive analytical techniques, and they present discrepancies when comparing different spatial and temporal scales.
Alternatively, whenages of relatively well preserved morphologic surfaces e. The purpose of this paper is to discuss the benefit of the application of the BTH function to the estimation of the long-term denudation rates for rejuvenated topography Fig.
We use a DEM generated by interpolation of digitized contour lines of 1: The BTH method geologiz of limited use in some cases, notably where a smooth morphology representing a relict topography affected by current hillsope erosion is present Fig. In this case, an alternative methodology for reconstructing morphologic surfaces, and consequently, estimating long-term denudation rates is proposed.
We discuss the results obtained from the application of the BTH and the alternative method on two drainage basins located on the western slope of the Central Andes Fig. We focus on the determination and propagation of the uncertainties associated with both the base-DEM used, and the morphologic reconstruction, in order to evaluate the uncertainties in the denudation rate. Furthermore, we propose an objective and effective criterion to recognize if ztrahler BTH function should or should not be applied to the considered landscape.
Finally, our denudation rates obtained will be compared to those estimated by other methods. In this region an arid climatic regime has been dominant since the Middle Miocene Alpers and Brimhall, ; Sillitoe and Syrahler, ; Nishiizumi et al, and the present hyperarid climate was established in the Late Pliocene Hartley and Chong, These climate conditions are responsible for Neo-gene geomorphologic evolution of the study area and the formation of an extensive pedimentation surface Atacama Pediplain of Sillitoe et al, The ignimbrite level marks the end of the alluvial fan landscape infilling related to pedimentation processes and the beginning of the strong vertical incision up to m that generated the current drainage basin systems Mortimer, ; Riquelme et al.
The interpreted evolution is corroborated by the exposure age of cobbles collected on alluvial fan surfaces that compose the Atacama Pediplain in the Precordillera: The vertical canyon incision is probably active geoloiga, but hillslope erosion related to headward propagation of the drainage is also observed.
We have studied two drainage basins of the Atacama Desert which geeologia both the pedimentation surface and the ignimbrite level, the latter providing a good time constraint on geologai start of incision: To the east, the east-vergent Potrerillos fold and thrust belt deforms strahelr a Mesozoic platform carbonate and clastic sequence and is oriented strahle to the elongation of the El Salado Basin Cornejo et al.
The north-eastern water divide exposes the Mesozoic carbonate and clastic sequence and coincides with a set of northwest-trending subvertical faults that belong to the DFS Tomlinson et al, ; Randall et al, Top Hat Formalism and its limits. The Top Hat Transform function is a mathematical morphology function which allows peak and valley extraction in a ID signal and 2D geopogia.
In geomorphology, this function was applied to a high-precision DEM as a relevant tool for estimating incision and the amount of material removed by recent fluvial erosion in a Pyrenean watershed Rodriguez et al, The mathematical formulation is based on a set of mathematical morphology concepts presented in appendix A. This formulation is provided by a number of specialized software for landscape image processing.
A DEM is a grey-tone image where, normally, clear zones represent landscape regions of relati vely higher elevations, whereas steahler zones represent regions of relatively lower elevation. A DEM can be viewed as a function where f x represents the elevation generally grey levels in a pixel located at the coordinate x. Considering the elementary grey level mathematical morphology operations: The initial DEM Fig. Dilation of the DEM is presented for lengths of A.
The dilated DEM of figure 3c is then eroded for a length of X equal to L pixels, resulting in the image of figure 3d and 2e. Dilation of the image f x to obtain the image of figure geologiqfollowed by erosion of the later resulting in the image of figure 3econstitutes the closing transformation of the initial DEM for a structuring element X of length equal to L pixels eq.
A5 of appendix A. The closing transformation is commonly used to join clear zones lightest grey levels while the opening transformation eq. A6 shrahler appendix A is used to separate them. The closing and opening transformations are the gsologia of the Top Hat Transform formalism. It strshler the extraction of valleys in a grey-tone level elevation image by subtraction of the image of closed valleys C x X and the initial image f x Fig.
The transformation considers a size condition equal to the size L for a given structuring element X Meyer, and a threshold t Fig. The threshold value t allows the extraction strauler valleys without the topographic noise, which corresponds to the darkest grey-levels Fig. Hence, only the information for the deepest geokogia is kept Rodriguez et al, The application of the BTH function is based on the selection of the length L, which corresponds to the width of the valley to be extracted.
In our case, the width corresponds to the greatest separation between pedimentation surfaces throughout the valleys for the entire basin. Therefore, a good reconstruction of the pedimentation surfaces can be achieved only if the hillslope gradients are high and if the inflection point between the preserved with a thresholding value oft surface and the hillslope is properly defined. This would be the case in a rejuvenated landscape with canyon formation. However, if the surface has low hillslope gradients, such as a preserved pedimentation surface, the determination of the length L is poorly defined geopogia to gellogia difficulty of identifying the inflection point.
It is important to note that hillslope erosion in the upper part of the basin can result in a larger separation of the pedimentation surfaces than those in the lower basin. Since the BTH method, in this case, does not lead to a good reconstraction of the pedimentation surface where hillslope erosion is important, an alternative methodology for reconstructing geomorphologic surfaces that better fits this scenario is presented below.
The reconstraction of the pedimentation surfaces is divided into three steps: Using these criteria it is possible to identify the set of points that comprise remnant pedimentation surfaces Fig. To reconstruct the pedimentation surface, we have selected an Inverse Distance Weighting method.
This is a simple algorithm that is designed to veologia the effects of interpolation that could distort the slope of the planated surface determined from the randomly selected points.
Alternatively, its mathematical expression eq. The interpolation equation is as follows: Where each Z x,y interpolated grid point is evaluated by considering the k-nearest neighbour point with grey-tone level Z. The estimation of the eroded volume that allows us to calculate the long-term denudation rate is determined by subtracting the DEM from the reconstructed surface Geologiq.
Apuntes Geología General: El ambiente fluvial
An error grid was then generated for the reconstructed surface that allows us to associate with each pixel grey-level a corresponding grey-level error value Fig. In order to sttahler the error grid we calculated the difference between control points and the corresponding grey-level in the reconstructed surface.
These differences are then interpolated to the entire basin by using a polynomial interpolation function. Comparison with the BTH. Where Z x,y is an elevation point, i.
Apuntes Geología General: Ambiente sedimentario
Determination of the present pedimentation surfaces. The hypsometric integral value I -i. These correspond essentially to remnant pedimentation surfaces but also include zones where hillslope erosion is present which is consistent with a relatively smoothed landscape surface.
From the DEM-extracted local slope image Fig. From this range of slope values and the range of threshold values we can obtain the points that grologia the remnant pedimentation surfaces Fig. For El Salado Basin. The area versus altitude histogram of El Salado is marked by an asymmetrical shape with a predominance of high altitudes Fig.
The hypsometric integral value is relatively high Fig. In the El Salado Basin an older landscape surface the pedimentation surface is affected by strong vertical incision the El Salado canyon. By thresholding the slope and the altitude of the DEM it is possible to observe that the low altitudes mainly correspond to the bottom of canyon and the high altitudes correspond to residual low sloping remnants of the pedimentation surface. This analysis combined with the morphology of the basin will allow determination of of the method best adapted to a given morphology.
The morphology of the catchment results from vertical incision of remnant pedimentation surface affected by important hillslope erosion. This type of catchment is easily identifiable either by field analysis or by the hypsometric integral which has a relatively low value Fig.
From the geomorpho-logical viewpoint the catchment corresponds to a pedimentation surface affected only by strong vertical incision, i. This erosional reactivation is marked by a relatively high hypsometric integral Strayler. Eroded volumes and uncertainties. Figure 7 clearly shows the cause of these differences: The volume evaluated by interpolation of the pediments km 3 is slightly smaller than that evaluated geolkgia the BTH geolgoia km 3.
This suggests that where the incised surface sgrahler a simple inclined plane with a localized canyon incision that strhler upstream, the BTH method is more accurate than the IDW method.
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The accurancy for the ‘Top Hat’ application is determined by about 80 m of imprecision in the selection of the structuring element. To determine the long-term denudation rates we used the methodbest adapted to morphology i. Uncertainties in the eroded volume have been calculated by error propagation considering the error grid previously discussed. Final uncertainties in the long-term denudation rate during the last 10 Myr are determined by considering the average of the eroded volume uncertainties and by averaging the uncertainties associated with the published stralher of the ignimbrite that seals the pedimentation surface.