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1.
Mandelbrot (Science, 1967, 156, 636–638) used the west coast of Britain as an example of a naturally occurring statistically self-similar fractal. Evidence from this study indicates that the west coast of Britain is not statistically self-similar over the range of scale of measurement, and that complexity reaches maxima at characteristic scales related to identifiable features on the coastline. A fractal analysis is conducted using the divider method, and although the resulting log–log plot of measured length against steplength appears linear, statistical tests for linearity strongly suggest that the coastline is not statistically self-similar. An angle measure technique (AMT) developed by the author to examine changes in line complexity with scale, shows that within the range of scale of measurement there are two peaks in complexity for the west coast of Britain, suggesting that two processes acting at different scales have influenced coastal development. The AMT is also used to identify differences in complexity between northern and southern sections of the coastline. Additionally, high r2 values associated with regressions of log L(G) against log G are shown to be insufficient evidence of statistical self-similarity, and apparently linear segments (fractal elements) often found in Richardson plots may contain systematic curvature revealed only by more rigorous tests for non-linearity.  相似文献   

2.
A wavetrain of high-frequency (HF) P waves from a large earthquake, when recorded at a distant station, looks like a segment of modulated noise, with its duration close to the duration of rupture. These wavetrains, with their bursts and fadings, look much more intermittent than a segment of common stationary random noise. We try to describe quantitatively this bursty behavior. To this end, variogram and spectral analyses are applied to time histories of P-wave envelopes (squared-amplitude or instant-power signals) in six HF bands of 1-Hz width. Nine M w = 7.6–9.2 earthquakes were examined, using, in total, 232 records and 992 single-band traces. Variograms of integrated instant power are approximately linear on a log–log scale, indicating that the correlation structure of the instant-power signal is approximately self-similar. Also, estimates of the power spectrum of the instant-power signal look approximately linear on a log–log scale. Log–log slopes of the variograms and spectra deliver estimates of the Hurst exponent H that are mostly in the range 0.6–0.9, markedly above the value H = 0.5 of uncorrelated (white-noise) signals. The preferred estimate over the entire data set is H = 0.83, still, this estimate may include some bias, and must be treated as preliminary. The inter-event scatter of H estimates is about 0.04, reflecting individual event-to-event variations of H. Many of the average log–log spectral plots show slight concavity that perturbs the approximately linear slope; this is a secondary effect that seems to be mostly related to the limited bandwidth of the data. Evidence is given in support of the idea that the observed approximately self-similar correlation structure of the P-wave envelope originates in a similar structure of the body wave instant-power signal radiated by the source, so that the propagation-related distortions can be regarded as limited. The facts presented suggest that the space–time organization of the earthquake rupture process is multiscaled and bears significant fractal features; it deviates from the brittle-crack model with its two well-separated characteristic scales. Phenomenologically, the high-frequency body-wave radiation from an earthquake source can be thought of as a product of stationary noise and the square root of a positive random envelope function with a power-law spectrum. From the viewpoint of applications, the self-similarity of body wave envelopes provides a useful constraint for earthquake source models used to simulate strong ground motions.  相似文献   

3.
It is important to evaluate the impacts of grasses on soil erosion process so as to use them effectively to control soil and water losses on the Loess Plateau. Laboratory-simulated rainfall experiments were conducted to investigate the runoff and sediment processes on sloped loess surfaces with and without the aboveground parts of grasses and moss (GAM: grass and moss; NGAM: no grass and moss) under slope gradients of 5°, 10°, 15°, 20°, 25° and 30°. The results show that runoff from GAM and NGAM plots increased up to a slope gradient of 10° and decreased thereafter, whereas the runoff coefficients increased with gradient. The average runoff rates and runoff coefficients of NGAM plots were less than those of GAM plots except for the 5° slope. This behaviour may be due to the reduction in water infiltration under moss. The difference between GAM and NGAM plots in average runoff rates varied from 1·4 to 8%. At the same gradients, NGAM plots yielded significantly (α = 0·05) more sediment than GAM plots. Average sediment deliveries for different slopes varied from 0·119 to 3·794 g m−2 min−1 from GAM plots, and from 0·765 to 16·128 g m−2 min−1 from NGAM plots. Sediment yields from GAM plots were reduced by 45 to 85%, compared with those from the NGAM plots. Plots at 30° yielded significantly higher sediments than at the other gradients. Total sediments S increased with slope gradients G in a linear form, i.e. S = 9·25G − 39·6 with R2 = 0·77*, for the GAM plots, and in an exponential model, i.e. S = 40·4 exp(0·1042G) with R2 = 0·93**, for the NGAM plots. In all cases, sediment deliveries decreased with time, and reached a relative steady state at a rainfall duration of 14 min. Compared with NGAM plots, the final percentage reductions in sediment delivery from GAM plots were higher than those at the initial time of rainfall at all slopes. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

4.
The Schmidt hammer (SH) is widely used in geomorphology for relative- and calibrated-exposure age dating surfaces and deposits within landforms. This study employs a laboratory-based methodology to assess the effects of surface roughness, clast roundness, and clast volume on SH rebound values (R-values) by analyzing samples from three modern depositional environments (i.e. river, alluvial fan, talus). Each environment contains clasts of Torlesse supergroup greywacke sandstones with distinct roundness and micro-scale roughness characteristics. Roundness, surface roughness, and clast volume were all found to influence R-values significantly. The R-values from different deposit types are statistically significant and could potentially create an apparent age divergence of several thousand years for samples with the same exposure-age. © 2020 John Wiley & Sons, Ltd.  相似文献   

5.
This software (which accompanies McCarroll and Nesje, 1996, Earth Surface Processes and Landforms Vol. 21, 963–977) is designed to quantify the roughness of rock surfaces from profiles recorded using either a micro-roughness meter or a simple profile gauge. The roughness index used is the standard deviation of the differences between adjacent height values recorded at set horizontal intervals. Profiles are assumed to be 19 cm long with heights recorded every 5 mm. The template provided assumes that four profiles are recorded from each of ten surfaces (e.g. boulders). Roughness values are calculated using (overlapping) measurement intervals of 5 mm, 10 mm, 15 mm, 20 mm, 25 mm and 30 mm. The results are tabulated and presented as ‘deviograms’ which display both the magnitude and scale of roughness. The spreadsheet used was Quattro-pro for Windows, version 1.00. © 1997 John Wiley & Sons, Ltd.  相似文献   

6.
Peatlands globally are at risk of degradation through increased susceptibility to erosion as a result of climate change. Quantification of peat erosion and an understanding of the processes responsible for their degradation is required if eroded peatlands are to be protected and restored. Owing to the unique material properties of peat, fine‐scale microtopographic expressions of surface processes are especially pronounced and present a potentially rich source of geomorphological information, providing valuable insights into the stability and dominant surface process regimes. We present a new process‐form conceptual framework to rigorously describe bare peat microtopography and use Structure‐from‐Motion (SfM) surveys to quantify roughness for different peat surfaces. Through the first geomorphological application of a survey‐grade structured‐light hand‐held 3D imager (HhI), which can represent sub‐millimetre topographic variability in field conditions, we demonstrate that SfM identifies roughness signatures reliably over bare peat plots (<1 m2), although some smoothing is observed. Across 55 plots, the roughness of microtopographic types is quantified using a suite of roughness metrics and an objective classification system derived from decision tree analysis with 98% success. This objective classification requires just five roughness metrics, each of which quantifies a different aspect of the surface morphology. We show that through a combination of roughness metrics, microtopographic types can be identified objectively from high resolution survey data, providing a much‐needed geomorphological process‐perspective to observations of eroded peat volumes and earth surface change. Copyright © 2018 John Wiley & Sons, Ltd.  相似文献   

7.
The surface roughness of agricultural soils is mainly related to the type of tillage performed, typically consisting of oriented and random components. Traditionally, soil surface roughness (SSR) characterization has been difficult due to its high spatial variability and the sensitivity of roughness parameters to the characteristics of the instruments, including its measurement scale. Recent advances in surveying have greatly improved the spatial resolution, extent, and availability of surface elevation datasets. However, it is still unknown how new roughness measurements relates with the conventional roughness measurements such as 2D profiles acquired by laser profilometers. The objective of this study was to evaluate the suitability of Terrestrial Laser Scanner (TLS) and Structure from Motion (SfM) photogrammetry techniques for quantifying SSR over different agricultural soils. With this aim, an experiment was carried out in three plots (5 × 5 m) representing different roughness conditions, where TLS and SfM photogrammetry measurements were co-registered with 2D profiles obtained using a laser profilometer. Differences between new and conventional roughness measurement techniques were evaluated visually and quantitatively using regression analysis and comparing the values of six different roughness parameters. TLS and SfM photogrammetry measurements were further compared by evaluating multi-directional roughness parameters and analyzing corresponding Digital Elevation Models. The results obtained demonstrate the ability of both TLS and SfM photogrammetry techniques to measure 3D SSR over agricultural soils. However, profiles obtained with both techniques (especially SfM photogrammetry) showed a loss of high-frequency elevation information that affected the values of some parameters (e.g. initial slope of the autocorrelation function, peak frequency and tortuosity). Nevertheless, both TLS and SfM photogrammetry provide a massive amount of 3D information that enables a detailed analysis of surface roughness, which is relevant for multiple applications, such as those focused in hydrological and soil erosion processes and microwave scattering. © 2019 John Wiley & Sons, Ltd.  相似文献   

8.
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9.
Soil surface roughness is a dynamic property which determines, to a large extent, erosion and infiltration rates. Although soils containing rock fragments are widespread in the Mediterranean region, the effect of the latter on surface roughness evolution is yet poorly understood. Therefore, laboratory experiments were conducted in order to investigate the effect of rock fragment content, rock fragment size and initial moisture content of the fine earth on the evolution of interrill surface roughness during simulated rainfall. Surface elevations of simulated plough layers along transects of 50 cm length were measured before and after simulated rainfall (totalling 192.5 mm, I = 70 mm h−1) with a laser microreliefmeter. The results were used to investigate whether systematic variations in interrill surface roughness along stony hillslopes in southeastern Spain could be attributed to rock fragment cover and rock fragment size. Soil surface elevations were measured along the contour lines (50 cm long transects) with a contact microreliefmeter. Roughness was expressed by two parameters related to the height and frequency of roughness elements, respectively: standard deviation of de-trended surface elevations (random roughness: RR), and correlation length (L) derived from exponential fits of the autocorrelation functions. The frequently used assumption that surface roughness (RR) of cultivated topsoils decreases exponentially with cumulative rain is not valid for soil surfaces covered by rock fragments. The RR of soils containing small rock fragments (1.7–2.7 cm) increased with cumulative rainfall after an initial decrease during the first 17.5 mm of rainfall. For soils containing large rock fragments (7.7 cm), RR increased with rainfall above a threshold rock fragment content by mass of 52 per cent. For a given rainfall application, RR increased non-linearly with rock fragment content. The correlation length for soils containing small rock fragments decreases with rock fragment content and is significantly lower than for soils with large rock fragments. Soils covered with small rock fragments (large RR and small L) are thus well protected against raindrop impact by a water film in the depressions between the rock fragments. On abandoned agricultural fields along hillslopes in southeastern Spain, rock fragments cover increases non-linearly with slope owing to selective erosion of finer particles on steep slopes. The increase of surface cover by large rock fragments (>25 mm) is even more pronounced. The simultaneous increase of rock fragment cover and rock fragment size with slope explains the non-linear increase of RR with slope. These relationships differ for soils covered by platy misaschists and those covered with cubic andesites. The variations in correlation length along the hillslopes are not clear, probably owing to a simultaneous increase in rock fragment cover and rock fragment size. These findings may provide a better prediction of soil surface roughness of interrill areas covered by rock fragments using slope angle and lithology.  相似文献   

10.
Fractals in geology and geophysics   总被引：21，自引：0，他引：21  
The definition of a fractal distribution is that the number of objectsN with a characteristic size greater thanr scales with the relationNr –D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. Fractals were originally introduced by Mandelbrot to relate the length of a coastline to the length of the measuring stick. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photographs of many geological features is one indication of the wide applicability of scale invariance to geological problems, scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.  相似文献   

11.
The effects of grid-size modification on the derived topographic attributes are analysed and a procedure for scaling model parameters and similarity assessment between flow variables is proposed. Hydrological simulations are performed with a physically-based and spatially-distributed quasi-2D mathematical model. The scaled model parameters are the effective roughness coefficient associated with overland flow (nov) and the transverse slope in the cell (TSC). To scale the selected parameters, the criterion of equilibrium storage conservation between the different grid sizes is applied. Three basins of the central-east region of Argentina are modelled. The spatial variability of basin geomorphology is quantified using the entropy concept. The simulation results show that when grid size is increased, to obtain similar hydrological responses it is necessary to increase the nov or to reduce the TSC. In terms of similarity, the best results are achieved when TSC is scaled, particularly when water depths are considered.  相似文献   

12.
Flow resistance in mountain streams is important for assessing flooding hazard and quantifying sediment transport and bedrock incision in upland landscapes. In such settings, flow resistance is sensitive to grain-scale roughness, which has traditionally been characterized by particle size distributions derived from laborious point counts of streambed sediment. Developing a general framework for rapid quantification of resistance in mountain streams is still a challenge. Here we present a semi-automated workflow that combines millimeter- to centimeter-scale structure-from-motion (SfM) photogrammetry surveys of bed topography and computational fluid dynamics (CFD) simulations to better evaluate surface roughness and rapidly quantify flow resistance in mountain streams. The workflow was applied to three field sites of gravel, cobble, and boulder-bedded channels with a wide range of grain size, sorting, and shape. Large-eddy simulations with body-fitted meshes generated from SfM photogrammetry-derived surfaces were performed to quantify flow resistance. The analysis of bed microtopography using a second-order structure function identified three scaling regimes that corresponded to important roughness length scales and surface complexity contributing to flow resistance. The standard deviation σz of detrended streambed elevation normalized by water depth, as a proxy for the vertical roughness length scale, emerges as the primary control on flow resistance and is furthermore tied to the characteristic length scale of rough surface-generated vortices. Horizontal length scales and surface complexity are secondary controls on flow resistance. A new resistance predictor linking water depth and vertical roughness scale, i.e.  H/σz, is proposed based on the comparison between σz and the characteristic length scale of vortex shedding. In addition, representing streambeds using digital elevation models (DEM) is appropriate for well-sorted streambeds, but not for poorly sorted ones under shallow and medium flow depth conditions due to the missing local overhanging features captured by fully 3D meshes which modulate local pressure gradient and thus bulk flow separation and pressure distribution. An appraisal of the mesh resolution effect on flow resistance shows that the SfM photogrammetry data resolution and the optimal CFD mesh size should be about 1/7 to 1/14 of the standard deviation of bed elevation. © 2019 John Wiley & Sons, Ltd.  相似文献   

13.
Knickpoint behaviour is a key to understanding both the landscape responses to a base‐level fall and the corresponding sediment fluxes from rejuvenated catchments, and must be accommodated in numerical models of large‐scale landscape evolution. Knickpoint recession in streams draining to glacio‐isostatically uplifted shorelines in eastern Scotland is used to assess whether knickpoint recession is a function of discharge (here represented by its surrogate, catchment area). Knickpoints are identified using DS plots (log slope versus log downstream distance). A statistically significant power relationship is found between distance of headward recession and catchment area. Such knickpoint recession data may be used to determine the values of m and n in the stream power law, E = KAmSn. The data have too many uncertainties, however, to judge definitively whether they are consistent with m = n = 1 (bedrock erosion is proportional to stream power and KPs should be maintained and propagate headwards) or m = 0·3, n = 0·7 (bedrock incision is proportional to shear stress and KPs do not propagate but degrade in place by rotation or replacement). Nonetheless, the E Scotland m and n values point to the dominance of catchment area (discharge) in determining knickpoint retreat rates and are therefore more consistent with the stream power law formulation in which bedrock erosion is proportional to stream power. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

14.
This paper has introduced the method of self-similarity analysis of time series into the analysis and study of earthquake sequence, and then researched its application in earthquake prediction. As parameter of earthquake time series, we can take the cumulated sum of the numbers of equivalent earthquakesQ=ΣN*, the numbers of equivalent earthquakeN*, maximum magnitudeM max, average magnitudeQ=ΣN*, and the difference ΔN* between the numbersN* in two adjacent time intervals. The given method may be applied to analysis of long-period seismic sequences in different regions as well as to anlysis of seismic sequence in the aftershock region of strong earthquake. For making quantitative analysis the coefficient of self-similarity of earthquake sequence in order of timeμs was introduced. The results of self-similarity analysis were obtained for the earthquake sequences in North China, West South China, the Capital region of China, and for the East Yamashi region of Japan. They show that in period or half year to several years beforeM⩾7.0 andM⩾6.0 earthquakes occurred in these regions separately, the self-similarity coefficientμs calculated by using the above-mentioned parameters had remarkably anamalous decrease variations. The duration time ofμs anomaly depends on the earthquake magnitude and may be different from different regions. Therefore, the self-similarity coefficient in order of timeμs can be considered as a long-medium term precursory index. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 455–462, 1993.  相似文献   

15.
Talus slopes are common places for debris storage in high-mountain environments and form an important step in the alpine sediment cascade. To understand slope instabilities and sediment transfers, detailed investigations of talus slope geomorphology are needed. Therefore, this study presents a detailed analysis of a talus slope on Col du Sanetsch (Swiss Alps), which is investigated at multiple time scales using high-resolution topographic (HRT) surveys and historical aerial photographs. HRT surveys were collected during three consecutive summers (2017–2019), using uncrewed aerial vehicle (UAV) and terrestrial laser scanning (TLS) measurements. To date, very few studies exist that use HRT methods on talus slopes, especially to the extent of our study area (2 km2). Data acquisition from ground control and in situ field observations is challenging on a talus slope due to the steep terrain (30–37°) and high surface roughness. This results in a poor spatial distribution of ground control points (GCPs), causing unwanted deformation of up to 2 m in the gathered UAV-derived HRT data. The co-alignment of UAV imagery from different survey dates improved this deformation significantly, as validated by the TLS data. Sediment transfer is dominated by small-scale but widespread snow push processes. Pre-existing debris flow channels are prone to erosion and redeposition of material within the channel. A debris flow event of high magnitude occurred in the summer of 2019, as a result of several convective thunderstorms. While low-magnitude (<5,000 m3) debris flow events are frequent throughout the historical record with a return period of 10–20 years, this 2019 event exceeded all historical debris flow events since 1946 in both extent and volume. Future climate predictions show an increase of such intense precipitation events in the region, potentially altering the frequency of debris flows in the study area and changing the dominant geomorphic process which are active on such talus slopes. © 2020 John Wiley & Sons, Ltd.  相似文献   

16.
Sections up to 3·5 m deep cut through the upper rectilinear segment of relict, vegetated talus slopes at the foot of the Trotternish escarpment reveal stacked debris-flow deposits intercalated with occasional slopewash horizons and buried organic soils. Radiocarbon dating of buried soil horizons indicates that reworking of sediment by debris flows predates 5·9–5·6 Cal ka BP , and has been intermittently active throughout the late Holocene. Particle size analyses of 18 bulk samples from these units indicates that c. 27–30 per cent of the talus deposit is composed of fine (<2 mm) sediment. Sedimentological comparison with tills excludes a glacigenic origin for the talus debris, and the angularity of constituent clasts suggests that in situ weathering has been insignificant in generating fine material. We conclude that the fine sediment within the talus is derived primarily by granular weathering of the rockwall, with syndepositional accumulation of both fine and coarse debris, implying that c. 27–30 per cent of rockwall retreat since deglaciation reflects granular weathering rather than rockfall. The abundance of fines within the talus deposits is inferred to have been of critical importance in facilitating build-up of porewater pressures during rainstorms, leading to episodic failure and flow of debris on the upper parts of the slope. A wider implication of these findings is that the mechanical properties of talus slopes cannot be regarded as those of free-draining accumulations of coarse clasts, and that models that treat talus slopes as such have limited value in explaining their form and evolution. Our findings lend support to models that envisage the upper straight slope on talus accumulations as the product of mass-transport as well as rockfall, and indicate that episodic debris flow has been the primary agent of mass-transport at this site. © 1998 John Wiley & Sons, Ltd.  相似文献   

17.
In this work, we study groundwater system temporal scaling in relation to plant water use and near‐river‐stage fluctuations in riparian zones where phreatophytes exist. Using detrended fluctuation analysis (DFA), we investigate the influence of regular diurnal fluctuations due to phreatophyte water use on temporal scaling properties of groundwater level variations. We found that groundwater use by phreatophytes, at the field site on the Colorado River, USA, results in distinctive crossovers (slope changes when the plots are fitted with straight lines) in the logarithm plots of root‐mean‐square fluctuations of the detrended water level time series versus time scales of groundwater level dynamics. For groundwater levels monitored at wells close to the river, we identified one crossover at ～1 day in the scaling characteristics of groundwater level variations. When time scale exceeds 1 day, the scaling properties decrease from persistent to close to 1/f noise, where f is the frequency. For groundwater levels recorded at wells further away from the river, the slope of the straight line fit (i.e. scaling exponent) is smallest when the time scale is between 1 and 3 days. When the time scale is < 1 day, groundwater variations become persistent. When the time scale is between 1 and 3 days, the variations are close to white noise, but return to persistent when the time scale is > 3 days. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

18.
Mingguo Zheng  Runkui Li  Jijun He 《水文研究》2015,29(26):5414-5423
Information is scarce on the spatial‐scale effect on sediment concentrations in run‐off. This study addressed this issue within an agricultural subwatershed of the Chinese Loess Plateau, using data observed at a hilltop plot, three nested hillslope plots, two entire‐slope plots (a combination of hillslope and valley side slope) and the subwatershed outlet. Dominated by the splash and sheet erosions, the hilltop plot has a minimum Cae (mean sediment concentration for all recorded events) of 45 kg m?3. Unexpectedly, the high sediment concentrations at the hilltop do not occur at high rainfall intensities or large run‐off events because of the protection of surface soils by relatively thick sheet flows. Because of the emergence of rills, Cae is as high as 310 kg m?3 even on the most upper hillslope. Downslope, both Cae and ESC (extreme large values of recorded sediment concentrations) increase; such a slope length effect attenuates with increasing slope length and event magnitude as a result of insufficient sediment availability associated with rill development. Active mass wastings ensure sufficient sediment supply and thus a spatially invariant Cae (approximately 700 kg m?3) and ESC (approximately 1000 kg m?3) at the scale of the entire slope and subwatershed. Detailed examination shows that most small events experience a decrease in sediment concentrations when moving from the entire slope to the subwatershed, indicating that the spatially invariant sediment concentration is valid only for large run‐off events. This study highlights the control of the spatial scale, which determines the dominant erosional process, on erosional regime. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

19.
Abstract

This study proposes a preliminary method for coding random self-similar river networks as a series of numbers, and investigates the corresponding algorithm that calculates the geometric distances from the code series. The coding method, generating random self-similar patterns with various probabilities of particular pattern links, and transferring the pattern into numerical code series, is proposed, based on the wide range of stochastic characteristics of natural patterns. The heredity of self-similarity and the connecting relationships inside the generated pattern are discussed. Finally, the algorithm to calculate the geometric distances of the generated pattern are developed.  相似文献   

20.
Faulting that results in surface ruptures through bedrock can be particularly difficult to date. For example, stratigraphic control on the age of faulting, based on the age of the bedrock, often leaves unacceptably large uncertainty on the age of the faulting. From a paleoseismological perspective, there is a clear need to determine if a bedrock fault scarp is actually a young feature. For young fault ruptures that create fresh mineral surfaces, analysis of microtopography developed by weathering of the mineral surface may provide a quantifiable method for determining the fault age. The direct quantitative measurement of mineral surface microtopography using Atomic Force Microscopy affords a novel method to study the rupture ages of active faults. The method for using microtopographic evolution of mineral surfaces depends on three conditions. The first condition is that freshly exposed mineral cleavage surfaces, which can be described geometrically as planes, are formed during a rupture event. The formation of these fresh surfaces is analogous to the initiation of a weathering ‘clock’ that defines time t=0. Following cleavage formation dissolution of the planar mineral surface occurs. The rate of dissolution for a mineral species under given climatic conditions, governs the rate of mineral surface alteration. Thus as dissolution proceeds, the roughness of the mineral surface increases. We suggest that the progression of microtopographic roughness over time, which can be estimated by computing quantitative statistics derived from digital mineral surface topography, will systematically vary until a steady state surface topography is reached. The fractal dimension, Df, is one such measure of surface roughness where, Df at time t=0 is 2. The dissolution of the mineral surface increases the fractal dimension as the removal of material proceeds. We posit that somewhere between Df=2 and Df=3, the microtopography reaches a steady state. Therefore, in the pre-steady state stage of surface roughness, the quantitative measure of roughness of the mineral may serve as a measure of time elapsed since faulting. The period of time this initial stage of surface roughening represents is dependent on the mineral and as a consequence, its dissolution rate, in a specific set of environmental conditions. The time elapsed since fault rupture and grain cleavage can also be estimated from the measurement of the volume of material removed through dissolution. If part of the original cleavage surface remains and can be identified then AFM measurements of the surface microtopography can be used to calculate the dissolved volume per unit area.  相似文献   

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