Quantifying weathering on variable rocks,an extension of geochemical mass balance: Critical zone and landscape evolution

We present a statistical model of soil and rock weathering in deep profiles to expand the capacity to assess weathering to heterogeneous bedrock types, which are common at the Earth's surface. We developed the Weathering Trends (WT) model by extending the fractional mass change calculation (tau) of the geochemical mass balance model in two important ways. First, WT log transforms the elemental ratio data, to discern the log‐linear patterns that naturally develop from thermodynamic and kinetic laws of chemistry. Second, WT statistically fits log‐transformed element concentration ratio data – log(c_j/c_i), the only depth‐varying term in tau – as a function of depth to determine characteristic depths of transitions in weathering processes, along with confidence intervals. With no prior assumptions, WT estimates average parent material composition, average composition of the upper weathered zone and mean fractional mass change of each element over the entire weathering profile. WT displays the mean shape of weathering profiles of log‐transformed geochemical data bounded by calculated confidence intervals. We share the WT model code as an open‐source R package ( https://github.com/fisherba/WeatheringTrends ). The WT model was designed to interpret two 21 m cores from the Laurels Schist bedrock in the Christina River Basin Critical Zone Observatory in the Pennsylvania Piedmont, where our morphological and elemental data provided inconclusive estimates of bedrock depth. The WT model differentiated between rock variability and weathering to delineate the maximum extent of weathering at 12.3 m (CI 95% [9.2, 21.3]) in Ridge Well 1 and 7.2 m (CI 95% [4.3, 13.0]) in Interfluve Well 2. The water table was 5–8 m below fresh rock at Ridge Well 1, but at the same depth as fresh rock at the lower elevation interfluve. We assess statistical approaches to identify the best immobile element for use in WT and tau calculations. Copyright © 2017 John Wiley & Sons, Ltd.     

The critical role of climate and saprolite weathering in landscape evolution

Landscapes evolve in response to external forces, such as tectonics and climate, that influence surface processes of erosion and weathering. Internal feedbacks between erosion and weathering also play an integral role in regulating the landscapes response. Our understanding of these internal and external feedbacks is limited to a handful of field‐based studies, only a few of which have explicitly examined saprolite weathering. Here, we report rates of erosion and weathering in saprolite and soil to quantify how climate influences denudation, by focusing on an elevation transect in the western Sierra Nevada Mountains, California. We use an adapted mass balance approach and couple soil‐production rates from the cosmogenic radionuclide (CRN) ¹⁰Be with zirconium concentrations in rock, saprolite and soil. Our approach includes deep saprolite weathering and suggests that previous studies may have underestimated denudation rates across similar landscapes. Along the studied climate gradient, chemical weathering rates peak at middle elevations (1200–2000 m), averaging 112·3 ± 9·7 t km^–2 y^–1 compared to high and low elevation sites (46·8 ± 5·2 t km^?2 y^?1). Measured weathering rates follow similar patterns with climate as those of predicted silica fluxes, modeled using an Arrhenius temperature relationship and a linear relationship between flux and precipitation. Furthermore, chemical weathering and erosion are tightly correlated across our sites, and physical erosion rates increase with both saprolite weathering rates and intensity. Unexpectedly, saprolite and soil weathering intensities are inversely related, such that more weathered saprolites are overlain by weakly weathered soils. These data quantify exciting links between climate, weathering and erosion, and together suggest that climate controls chemical weathering via temperature and moisture control on chemical reaction rates. Our results also suggest that saprolite weathering reduces bedrock coherence, leading to faster rates of soil transport that, in turn, decrease material residence times in the soil column and limit soil weathering. Copyright © 2009 John Wiley & Sons, Ltd.     

Geophysical constraints on deep weathering and water storage potential in the Southern Sierra Critical Zone Observatory

The conversion of bedrock to regolith marks the inception of critical zone processes, but the factors that regulate it remain poorly understood. Although the thickness and degree of weathering of regolith are widely thought to be important regulators of the development of regolith and its water‐storage potential, the functional relationships between regolith properties and the processes that generate it remain poorly documented. This is due in part to the fact that regolith is difficult to characterize by direct observations over the broad scales needed for process‐based understanding of the critical zone. Here we use seismic refraction and resistivity imaging techniques to estimate variations in regolith thickness and porosity across a forested slope and swampy meadow in the Southern Sierra Critical Zone Observatory (SSCZO). Inferred seismic velocities and electrical resistivities image a weathering zone ranging in thickness from 10 to 35 m (average = 23 m) along one intensively studied transect. The inferred weathering zone consists of roughly equal thicknesses of saprolite (P‐velocity < 2 km s^?1) and moderately weathered bedrock (P‐velocity = 2–4 km s^?1). A minimum‐porosity model assuming dry pore space shows porosities as high as 50% near the surface, decreasing to near zero at the base of weathered rock. Physical properties of saprolite samples from hand augering and push cores are consistent with our rock physics model when variations in pore saturation are taken into account. Our results indicate that saprolite is a crucial reservoir of water, potentially storing an average of 3 m³ m^?2 of water along a forested slope in the headwaters of the SSCZO. When coupled with published erosion rates from cosmogenic nuclides, our geophysical estimates of weathering zone thickness imply regolith residence times on the order of 10⁵ years. Thus, soils at the surface today may integrate weathering over glacial–interglacial fluctuations in climate. Copyright © 2013 John Wiley & Sons, Ltd.     

Field evidence for the influence of weathering on rock erodibility and channel form in bedrock rivers

Erosion processes in bedrock‐floored rivers shape channel cross‐sectional geometry and the broader landscape. However, the influence of weathering on channel slope and geometry is not well understood. Weathering can produce variation in rock erodibility within channel cross‐sections. Recent numerical modeling results suggest that weathering may preferentially weaken rock on channel banks relative to the thalweg, strongly influencing channel form. Here, we present the first quantitative field study of differential weathering across channel cross‐sections. We hypothesize that average cross‐section erosion rate controls the magnitude of this contrast in weathering between the banks and the thalweg. Erosion rate, in turn, is moderated by the extent to which weathering processes increase bedrock erodibility. We test these hypotheses on tributaries to the Potomac River, Virginia, with inferred erosion rates from ~0.1 m/kyr to >0.8 m/kyr, with higher rates in knickpoints spawned by the migratory Great Falls knickzone. We selected nine channel cross‐sections on three tributaries spanning the full range of erosion rates, and at multiple flow heights we measured (1) rock compressive strength using a Schmidt hammer, (2) rock surface roughness using a contour gage combined with automated photograph analysis, and (3) crack density (crack length/area) at three cross‐sections on one channel. All cross‐sections showed significant (p < 0.01 for strength, p < 0.05 for roughness) increases in weathering by at least one metric with height above the thalweg. These results, assuming that the weathered state of rock is a proxy for erodibility, indicate that rock erodibility varies inversely with bedrock inundation frequency. Differences in weathering between the thalweg and the channel margins tend to decrease as inferred erosion rates increase, leading to variations in channel form related to the interplay of weathering and erosion rate. This observation is consistent with numerical modeling that predicts a strong influence of weathering‐related erodibility on channel morphology. Copyright © 2017 John Wiley & Sons, Ltd.     

Weathering,erosion and sediment composition in a high‐gradient river,Calabria, Italy

Source rock lithology and immediate modifying processes, such as chemical weathering and mechanical erosion, are primary controls on fluvial sediment supply. Sand composition and Chemical Index of Alteration (CIA) of parent rocks, soil and fluvial sand of the Savuto River watershed, Calabria (Italy), were used to evaluate the modifications of source rocks through different sections of the basin, characterized by different geomorphic processes, in a sub‐humid Mediterranean climate. The headwaters, with gentle topography, produce a coarse‐grained sediment load derived from deeply weathered gneiss, having sand of quartzofeldspathic composition, compositionally very different from in situ degraded bedrock. Maximum estimated CIA values suggest that source rock has been affected significantly by weathering, and it testifies to a climatic threshold on the destruction of the bedrock. The mid‐course has steeper slopes and a deeply incised valley; bedrock consists of mica‐schist and phyllite with a very thin regolith, which provides large cobble to very coarse sand sediments to the main channel. Slope instability, with an areal incidence of over 40 per cent, largely supplies detritus to the main channel. Sand‐sized detritus of soil and fluvial sand is lithic. Estimated CIA value testifies to a significant weathering of the bedrock too, even if in this part of the drainage basin steeper slopes allow erosion to exceed chemical weathering. The lower course has a braided pattern and sediment load is coarse to medium–fine grained. The river cuts across Palaeozoic crystalline rocks and Miocene siliciclastic deposits. Sand‐sized detritus, contributed from these rocks and homogenized by transport processes, has been found in the quartzolithic distal samples. Field and laboratory evidence indicates that landscape development was the result of extensive weathering during the last postglacial temperature maximum in the headwaters, and of mass‐failure and fluvial erosional processes in the mid‐ and low course. Copyright © 2000 John Wiley & Sons, Ltd.     

Spatial Variability of the Depth of Weathered and Engineering Bedrock using Multichannel Analysis of Surface Wave Method

In this paper an attempt has been made to evaluate the spatial variability of the depth of weathered and engineering bedrock in Bangalore, south India using Multichannel Analysis of Surface Wave (MASW) survey. One-dimensional MASW survey has been carried out at 58 locations and shear-wave velocities are measured. Using velocity profiles, the depth of weathered rock and engineering rock surface levels has been determined. Based on the literature, shear-wave velocity of 330 ± 30 m/s for weathered rock or soft rock and 760 ± 60 m/s for engineering rock or hard rock has been considered. Depths corresponding to these velocity ranges are evaluated with respect to ground contour levels and top surface levels have been mapped with an interpolation technique using natural neighborhood. The depth of weathered rock varies from 1 m to about 21 m. In 58 testing locations, only 42 locations reached the depths which have a shear-wave velocity of more than 760 ± 60 m/s. The depth of engineering rock is evaluated from these data and it varies from 1 m to about 50 m. Further, these rock depths have been compared with a subsurface profile obtained from a two-dimensional (2-D) MASW survey at 20 locations and a few selected available bore logs from the deep geotechnical boreholes.     

Application of HVSR to estimating thickness of laterite weathering profiles in basalt

Lateritic weathering profiles (LWPs) are widespread in the tropics and comprise an important component of the Critical Zone (CZ). The Hawaiian Islands make an excellent natural laboratory for examining the tropical CZ, where the bedrock composition (basalt) is nearly uniform and rainfall varies greatly. This natural laboratory is employed to assess the utility of the HVSR (horizontal/vertical spectral ratio) method to characterize the shear-wave velocity (V_s) structure of LWPs, particularly the depth to the contact between saprolite and basalt bedrock. LWP thicknesses determined from HVSR provide good agreement with multi-channel analysis of surface waves (MASW) profiles, well logs and outcrop. LWP thicknesses may be estimated from the fundamental mode equation or through forward models. Prior knowledge about the subsurface from well, outcrop, and MASW profiles may greatly aid modeling in some cases. For the 3.2 to 1.8 Ma Koolau Volcano on Oahu, the downward rate of advance of the weathering front varies from 0.004 to 0.041 m/ka. For the 0.44 to 0.10 Ma Kohala Volcano (Big Island of Hawaii) rates vary from 0.013 to 0.047 m/ka. Simple H/V spectra develop in areas where the combined effects of time and elevated rainfall produce thick LWPs with a flat base and a general absence of core stones with an ideal layered geometry. Abundant buried core stones violate the assumption of simple layered geometries and scatter acoustic energy, leading to uninterpretable results. This is common where low rainfall and a young basaltic substrate leave abundant core stones as well as an undulating contact between saprolite and bedrock. Velocity inversions (high V_s intervals within low V_s saprolite) may also be present and originate from relatively intact bedrock horizons or mineralogical changes within saprolite. At Kohala, a gibbsite-rich horizon produces such a velocity inversion due to enhanced weathering and subsequent collapse of saprolite in a discrete horizon. © 2019 John Wiley & Sons, Ltd.     

A METHOD OF WEATHERING CORRECTION *

In western Canada, the near surface weathered zone has variable velocity and is underlain by more uniform subweathering material. The uphole time is often used to compensate for the weathered zone, but there are limitations to its use. A method is proposed using the refraction delay time which is exactly proportional to the weathering correction time for several commonly assumed weathering velocity functions. The method does not require accurate determination of velocities or weathering depth nor even the depth of shot, yet is theoretically exact. A strip off time t_r is used to replace the weathered zone mathematically with high velocity material where t_r= zD/F, where D is the delay time and F the Blondeau factor. An algorithm using first break times is proposed that is amenable to computer use for determining D for each geophone point. F might be constant in some areas but is more likely a variable to be solved in an automatic static program. Thus, structure and residual statics can be handled at once.     

Tafoni on coastal slopes,South Devon,U.K.

Cavernous weathering (tafoni development) occurs on coastal slopes in greenschist bedrock at elevations up to 40 m above sea level. The freshly weathered surfaces of the cavern interiors are irregular in morphology, discordant to major rock structure, formed by substantially weakened rock and associated with granular weathering debris. The weathering debris contains soluble elements in proportions similar to those present in seawater, and the penetration of elements associated with sea salts into the weathering surface to estimated depths of at least 0·1–0·2 m is indicated by the presence of chlorine. Scanning electron microscopy and microprobe analyses suggest that rock breakdown occurs principally through limited chemical weathering at grain boundaries. The mechanism for the emplacement of marine salts within sheltered rock surfaces in the tafoni is postulated to be a combination of dry deposition under turbulent atmospheric conditions and wetting by coastal fog.     

Bedrock erosion due to hoeing as tillage technique in a hilly agricultural landscape,southwest China

Tillage on hillslopes may not only induce severe soil erosion, but may also cause bedrock erosion under certain conditions. Yet, little is known about bedrock erosion by tillage in a hilly agricultural landscape, southwest China. The aim of this study is to quantify the translocation of rock fragments derived from bedrock fragmentation by hoeing under different conditions, including slope gradient, hoeing depth and soil-covered thickness using a gravel tracing method. The reliability of the gravel tracing method was confirmed by the bedrock dyeing tracing method. Hoeing depth is a significant factor affecting the translocation rate of rock fragments (Q_r ). Meanwhile, under the condition of overlying soil layers (0.06−0.10 m thick), the values of Q_r were significantly smaller with a reduction of 20.7−25.6%, compared with rock fragmentation by hoeing for bare bedrock. However, slope gradient was found to have insignificant effects on Q_r . Fractured bedrock moved as individual small fragments, which was mainly controlled by the hitting force of the hoe, while soil moved in the shape of lumps, which was dominated by both drag force of the hoe and gravity. This study suggests that hoeing into soil-covered bedrock can diminish bedrock erosion while providing soil matrix for shallow soil layers. Our work presents a quantitative assessment of bedrock erosion by hoeing and an underlying insight into characteristics of bedrock erosion by tillage operations in hilly agricultural regions with mudstone and shale, southwest China. © 2020 John Wiley & Sons, Ltd.     

Soil characterization of Tınaztepe region (İzmir/Turkey) using surface wave methods and nakamura (HVSR) technique

To determine the shear wave velocity structure and predominant period features of T?naztepe in ?zmir, Turkey, where new building sites have been planned, active–passive surface wave methods and single-station microtremor measurements are used, as well as surface acquisition techniques, including the multichannel analysis of surface waves (MASW), refraction microtremor (ReMi), and the spatial autocorrelation method (SPAC), to pinpoint shallow and deep shear wave velocity. For engineering bedrock (V _s > 760 m/s) conditions at a depth of 30 m, an average seismic shear wave velocity in the upper 30 m of soil (AV_s30) is not only accepted as an important parameter for defining ground behavior during earthquakes, but a primary parameter in the geotechnical analysis for areas to be classified by V _s30 according to the National Earthquake Hazards Reduction Program (NEHRP). It is also determined that Z1.0, which represents a depth to V _s = 1000 m/s, is used for ground motion prediction and changed from 0 to 54 m. The sediment–engineering bedrock structure for T?naztepe that was obtained shows engineering bedrock no deeper than 30 m. When compared, the depth of engineering bedrock and dominant period map and geology are generally compatible.     

A low‐dimensional model of bedrock weathering and lateral flow coevolution in hillslopes: 1. Hydraulic theory of reactive transport

This is the first of a two‐part paper exploring the coevolution of bedrock weathering and lateral flow in hillslopes using a simple low‐dimensional model based on hydraulic groundwater theory (also known as Dupuit or Boussinesq theory). Here, we examine the effect of lateral flow on the downward fluxes of water and solutes through perched groundwater at steady state. We derive analytical expressions describing the decline in the downward flux rate with depth. Using these, we obtain analytical expressions for water age in a number of cases. The results show that when the permeability field is homogeneous, the spatial structure of water age depends qualitatively on a single dimensionless number, Hi. This number captures the relative contributions to the lateral hydraulic potential gradient of the relief of the lower‐most impermeable boundary (which may be below the weathering front within permeable or incipiently weathered bedrock) and the water table. A “scaled lateral symmetry” exists when Hi is low: age varies primarily in the vertical dimension, and variations in the horizontal dimension x almost disappear when the vertical dimension z is expressed as a fraction z/H(x) of the laterally flowing system thickness H(x). Taking advantage of this symmetry, we show how the lateral dimension of the advection–diffusion‐reaction equation can be collapsed, yielding a 1‐D vertical equation in which the advective flux downward declines with depth. The equation holds even when the permeability field is not homogeneous, as long as the variations in permeability have the same scaled lateral symmetry structure. This new 1‐D approximation is used in the accompanying paper to extend chemical weathering models derived for 1‐D columns to hillslope domains.     

Investigations regarding Alpine talus slopes using ground‐penetrating radar (GPR) in the Bavarian Alps,Germany

The applicability of ground‐penetrating radar (GPR) for the investigation of loose debris was tested at two sites (Viererkar and Zugspitzplatt). A pulseEKKO 100 GPR system equipped with 25 MHz antennae was utilized. The aim of the investigation was to record the base of the debris layer, and thereby acquire an estimation of the backweathering rates of the adjacent rockwalls. The study areas are situated in the Northern Alps near the German–Austrian border. The sites are characterized by steep limestone rockwalls and extensive talus accumulations. A total of six profiles was surveyed. The method is suitable and effective for a quick survey in this dry, high‐ohmic substrate. The GPR system was able to deliver information about the subsurface stratigraphy to c. 70 m depth. The boundary line to the bedrock was discovered – depending upon the profile surveyed ?5 to 25 m below the surface. The base of the debris material sometimes shows no distinct reflection. Buried features (V‐shaped furrows, zones overdeepened by ice action, geological structures) could be detected. Arched structures well below the talus–bedrock interface can be interpreted as drainage systems in the karstic bedrock. A thick scree layer of Late Glacial age was separated from a thinner layer on the talus surface, which was related to the Holocene. The backweathering rates were fixed by a calculation of talus volume to c. 100 mm/10³ a during the Holocene (Viererkar) and 150–300 mm/10³ a (Zugspitzplatt). The detrital formation in north‐exposed sites is twice as intense as in south‐exposed sites. These results match the rates of recent rockfall in the same area of investigation. The calculated backweathering for the late glacial period is 150–730 mm/10³ a. The magnitude of the calculated rockwall retreat lies well within the range of previous measurements. The discrepancy between some weathering rates highlights the fact that recent and past relief formation must be differentiated. Otherwise recent removal rates may be overestimated. Copyright © 2001 John Wiley & Sons, Ltd.     

The spatial variation of weathering and soil depth across a Triassic sandstone outcrop

In this study, we used an archive of borehole logs from the British Geological Survey to collect information on the spatial structure of weathering that extends from the surface to competent bedrock across the Triassic Sherwood Sandstone Group outcrop (750 km²), in the East Midlands, UK. The borehole logs were used to estimate the thickness of the soil (n = 280) and soil and saprolite (S&S) to competent rock (n = 500). The weathering profile of the sandstone consisted of soil (median thickness ～ 1·5 m) overlying a transition zone of compacted and weakly cemented weathered sandstone saprolite over bedrock. Topographic analysis using a NEXTMAP 5 m × 5 m digital elevation model (DEM) revealed no significant relationships between slope properties (relief, flow length, flow accumulation or slope angle) and soil or S&S thickness. A weak, but statistically significant correlation was found between the thickness of the soil and S&S (r_s = 0·25, p < 0·001, n = 192). The variation in soil thickness may be related to changes in current and historic and land‐use, variation in sandstone properties and the influence of glacial/peri‐glacial processes. The thickness of the saprolite was more variable towards the southern part of the study area, where it increased to a maximum 40 m. We hypothesize and provide evidence that the greater weathering thickness is related to the occurrence of increased faulting in this part of the study region, allowing increased access to meteoric waters. A possible source of increased water supply is meltwater from Quaternary ice sheets; the overburden of ice may have increased sub‐glacial pore water pressure, with the fractures and faults acting as a drainage system for the removal of dissolved weathering products. British Geological Survey © NERC 2010     

A low‐dimensional model of bedrock weathering and lateral flow coevolution in hillslopes: 2. Controls on weathering and permeability profiles,drainage hydraulics,and solute export pathways

The advance of a chemical weathering front into the bedrock of a hillslope is often limited by the rate weathering products that can be carried away, maintaining chemical disequilibrium. If the weathering front is within the saturated zone, groundwater flow downslope may affect the rate of transport and weathering—however, weathering also modifies the rock permeability and the subsurface potential gradient that drives lateral groundwater flow. This feedback may help explain why there tends to be neither “runaway weathering” to great depth nor exposed bedrock covering much of the earth and may provide a mechanism for weathering front advance to keep pace with incision of adjacent streams into bedrock. This is the second of a two‐part paper exploring the coevolution of bedrock weathering and lateral flow in hillslopes using a simple low‐dimensional model based on hydraulic groundwater theory. Here, we show how a simplified kinetic model of 1‐D rock weathering can be extended to consider lateral flow in a 2‐D hillslope. Exact and approximate analytical solutions for the location and thickness of weathering within the hillslope are obtained for a number of cases. A location for the weathering front can be found such that lateral flow is able to export weathering products at the rate required to keep pace with stream incision at steady state. Three pathways of solute export are identified: “diffusing up,” where solutes diffuse up and away from the weathering front into the laterally flowing aquifer; “draining down,” where solutes are advected primarily downward into the unweathered bedrock; and “draining along,” where solutes travel laterally within the weathering zone. For each pathway, a different subsurface topography and overall relief of unweathered bedrock within the hillslope is needed to remove solutes at steady state. The relief each pathway requires depends on the rate of stream incision raised to a different power, such that at a given incision rate, one pathway requires minimal relief and, therefore, likely determines the steady‐state hillslope profile.     

Subsurface architecture of the Boulder Creek Critical Zone Observatory from electrical resistivity tomography

The architecture of the critical zone includes the distribution, thickness, and contacts of various types of slope deposits and weathering products such as saprolite and weathered bedrock resting on solid bedrock. A quantitative analysis of architecture is necessary for many model‐driven approaches used by pedologic, geomorphic, hydrologic or biologic studies. We have used electrical resistivity tomography, a well‐established geophysical technique causing minimum surficial disturbance, to portray the subsurface electrical resistivity differences at three study sites (Green Lakes Valley; Gordon Gulch; Betasso) at the Boulder Creek Critical Zone Observatory (BcCZO). Possible limitations of the technique are discussed. Interpretation of the specific resistivity values using natural outcrops, pits, roadcuts and drilling data as ground truth information allows us to image the critical zone architecture of each site. Green Lakes Valley (3700 MASL), a glacially eroded alpine basin, shows a rather simple, split configuration with coarse blockfields and sediments, partly containing permafrost above bedrock. The critical zone in Gordon Gulch (2650 MASL), a montane basin with rolling hills, and Betasso (1925 MASL), a lower montane basin with v‐shaped valleys, is more variable due to a complex Quaternary geomorphic history. Boundaries between overlying stratified slope deposits and saprolite were identified at mean depths of 3.0 ± 2.2 m and 4.1 ± 3.6 m in the respective sites. The boundary between saprolite and weathered bedrock is deeper in Betasso at 5.8 ± 3.7 m, compared with 4.3 ± 3.0 m in Gordon Gulch. In general, the data are consistent with results from seismic studies, but electrical resistivity tomography documents a 0.5–1.5 m shallower critical zone above the weathered bedrock on average. Additionally, we document high lateral variability, which results from the weathering and sedimentation history and seems to be a consistent aspect of critical zone architecture within the BcCZO. Copyright © 2013 John Wiley & Sons, Ltd.     

Topographic stress and rock fracture: a two‐dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations

Theoretical calculations indicate that elastic stresses induced by surface topography may be large enough in some landscapes to fracture rocks, which in turn could influence slope stability, erosion rates, and bedrock hydrologic properties. These calculations typically have involved idealized topographic profiles, with few direct comparisons of predicted topographic stresses and observed fractures at specific field sites. We use a numerical model to calculate the stresses induced by measured topographic profiles and compare the calculated stress field with fractures observed in shallow boreholes. The model uses a boundary element method to calculate the stress distribution beneath an arbitrary topographic profile in the presence of ambient tectonic stress. When applied to a topographic profile across the Susquehanna Shale Hills Critical Zone Observatory in central Pennsylvania, the model predicts where shear fractures would occur based on a Mohr–Coulomb criterion, with considerable differences in profiles of stresses with depth beneath ridgetops and valley floors. We calculate the minimum cohesion required to prevent shear failure, C_min, as a proxy for the potential for fracturing or reactivation of existing fractures. We compare depth profiles of C_min with structural analyses of image logs from four boreholes located on the valley floor, and find that fracture abundance declines sharply with depth in the uppermost 15 m of the bedrock, consistent with the modeled profile of C_min. In contrast, C_min increases with depth at comparable depths below ridgetops, suggesting that ridgetop fracture abundance patterns may differ if topographic stresses are indeed important. Thus, the present results are consistent with the hypothesis that topography can influence subsurface rock fracture patterns and provide a basis for further observational tests. Copyright © 2014 John Wiley & Sons, Ltd.     

Arctic rockwall retreat rates estimated using laboratory‐calibrated ERT measurements of talus cones in Longyeardalen,Svalbard

Holocene rockwall retreat rates quantify integral values of rock slope erosion and talus cone evolution. Here we investigate Holocene rockwall retreat of exposed arctic sandstone cliffs in Longyeardalen, central Svalbard and apply laboratory‐calibrated electrical resistivity tomography (ERT) to determine talus sediment thickness. Temperature–resistivity functions of two sandstone samples are measured in the laboratory and compared with borehole temperatures from the talus slope. The resistivity of the higher and lower‐porosity sandstone at relevant borehole permafrost temperatures defines a threshold range that accounts for the lithological variability of the dominant bedrock and debris material. This helps to estimate the depth of the transition from higher resistivities of ice‐rich debris to lower resistivities of frozen bedrock in the six ERT transects. The depth of the debris–bedrock transition in ERT profiles is confirmed by a pronounced apparent resistivity gradient in the raw data plotted versus depth of investigation. High‐resolution LiDAR‐scanning and ERT subsurface information were collated in a GIS to interpolate the bedrock surface and to calculate the sediment volume of the talus cones. The resulting volumes were referenced to source areas to calculate rockwall retreat rates. The rock mass strength was estimated for the source areas. The integral rockwall retreat rates range from 0.33 to 1.96 mm yr^–1, and are among the highest rockwall retreat rates measured in arctic environments, presumably modulated by harsh environmental forcing on a porous sandstone rock cliff with a comparatively low rock mass strength. Here, we show the potential of laboratory‐calibrated ERT to provide accurate estimates of rockwall retreat rates even in ice‐rich permafrost talus slopes. Copyright © 2012 John Wiley & Sons, Ltd.