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.     

Migration velocity analysis for tilted transversely isotropic media

Tilted transversely isotropic formations cause serious imaging distortions in active tectonic areas (e.g., fold‐and‐thrust belts) and in subsalt exploration. Here, we introduce a methodology for P‐wave prestack depth imaging in tilted transversely isotropic media that properly accounts for the tilt of the symmetry axis as well as for spatial velocity variations. For purposes of migration velocity analysis, the model is divided into blocks with constant values of the anisotropy parameters ε and δ and linearly varying symmetry‐direction velocity V_P0 controlled by the vertical (k_z) and lateral (k_x) gradients. Since determination of tilt from P‐wave data is generally unstable, the symmetry axis is kept orthogonal to the reflectors in all trial velocity models. It is also assumed that the velocity V_P0 is either known at the top of each block or remains continuous in the vertical direction. The velocity analysis algorithm estimates the velocity gradients k_z and k_x and the anisotropy parameters ε and δ in the layer‐stripping mode using a generalized version of the method introduced by Sarkar and Tsvankin for factorized transverse isotropy with a vertical symmetry axis. Synthetic tests for several models typical in exploration (a syncline, uptilted shale layers near a salt dome and a bending shale layer) confirm that if the symmetry‐axis direction is fixed and V_P0 is known, the parameters k_z, k_x, ε and δ can be resolved from reflection data. It should be emphasized that estimation of ε in tilted transversely isotropic media requires using nonhyperbolic moveout for long offsets reaching at least twice the reflector depth. We also demonstrate that application of processing algorithms designed for a vertical symmetry axis to data from tilted transversely isotropic media may lead to significant misfocusing of reflectors and errors in parameter estimation, even when the tilt is moderate (30°). The ability of our velocity analysis algorithm to separate the anisotropy parameters from the velocity gradients can be also used in lithology discrimination and geologic interpretation of seismic data in complex areas.     

Phase-shift migration with a variable-length spatial transform–an algorithm for moderately varying lateral velocities1

A migration algorithm appropriate for moderately varying lateral velocity changes is developed as an extension of phase-shift migration by using a variable-length spatial transform. This process significantly reduces the number of lateral wave-numbers necessary to downward continue the data, and it replaces the spatial FFT with a simple recursion relationship. For a given frequency and position x, ten lateral wavenumbers are typically sufficient, and the migration algorithm produces accurate images when the velocity structure V (X, z) changes over a few depth intervals of thickness Δz, with lateral velocity gradients up to 1.4 to 1.0.     

Seismoelectric measurements in a porous quartz‐sand sample with anisotropic permeability

Seismoelectric coupling coefficients are difficult to predict theoretically because they depend on a large numbers of rock properties, including porosity, permeability, tortuosity, etc. The dependence of the coupling coefficient on rock properties such as permeability requires experimental data. In this study, we carry out a set of laboratory measurements to determine the dependence of seismoelectric coupling coefficient on permeability. We use both an artificial porous “sandstone” sample, with cracks, built using quartz‐sand and Berea sandstone samples. The artificial sample is a cube with 39% porosity. Its permeability levels are anisotropic: 14.7 D, 13.8 D, and 8.3 D in the x‐, y‐, and z‐directions, respectively. Seismoelectric measurements are performed in a water tank in the frequency range of 20 kHz–90 kHz. A piezoelectric P‐wave source is used to generate an acoustic wave that propagates through the sample from the three different (x, y, and z) directions. The amplitudes of the seismoelectric signal induced by the acoustic waves vary with the direction. The highest signal is in the direction of the highest permeability, and the lowest signal is in the direction of the lowest permeability. Since the porosity of the sample is constant, the results directly show the dependence of seismoelectric coefficients on permeability. Seismoelectric measurements with natural rocks are performed using Berea sandstone 500 and 100 samples. Because the Berea samples are nearly isotropic in permeability, the amplitudes of the seismoelectric signals induced in the different directions are the same within the measurement error. Because the permeability of Berea 500 is higher than that of Berea 100, the amplitude of the seismoelectric signals induced in Berea 500 is higher than those in Berea 100. To determine the relative contributions of porosity and permeability on seismoelectric conversion, we carried out an analysis, using Pride (1994) formulation and Kozeny–Carman relationship; the normalized amplitudes of seismoelectric coupling coefficients in three directions are calculated and compared with the experimental results. The results show that the seismoelectric conversion is related to permeability in the frequency range of measurements. This is an encouraging result since it opens the possibility of determining the permeability of a formation from seismoelectric measurements.     

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.     

Anisotropic migration velocity analysis: Application to a data set from West Africa

Although it is widely recognized that anisotropy can have a significant influence on the focusing and positioning of migrated reflection events, conventional depth imaging methods still operate with isotropic velocity fields. Here, we present an application of a 2D migration velocity analysis (MVA) algorithm, designed for factorized v(x, z) VTI (transversely isotropic with a vertical symmetry axis) media, to an offshore data set from West Africa. By approximating the subsurface with factorized VTI blocks, it is possible to decouple the spatial variations in the vertical velocity from the anisotropic parameters with minimal a priori information. Since our method accounts for lateral velocity variation, it produces more accurate estimates of the anisotropic parameters than those previously obtained with time‐domain techniques. The values of the anellipticity parameter η found for the massive shales exceed 0.2, which confirms that ignoring anisotropy in the study area can lead to substantial imaging distortions, such as mis‐stacking and mispositioning of dipping events. While some of these distortions can be removed by using anisotropic time processing, further marked improvement in image quality is achieved by prestack depth migration with the estimated factorized VTI model. In particular, many fault planes, including antithetic faults in the shallow part of the section, are better focused by the anisotropic depth‐migration algorithm and appear more continuous. Anisotropic depth migration facilitates structural interpretation by eliminating false dips at the bottom of the section and improving the images of a number of gently dipping features. One of the main difficulties in anisotropic MVA is the need to use a priori information for constraining the vertical velocity. In this case study, we successfully reconstructed the time–depth curve from reflection data by assuming that the vertical velocity is a continuous function of depth and estimating the vertical and lateral velocity gradients in each factorized block. If the subsurface contains strong boundaries with jumps in velocity, knowledge of the vertical velocity at a single point in a layer is sufficient for our algorithm to determine all relevant layer parameters.     

Wavefield downward extrapolation for migration velocity analysis on Marmousi data-set

The authors present a method for estimation of interval velocities using the downward continuation of the wavefield to perform layer-stripping migration velocity analysis. The generalized, phase-shift migration MG(F-K) in wavenumber-frequency domain was used for fulltime downward extrapolation of the wavefield. Such downward depth extrapolation accounts for strong changes of velocity in lateral and vertical directions and helps in correct positioning of the wavefield image in complex structures. Determination of velocity is the recursive process which means that the wavefield on depth level z _n−1 (n = 0, 1, ...) is an input data-set for determination of velocity on level z _n . The velocity ν [x, z _n − z _n−1] can be thus treated as interval velocity in Δz _n = z _n − z _n−1 step. This method was tested on synthetic Marmousi data-set and showed satisfactory results for complex, inhomogeneous media.     

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.     

Directions of preferential flow in a hillslope soil, 1. Quasi‐steady flow

Preferred infiltration is mainly perceived as vertically down whereas subsurface storm flow is thought to occur parallel to slopes. The transition from vertical to lateral flow in a layered hillslope soil is the focus of the contribution. Transient flow is assumed to move as a wetting front. Three time‐domain reflectometry (TDR) wave‐guides, each 0·15 m long, were mounted in the shape of a truncated tetrahedron with its peak pointing down. Each wave‐guide focuses the front velocity along its axis. The three front‐velocity vectors are decomposed into their x, y and z components, which are then assembled to the resultant velocity vector. The volume density flux of preferred flow is the product of the front velocity and the mobile water content. The latter is the amplitude of transient soil moisture measured with each wave‐guide. The resultant vector of the volume flux density is computed similarly to the velocity vector. The experimental approach allows for the rapid assessment of transient flows without relying on the variation of water potentials. The experiments indicate that the directions of the resultant vectors of velocity and volume flux density can be estimated if the moisture variations of the three TDR wave‐guides are strongly correlated during the passing of the wetting front. Copyright © 2004 John Wiley & Sons, Ltd.     

Strong variation in weathering of layered rock maintains hillslope‐scale strength under high precipitation

The evolution of volcanic landscapes and their landslide potential are both dependent upon the weathering of layered volcanic rock sequences. We characterize critical zone structure using shallow seismic V_p and V_s profiles and vertical exposures of rock across a basaltic climosequence on Kohala peninsula, Hawai’i, and exploit the dramatic gradient in mean annual precipitation (MAP) across the peninsula as a proxy for weathering intensity. Seismic velocity increases rapidly with depth and the velocity–depth gradient is uniform across three sites with 500–600 mm/yr MAP, where the transition to unaltered bedrock occurs at a depth of 4 to 10 m. In contrast, velocity increases with depth less rapidly at wetter sites, but this gradient remains constant across increasing MAP from 1000 to 3000 mm/yr and the transition to unaltered bedrock is near the maximum depth of investigation (15–25 m). In detail, the profiles of seismic velocity and of weathering at wet sites are nowhere monotonic functions of depth. The uniform average velocity gradient and the greater depths of low velocities may be explained by the averaging of velocities over intercalated highly weathered sites with less weathered layers at sites where MAP > 1000 mm/yr. Hence, the main effect of climate is not the progressive deepening of a near‐surface altered layer, but rather the rapid weathering of high permeability zones within rock subjected to precipitation greater than ~1000 mm/yr. Although weathering suggests mechanical weakening, the nearly horizontal orientation of alternating weathered and unweathered horizons with respect to topography also plays a role in the slope stability of these heterogeneous rock masses. We speculate that where steep, rapidly evolving hillslopes exist, the sub‐horizontal orientation of weak/strong horizons allows such sites to remain nearly as strong as their less weathered counterparts at drier sites, as is exemplified by the 50°–60° slopes maintained in the amphitheater canyons on the northwest flank of the island. Copyright © 2017 John Wiley & Sons, Ltd.     

Analogue model studies of induction effects at auroral latitudes

In addition to field observations and numerical models, geomagnetic induction effects can be studied by scaled analogue model experiments. We present here results of analogue model studies of the auroral electrojet with an Earth model simulating the Arctic Ocean and inland conductivity structures in northern Fennoscandia. The main elements of the analogue model used were salt water simulating the host rock, an aluminium plate corresponding to the ocean and graphite pieces producing the inland highly conducting anomalies. The electrojet was a time-harmonic line current flowing at a (simulated) height of 100 km above northern Fennoscandia. The period simulated was 9 min.The analogue model results confirmed the well-known rapid increase of the vertical field when the coast is approached from the continent. The increase of the horizontal field due to induced ocean currents was demonstrated above the ocean, as well as the essentially negligible effect of these currents on the horizontal field on the continent.The behaviour of the magnetic field is explained with a simple two-dimensional thin-sheet model. The range, or the adjustment distance, of the ocean effect inland was found to be some hundreds of kilometers, which also agrees with earlier results of the Siebert-Kertz separation of IMAGE magnetometer data. The modelled inland anomalies evidently had too large conductivities, but on the other hand, their influence decayed on scales of only some tens of kilometers.Analogue model results, thin-sheet calculations, and field observations show that the induction effect on the horizontal magnetic field B_x near the electrojet is negligible. On the other hand, the vertical component B_z is clearly affected by induced currents in the ocean. Evidence of this is the shift of the zero point of B_z 0-1° southwards from the maximum of B_x. The importance of these results are discussed, emphasizing the determination of ionospheric currents.     

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.     

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     

Feasibility study for an anisotropic full waveform inversion of cross‐well seismic data

Anisotropy is often observed due to the thin layering or aligned micro‐structures, like small fractures. At the scale of cross‐well tomography, the anisotropic effects cannot be neglected. In this paper, we propose a method of full‐wave inversion for transversely isotropic media and we test its robustness against structured noisy data. Optimization inversion techniques based on a least‐square formalism are used. In this framework, analytical expressions of the misfit function gradient, based on the adjoint technique in the time domain, allow one to solve the inverse problem with a high number of parameters and for a completely heterogeneous medium. The wave propagation equation for transversely isotropic media with vertical symmetry axis is solved using the finite difference method on the cylindrical system of coordinates. This system allows one to model the 3D propagation in a 2D medium with a revolution symmetry. In case of approximately horizontal layering, this approximation is sufficient. The full‐wave inversion method is applied to a crosswell synthetic 2‐component (radial and vertical) dataset generated using a 2D model with three different anisotropic regions. Complex noise has been added to these synthetic observed data. This noise is Gaussian and has the same amplitude f?k spectrum as the data. Part of the noise is localized as a coda of arrivals, the other part is not localized. Five parameter fields are estimated, (vertical) P‐wave velocity, (vertical) S‐wave velocity, volumetric mass and the Thomsen anisotropic parameters epsilon and delta. Horizontal exponential correlations have been used. The results show that the full‐wave inversion of cross‐well data is relatively robust for high‐level noise even for second‐order parameters such as Thomsen epsilon and delta anisotropic parameters.     

Gopher bioturbation: field evidence for non‐linear hillslope diffusion

It has generally been assumed that diffusive sediment transport on soil‐mantled hillslopes is linearly dependent on hillslope gradient. Fieldwork was done near Santa Barbara, California, to develop a sediment transport equation for bioturbation by the pocket gopher (Thomomys bottae) and to determine whether it supports linear diffusion. The route taken by the sediment is divided into two parts, a subsurface path followed by a surface path. The first is the transport of soil through the burrow to the burrow opening. The second is the discharge of sediment from the burrow opening onto the hillslope surface. The total volumetric sediment flux, as a function of hillslope gradient, is found to be: q_s (cm³ cm⁻¹ a⁻¹) = 176(dz/dx)³ − 189(dz/dx)² + 68(dz/dx) + 34(dz/dx)^0·4. This result does not support the use of linear diffusion for hillslopes where gopher bioturbation is the dominant mode of sediment transport. A one‐dimensional hillslope evolution program was used to evolve hillslope profiles according to non‐linear and linear diffusion and to compare them to a typical hillslope. The non‐linear case more closely resembles the actual profile with a convex cap at the divide leading into a straight midslope section. Copyright © 2000 John Wiley & Sons, Ltd.     

A methodology for regionalizing 3‐D effective porosity at watershed scale in crystalline aquifers

An innovative approach for regionalizing the 3‐D effective porosity field is presented and applied to two large, overexploited, and deeply weathered crystalline aquifers located in southern India. The method derives from earlier work on regionalizing a 2‐D effective porosity field in that part of an aquifer where the water table fluctuates, which is now extended over the entire aquifer using a 3‐D approach. A method based on geological and geophysical surveys has also been developed for mapping the weathering profile layers (saprolite and fractured layers). The method for regionalizing 3‐D effective porosity combines water table fluctuation and groundwater budget techniques at various cell sizes with the use of satellite‐based data (for groundwater abstraction), the structure of the weathering profile, and geostatistical techniques. The approach is presented in detail for the Kudaliar watershed (983 km²) and tested on the 730 km² Anantapur watershed. At watershed scale, the effective porosity of the aquifer ranges from 0.5% to 2% in Kudaliar and between 0.3% and 1% in Anantapur, which agrees with earlier works. Results show that (a) depending on the geology and on the structure of the weathering profile, the vertical distribution of effective porosity can be very different and that the fractured layers in crystalline aquifers are not necessarily characterized by a rapid decrease in effective porosity and (b) that the lateral variations in effective porosity can be larger than the vertical ones. These variations suggest that within a same weathering profile, the density of open fractures and/or degree of weathering in the fractured zone may significantly vary from a place to another. The proposed method provides information on the spatial distribution of effective porosity that is of prime interest in terms of flux and contaminant transport in crystalline aquifers. Implications for mapping groundwater storage and scarcity are also discussed, which should help in improving groundwater resource management strategies.     

Testing etching hypothesis for the shaping of granite dome structures beneath lateritic weathering landsurfaces using ERT method

An Erratum has been published for this article in Earth Surface Processes and Landforms 28(13) 2003, 1491. Granite domes, boulders and knobs buried within saprolite have been detected beneath lateritic weathering landsurfaces using 2D electrical resistivity tomography (ERT). This technique provides a valuable means of mapping the bedrock topography and the regolith structures underneath landsurfaces, as it is intrinsically very sensitive to the electrical properties of superimposed pedological, hydrological and geological layers, allowing the determination of their relative geometry and spatial relationships. For instance, 2D inverse electrical resistivity models including topographic data permit the de?nition of lithostratigraphic cross‐sections. It shows that resistive layers, such as the more or less hardened ferruginous horizons and/or the bedrock, are generally well differentiated from poorly resistive layers, such as saprolite, including water‐saturated lenses, as has been corroborated by past and actual borehole observations. The analysis of the 2D geometrical relations between the weathering front, i.e. the bedrock topography, and the erosion surface, i.e. the landsurface topography, documents the weathering and erosion processes governing the development of the landforms and the underlying structures, thus allowing the etching hypothesis to be tested. The in?ltration waters are diverted by bedrock protrusions, which behave as structural thresholds compartmentalizing the saprolite domain, and also the regolith water table, into distinct perched saturated subdomains. The diverted waters are thus accumulated in bedrock troughs, which behave like underground channels where the saprolite production rate may be enhanced, provided that the water drainage is ef?cient. If the landsurface topography controls the runoff dynamics, the actual bedrock topography as depicted by ERT imaging in?uences the hydrodynamics beneath the landsurface. In some way, this may control the actual weathering rate and the shaping of bedrock protrusions as granite domes and knobs within thick saprolite, before their eventual future exposure. Copyright © 2003 John Wiley & Sons, Ltd.     

Non-hyperbolic moveout inversion of wide-azimuth P-wave data for orthorhombic media

The azimuthally varying non‐hyperbolic moveout of P‐waves in orthorhombic media can provide valuable information for characterization of fractured reservoirs and seismic processing. Here, we present a technique to invert long‐spread, wide‐azimuth P‐wave data for the orientation of the vertical symmetry planes and five key moveout parameters: the symmetry‐plane NMO velocities, V⁽¹⁾_nmo and V⁽²⁾_nmo , and the anellipticity parameters, η⁽¹⁾, η⁽²⁾ and η⁽³⁾ . The inversion algorithm is based on a coherence operator that computes the semblance for the full range of offsets and azimuths using a generalized version of the Alkhalifah–Tsvankin non‐hyperbolic moveout equation. The moveout equation provides a close approximation to the reflection traveltimes in layered anisotropic media with a uniform orientation of the vertical symmetry planes. Numerical tests on noise‐contaminated data for a single orthorhombic layer show that the best‐constrained parameters are the azimuth ? of one of the symmetry planes and the velocities V⁽¹⁾_nmo and V⁽²⁾_nmo , while the resolution in η⁽¹⁾ and η⁽²⁾ is somewhat compromised by the trade‐off between the quadratic and quartic moveout terms. The largest uncertainty is observed in the parameter η⁽³⁾ , which influences only long‐spread moveout in off‐symmetry directions. For stratified orthorhombic models with depth‐dependent symmetry‐plane azimuths, the moveout equation has to be modified by allowing the orientation of the effective NMO ellipse to differ from the principal azimuthal direction of the effective quartic moveout term. The algorithm was successfully tested on wide‐azimuth P‐wave reflections recorded at the Weyburn Field in Canada. Taking azimuthal anisotropy into account increased the semblance values for most long‐offset reflection events in the overburden, which indicates that fracturing is not limited to the reservoir level. The inverted symmetry‐plane directions are close to the azimuths of the off‐trend fracture sets determined from borehole data and shear‐wave splitting analysis. The effective moveout parameters estimated by our algorithm provide input for P‐wave time imaging and geometrical‐spreading correction in layered orthorhombic media.     

Field estimate of paleoseismic slip on a normal fault using the Schmidt hammer and terrestrial LiDAR: Methods and application to the Hebgen fault (Montana,USA)

The weathering characteristics of bedrock fault scarps provide relative age constraints that can be used to determine fault displacements. Here, we report Schmidt hammer rebound values (R‐values) for a limestone fault scarp that was last exposed in the 1959 Mw 7.3 Hebgen Lake, Montana earthquake. Results show that some R‐value indices, related to the difference between minimum and maximum R‐values in repeated impacts at a point, increase upward along the scarp, which we propose is due to progressive exposure of the scarp in earthquakes. An objective method is developed for fitting slip histories to the Schmidt hammer data and produces the best model fit (using the Bayesian Information Criterion) of three earthquakes with single event displacements of ≥ 1.20 m, 3.75 m, and c. 4.80 m. The same fitting method is also applied to new terrestrial LiDAR data of the scarp, though the LiDAR results may be more influenced by macro‐scale structure of the outcrop than by differential weathering. We suggest the use of this fitting procedure to define single event displacements on other bedrock fault scarps using other dating techniques. Our preliminary findings demonstrate that the Schmidt hammer, combined with other methods, may provide useful constraints on single event displacements on exposed bedrock fault scarps. Copyright © 2018 John Wiley & Sons, Ltd.     

Architecture of the deep critical zone in the Río Icacos watershed (Luquillo Critical Zone Observatory,Puerto Rico) inferred from drilling and ground penetrating radar (GPR)

In the critical zone, surficial bedrock interactions result in the formation of a mantle of chemically‐ and physically‐altered material defined here as regolith. In the watershed of the Río Icacos, an upland river draining the Luquillo Mountains in tropical Puerto Rico, we explored the influence of lithology (quartz diorite versus hornfels‐facies volcaniclastic rock) on weathering. Regolith profiles were studied by drilling boreholes and imaging the subsurface using ground penetrating radar (GPR). Overall, the regolith structure is not laterally continuous but rather is punctuated by zones of deep fractures that host in situ weathering, corestones, and colluvial material. GPR images of these vertical zones show reflectors at 15–20 m depth. Thus, the architecture of the critical zone in the upper Luquillo Mountains is highly dependent on lithology and its influence on fracture development. At the highest elevations where hornfels overlies quartz diorite, positive feedbacks occur when the water table drops so that oxidative weathering of biotite in the more felsic rock creates microfractures and allows deeper infiltration of meteoric waters. Such exposure results in some of the fastest weathering rocks in the world and may contribute to formation of the knickpoint in the Río Icacos watershed. This work represents the first study combining GPR and drilling to look at the structure of the deep critical zone and demonstrates: (1) the importance of combining direct methods (such as drilling) with indirect methods (such as GPR) to understand the architecture of the critical zone in tropical systems; (2) the interplay of the surficial stress regime, lithology and climate in dictating the architecture of weathering. Copyright © 2016 John Wiley & Sons, Ltd.