A note on fault reactivation

Reactivation of existing faults whose normal lies in the σ₁^′σ₃^′ plane of a stress field with effective principal compressive stresses σ₁^′ >σ₂^′ >σ₃^′ is considered for the simplest frictional failure criterion, τ = μσ_n^′ = μ(σ_n − P), where τ and σ_n are respectively the shear and normal stresses to the existing fault, P is the fluid pressure and μ is the static friction. For a plane oriented at θ to σ₁^′, the stress ratio for reactivation is (σ₁^′/σ₃^′) = (1 + μ cot θ)/(1 − μ tan θ). This ratio has a minimum positive value at the optimum angle for reactivation given by (1/μ) but reaches infinity when θ = 2θ^*, beyond which σ₃^′ < 0 is a necessary condition for reactivation. An important consequence is that for typical rock friction coefficients, it is unlikely that normal faults will be reactivated as high-angle reverse faults or thrusts as low-angle normal faults, unless the effective least principal stress is tensile.     

Geotechnical characterization of the upper Pleistocene–Holocene alluvial deposits of Roma (Italy) by means of multivariate geostatistics: Cross-validation results

We are presenting an attempt to evaluate the spatial variability of geotechnical parameters in the upper Pleistocene–Holocene alluvial deposits of Roma (Italy) by means of multivariate geostatistics.The upper Pleistocene–Holocene alluvial deposits of Roma are sensitive to high levels of geohazard. They occupy a sizable and significant part of the city, being the foundation for many monuments, historical neighborhoods, and archaeological areas, and the main host of the present and future subway lines. We have stored information from more than 2000 geotechnical boreholes crossing the alluvial deposits into a relational database. For the present study, only the boreholes with lithologic/textural interpretation and geotechnical information were selected. The set includes 283 boreholes and 719 samples, which have a set of geotechnical information comprising physical properties and mechanical parameters.Techniques of multivariate statistics and geostatistics were combined and compared to evaluate the estimation methods of the mechanical parameters, with special reference to the drained friction angle from direct shear test (φ′). Principal Component Analysis was applied to the dataset to highlight the relationships between the geotechnical parameters. Through cross-validation analysis, multiple linear regression, kriging, and cokriging were tested as estimators of φ′. Cross-validation demonstrates that the cokriging with granulometries as auxiliary variables is the most suitable method to estimate φ′. In addition to proving that cokriging is a good estimator of φ′, cross-validation demonstrates that input data are coherent and this allows us to use them for estimation of geotechnical parameters, although they come from different laboratories and different vintages.Nevertheless, to get the same good results of cross-validation in estimation, it is necessary for granulometries to be available at grid points. Since this information being not available at all grid points, it is expected that, in the future, textural information can be derived in an indirect way, i.e., from lithologic/textural spatial reconstructions.     

Circular scanlines and circular windows: new tools for characterizing the geometry of fracture traces

We introduce new estimators for fracture trace intensity, trace density and mean trace length that exploit the use of circles as efficient sampling tools. A fracture trace is the commonly observed surface expression of a fracture, i.e. the intersection of a fracture with an exposed surface such as a rock pavement or a mine drive wall. Trace intensity, trace density and mean trace length estimators are derived and shown to form a self-consistent set of two-dimensional fracture abundance measures. The intensity estimator n/4r uses the number, n, of intersections between fracture traces and a circular scanline of radius r. The density estimator m/2πr² uses the number, m, of trace endpoints inside a circular window. The mean trace length estimator (n/m)πr/2 uses the ratio of the number of trace intersections on the circle to the number of endpoints in the circle.The circular sampling tools and estimators described here eliminate most sampling biases due to orientation and also correct many errors due to censoring and length bias that plague established scanline and areal measurement techniques. Performance of the estimators is demonstrated by comparison with areal samples of a synthetic fracture trace population with known intensity, density and mean trace length. The estimators are also applied successfully to a natural rock pavement with two orthogonal fracture sets, one of which is severely censored. Because the new circle-based estimators only require counts of trace–circle intersections and/or trace endpoints, they are more time-efficient than current methods for estimating geometric characteristics of fracture traces.     

Determination of Shear Strength and Three-dimensional Yield Strength for the Hoek-Brown Criterion

Summary. Most currently used techniques for analysing the stability of near surface structures, such as rock slopes, are based on the application of the effective Coulomb shear strength parameters cohesion c′, and the angle of friction φ′ on some known or anticipated shear surface subjected to an effective normal stress σ′_n. The most widely used of these techniques are the variants of the method of slices and related upper bound techniques. If the Hoek-Brown criterion is to be used to model the strength of near surface fractured rocks, it is necessary to determine equivalent Coulomb shear strength parameters for the specified level of effective normal stress. Calculation of the equivalent Coulomb parameters for the Hoek-Brown criterion for cases when a ≠ 0.5 is not a straightforward matter. A simple procedure for calculating instantaneous values of c′_i and φ′_i has been developed based on spreadsheet calculations and the application of a numerical optimisation routine. This procedure can also be applied to calculating the Hoek-Brown envelope plotted in shear stress/normal stress space. A simple closed form solution for c′_i and tan φ′_i has also been developed for the special case when a = 1. A three-dimensional version of the Hoek-Brown criterion has been developed by combining it with the Drucker-Prager criterion. This new yield criterion has been implemented by numerical solution of the governing equations. A simplification of this three-dimensional yield criterion has been developed by introducing an intermediate principal stress weighting factor. Comparison with published results demonstrates that this simplified criterion has the capacity to model the results of true triaxial tests for a range of different rock types over a wide range of stress levels. The new three-dimensional yield criterion has the advantage that its input parameters can be determined from routine uniaxial compression tests and mineralogical examination.     

The importance of the effective intermediate principal stress (σ′2) to fault slip patterns

In normal faulting regimes, the magnitudes and orientations of the maximum and minimum principal compressive stresses may be known with some confidence. However, the magnitude of the intermediate principal compressive stress is generally much more difficult to constrain and is often not considered to be an important factor. In this paper, we show that the slip characteristics of faults and fractures with complex or nonoptimal geometry are highly sensitive to variation or uncertainty in the ambient effective intermediate principal stress (σ′₂). Optimally oriented faults and fractures may be less sensitive to such variations or uncertainties. Slip tendency (T_s) analysis provides a basis for quantifying the effects of uncertainty in the magnitudes and orientations of all principal stresses and in any stress regime, thereby focusing efforts on the most important components of the system. We also show, for a normal faulting stress regime, that the proportion of potential surfaces experiencing high slip tendency (e.g., T_s ≥ 0.6) decreases from a maximum of about 38% where σ′₂ = σ′₃, to a minimum of approximately 14% where σ′₂ is halfway between σ′₃ and σ′₁, and increases to another high of approximately 29% where σ′₂ = σ′₁. This analysis illustrates the influence of the magnitude of σ′₂ on rock mass strength, an observation previously documented by experimental rock deformation studies. Because of the link between fault and fracture slip characteristics and transmissivity in critically stressed rock, this analysis can provide new insights into stress-controlled fault transmissivity.     

Presence of Hippidion at two sites of western Argentina: Diet composition and contribution to the study of the extinction of Pleistocene megafauna

The composition of Hippidion diet, and possible changes that could relate to its extinction, were evaluated in the Argentinean-Chilean Central Andes, a Neotropical environment characterized by arid to semiarid conditions (Andean hot and cold deserts). Microhistological analyses were made on feces of Hippidion found at Los Morrillos (31°43′S–68°42′W, 3000 m a.s.l.) and Gruta del Indio (34°35′S, 68°22′W, 660 m a.s.l.). At Gruta del Indio the diet of Hippidion was based mainly on woody species. At Los Morrillos, it was based on herbaceous species.This flexibility in diet composition could be a relative adaptive advantage allowing a longer permanence of this species in comparison to others recorded in the region (such as Megatheriumand Mylodon). Nevertheless, this advantage was not enough to guarantee its survival during the Holocene. Extinction could have been affected by diverse agents, such as growing aridification of the area, increasing competition with other species (mainly Lama guanicoe), and human presence, along with a relatively low population density (as expected from the limited presence of Hippidion at the archaeological and palaeontological sites of South America. At Gruta del Indio significant changes in the diet of Hippidion corresponding to different intervals of the period 31,000–9000 ¹⁴C BP are not evident. Given this evidence for similar diets for Hippidion throughout the late Quaternary, other factors need to be considered to explain the extinction of this horse.     

Pesticides and lipids occurrence in Tangier agricultural soil (northern Morocco)

This study evaluates pesticide occurrence in Tangier agricultural soil (northern Morocco). Soil samples were measured for alpha endosulfan, beta endosulfan, endosulfan sulfate, alpha HCH, beta HCH, gamma HCH, aldrin, dieldrin, endrin, o,p′ DDT, p,p′ DDD, p,p′ DDE and p,p′ DDT. The analyses were performed by gas chromatography coupled with mass spectrometry (GC/MS). Endosulfan isomers (alpha and beta) and endosulfan sulfate were detected in soil samples, in which the beta isomer showed the highest concentrations. Some DDT metabolites (o,p′ DDT and p,p′ DDE) and alpha HCH were also detected in the analyzed soil. The lipid fraction of the soil samples was extracted by accelerated solvent extraction and fractionated using chromatographic techniques. The principal biomarkers obtained were alcohols, esters, ketones, aldehydes, fatty acids and hydrocarbons. Lipid biomarkers were characterized to determine soil organic matter sources. Experimental results showed that the organic matter was mainly of plant origin, although the bacterial contribution was significant.     

Influencing factors of geometrical structure of surface shrinkage cracks in clayey soils

In order to investigate the effects of temperature, thickness of soil layer, wetting and drying cycles and soil types on geometrical structure of surface shrinkage cracks in clayey soils, special software Crack Image Analysis System (CIAS) for analyzing shrinkage crack patterns was developed. Eight groups of soil samples were prepared and subjected to drying to crack in laboratory. The number of crack segments and intersections, average crack length, width and aggregate area, crack intensity factor (CIF), and the corresponding probability density functions (PDF) of these parameters were determined by analyzing several crack patterns derived from different experimental conditions. The results show that the soil cracking behavior and the geometrical structure of crack patterns are significantly influenced by these considered factors. There is a tendency of crack length, width, aggregate area and their most probable value (MPV) related to the PDF increases with temperature increase. With thicker soil layers, the average crack length, width, aggregate area and CIF are increased, and the main distribution ranges of crack length, width and aggregate area are increased also. When the soil is subjected to multiple wetting–drying cycles, the soil surface generates more irregular and coarse cracks. The number of short and narrow crack segments increases significantly, and the CIF decreases with an increase in wetting–drying cycles. It is also observed that the extent of cracking is directly related to the soil fines fraction and its plasticity index (I_P). The greatest CIF and crack width are observed in the soils with the largest fines fraction and highest I_P. In addition, the ratio of numbers of crack segments to intersections ranges from 1.5 to 2, and cracking mainly takes place in three stages: main-cracks initiation stage; sub-cracks initiation stage; terminal stable stage.     

European continuous active tectonic strain–stress map

This paper shows a new continuous strain–stress map for Europe obtained from the direct inversion of earthquake focal mechanisms calculated from the centroid tensor method. A total of 1608 focal mechanisms have been selected with several quality criteria from different catalogues (CMT Harvard, ETH, Med-Net, I.G.N. and I.A.G.) from 1973 to the present day. Values for the maximum horizontal shortening direction and brittle strain–stress regime defined by the k′ ratio (e_y/e_z, horizontal maximum/vertical strain) have been calculated following in Europe and Pannonian Basin the slip model of tri-axial deformation. The individual results including Dey and the shape of the active brittle strain ellipsoid have been interpolated to a final 15′ regular grid taking into account the relationship between the tectonic horizontal strain–stress value and the vertical load. Both continuous strain regime and maximum horizontal shortening (Dey) maps show a good correlation with the primary tectonic forces generated along the plate boundaries, plate kinematics and also some local perturbations related with main crustal heterogeneities and topography, as well as significant spatial variations in integrated crustal strength.     

Temperature and Salinity Effects on Alkenone Ratios Measured in Surface Sediments from the Indian Ocean

We compare alkenone unsaturation ratios measured on recent sediments from the Indian Ocean (20°N–45°S) with modern sea oceanographic parameters. For each of the core sites we estimated average seasonal cycles of sea surface temperature (SST) and salinity, which we then weighted with the seasonal productivity cycle derived from chlorophyll satellite imagery. The unsaturation index (U₃₇^K′) ranges from 0.2 to 1 and correlates with water temperature but not with salinity. TheU₃₇^K′versus SST relationship for Indian Ocean sediments (U₃₇^K′= 0.033 SST + 0.05) is similar to what has been observed for core tops from the Pacific and Atlantic oceans and the Black Sea. A global compilation for core tops givesU₃₇^K′= 0.031 T + 0.084 (R= 0.98), which is close to a previously reported calibration based on particulate organic matter from the water column. For temperatures between 24° and 29°C, however, the slope seems to decrease to about 0.02U₃₇^K′unit/°C. For Indian Ocean core tops, the ratios of total C₃₇alkenones/total C₃₈alkenones and the slope of theU₃₇^K′-SST relationship are similar to those previously observed for cultures ofEmiliania huxleyibut different from those previously published forGephyrocapsa oceanica.EitherE. huxleyiis a major producer of alkenones in the Indian Ocean or strains ofG. oceanicaliving in the northern Indian Ocean behave differently from the one cultured. In contrast with coccolithophorid assemblages, the ratios of C₃₇alkenones to total C₃₈alkenones lack clear geographic pattern in the Indian Ocean.     

Talc friction in the temperature range 25°–400 °C: Relevance for Fault-Zone Weakening

Talc is one of the weakest minerals that is associated with fault zones. Triaxial friction experiments conducted on water-saturated talc gouge at room temperature yield values of the coefficient of friction, μ (shear stress, τ/effective normal stress, σ′_N) in the range 0.16–0.23, and μ increases with increasing σ′_N. Talc gouge heated to temperatures of 100°–400 °C is consistently weaker than at room temperature, and μ < 0.1 at slow strain rates in some heated experiments. Talc also is characterized by inherently stable, velocity-strengthening behavior (strength increases with increasing shear rate) at all conditions tested. The low strength of talc is a consequence of its layered crystal structure and, in particular, its very weak interlayer bond. Its hydrophobic character may be responsible for the relatively small increase in μ with increasing σ′_N at room temperature compared to other sheet silicates.Talc has a temperature–pressure range of stability that extends from surficial to eclogite-facies conditions, making it of potential significance in a variety of faulting environments. Talc has been identified in exhumed subduction zone thrusts, in fault gouge collected from oceanic transform and detachment faults associated with rift systems, and recently in serpentinite from the central creeping section of the San Andreas fault. Typically, talc crystallized in the active fault zones as a result of the reaction of ultramafic rocks with silica-saturated hydrothermal fluids. This mode of formation of talc is a prime example of a fault-zone weakening process. Because of its velocity-strengthening behavior, talc may play a role in stabilizing slip at depth in subduction zones and in the creeping faults of central and northern California that are associated with ophiolitic rocks.     

ULF geomagnetic anomalies of possible seismogenic origin observed at Teoloyucan station, México, in 1999–2001: Intermediate and short-time analysis

The analysis of ULF geomagnetic field measured at Teoloyucan station (Central Mexico, 11′35.735″ W, 19 44′45.100″ N, 2280 m height) is presented in an intermediate (± 15 days) and short time scale (the day of the EQ occurrence) in relation to 7 major earthquakes occurred in Mexico in 1999–2001. Local changes in the fractal dynamics of the magnetic field are found to be important: a pronounced fall of the fractal index is frequently observed prior to the main shock. The study of the ULF resonant structure recently discovered in the frequencies f_R1 = 10.2−11.1 mHz and f_R2 = 13.6−14.5 mHz reveals changes in their character probably related to the processes of the earthquakes preparation. The success of the observation of the mentioned anomalies (specially the fractal index decrease) strongly depends on how close is the station from the epicenter, and what is the magnitude of the earthquake.     

Earthquake recurrence on the Calaveras fault east of San Jose, California

Occurrence of small (3 M_L < 4) earthquakes on two 10-km segments of the Calaveras fault between Calaveras and Anderson reservoirs follows a simple linear pattern of elastic strain accumulation and release. The centers of these independent patches of earthquake activity are 20 km apart. Each region is characterized by a constant rate of seismic slip as computed from earthquake magnitudes, and is assumed to be an isolated locked patch on a creeping fault surface. By calculating seismic slip rates and the amount of seismic slip since the time of the last significant (M 3) earthquake, it is possible to estimate the most likely date of the next (M - 3) event on each patch. The larger the last significant event, the longer the time until the next one. The recurrence time also appears to be increased according to the moment of smaller (2 < M_L < 3) events in the interim. The anticipated times of future larger events on each patch, on the basis of preliminary location data through May 1977 and estimates of interim activity, are tabulated below with standard errors. The occurrence time for the southern zone is based on eight recurrent events since 1969, the northern zone on only three. The 95% confidence limits can be estimated as twice the standard error of the projected least-squares line. Events of M 3 should not occur in the specified zones at times outside these limits. The central region between the two zones was the locus of two events (M = 3.6, 3.3) on July 3, 1977. These events occurred prior to a window based on the three point, post-1969 slip-time line for the central region.

Latitude	Longitude	Depth	Mag.	Target date	Standard error (days)
37°17′± 2′N	121°39′±2′W	5.0 ±2 km	3.0–4.0	7-22-77	22.3
37°26′± 2′N	121°47′±2′W	6.0 ± 2 km	3.0–4.0	9-02-77	8.0

Full-size table

     

Non-aromatic biomarkers associated with a Palaeogene salt formation (Bresse, France)

This study provides information on non-aromatic hydrocarbons contained in thick Palaeogene halite sequences in the Bresse region (France). The presence of almost uniquely biological markers and the absence of thermogenic compounds denote the low maturity of the corresponding samples consistent with Rock-Eval pyrolysis data. The distribution of n-alkanes enables the distinction of three main biological signatures: algal (mode in nC17–nC18); terrestrial (mode in nC29–nC31) and bacterial (mode in nC25–nC26 with no odd-even carbon number predominance). As to the cyclic biomarkers, hopanes and hopenes are largely predominant over steranes and diasterenes in samples having received appreciable amounts of terrestrial inputs (Type B) and conversely for the samples containing high proportions of algal debris (Type A, Type C).     

A refined technique for measuring crystal size distributions in thin section

 Log-normal size distributions are of the form n=n_oe^−L/α, where n=number density, L=crystal length, and α is a constant. A method for measuring three-dimensional log-normal crystal or grain size distributions (CSDs) in thin section has been deduced from computer experiments, in which 2D sections were cut through assemblages of 3D solids. The size ranges and distributions studied were appropriate for igneous microphenocryst to megacryst populations. Conversion from 2D to 3D is based on an exact correction for spheres of uniform diameter. Cumulate numbers of polygons with length≥L (N_2D) are converted to N_3D by the equation: ln(N_3D)=ln(N_2D/[L·S])+ln(γ)−β/[L·S] The number density is then obtained as n=−dN/dL. The parameters S and γ correct the measured lengths and n_o (n_o=number density at L=0) respectively, and are functions of crystal shape. The parameter β is a weak function of the degree of spatial orientation of the crystals. Highly symmetrical shapes such as cubes, octahedra, and elongated prisms can be accurately measured when randomly oriented; however, rectangular solids with a≠b≠c cannot be accurately measured because they produce bimodal length distributions in cross section. Strongly oriented textures (trachytic or lineated) can be accurately measured regardless of crystal shape. New CSD data from alkaline rocks and a kimberlite give examples of CSDs modified by megacryst retention, xenocryst addition, phenocryst accumulation, and groundmass nucleation. Received: 25 November 1994 / Accepted: 14 November 1995     

A molecular dynamics study of natural organic matter: 1. Lignin, kerogen and soot

Molecular dynamics (MD) simulations were performed on molecular models of a spectrum of natural organic matter (NOM) samples represented by two lignin samples (a softwood lignin and a hardwood lignin), a kerogen (Green River Shale kerogen) and a soot sample (n-hexane soot). Simulated thermodynamic properties of each model, including glass transition temperature (T_g), thermal expansion coefficient (α), density (ρ) and solubility parameter (δ) were compared against experimental data for corresponding samples. Results revealed relatively good agreement for glass transition temperature and solubility parameter for softwood lignin, Green River Shale kerogen and n-hexane soot models. An unexpectedly low solubility parameter for a hardwood lignin model suggests, however, certain model deficiencies in terms of intermolecular interactions. In addition, a lower density for a n-hexane soot model relative to the sample was attributed to the small cluster size and poor parallel stacking of aromatic clusters in the model. Discussion of the results is provided in the context of utilizing thermodynamic properties as constraints for improved structural modeling of NOM.     

Aftershock sequences in the mid-ocean ridge environment: an analysis using hydroacoustic data

Hydroacoustic data from autonomous arrays and the U.S. Navy's Sound Surveillance System (SOSUS) provide an opportunity to examine the temporal and spatial properties of seismicity along portions of the slow-spreading Mid-Atlantic Ridge (MAR), intermediate-spreading Juan de Fuca Ridge (JdFR) and fast-spreading East Pacific Rise (EPR). Aftershock and foreshock events are selected from the hydroacoustic earthquake catalog using single-link cluster (SLC) analysis, with a combined space–time metric. In the regions examined, hydroacoustic data improve the completeness level of the earthquake catalog by 1.5–2.0 orders of magnitude, allowing the decay constant, p, of the modified Omori law (MOL) to be determined for individual sequences. A non-parametric goodness-of-fit test indicates six of the seven sequences examined are described well by a MOL model. The p-values obtained for individual ridge and transform sequences using hydroacoustic data are larger than that previously estimated from the analysis of a stacked sequence generated from teleseismic data. For three sequences along the Siqueiros, Discovery and western Blanco Transforms, p-values are estimated to be 0.94–1.29. The spatial distribution of aftershocks suggests that the mainshock rupture is constrained by intra-transform spreading centers at these locations. An aftershock sequence following a 7.1M_s thrust event near the northern edge of the Easter Microplate exhibits p=1.02±0.11. Within the sequence, aftershocks are located to the north of a large topographic ridge, which may represent the surface expression of the shallow-dipping fault that ruptured during the mainshock. Two aftershock sequences near 24°25′N and 16°35′N on the MAR exhibit higher p-values, 1.74±0.23 and 2.37±1.65, although the latter estimate is not well constrained because of the small number of aftershocks. Larger p-values along the ridge crest might reflect a hotter thermal regime in this setting. Additional monitoring, however, will be needed to determine if p-value differences between the ridge and transform sequences are robust. A 1999 sequence on the Endeavour segment of the JdFR, which has been correlated with changes in the hydrothermal system, is described poorly by the MOL model. The failure of the MOL model, the anomalously large number of earthquakes within the sequence and absence of a clearly dominant mainshock are inconsistent with aftershock activity and the simple tectonic origin that has been proposed previously for this sequence.     

Reversal asymmetry in Mesoproterozoic overprinting of the 1.88-Ga Gunflint Formation, Ontario, Canada: non-dipole effects or apparent polar wander?

Eighty-two palaeomagnetic samples of calcareous and jaspilitic grainstones (iron-formation or ‘taconite’) and chert carbonate were collected from the 1.88-Ga Gunflint Formation at 22 sites in the Thunder Bay area, Ontario. Twenty clasts of Gunflint taconite also were sampled from the basal conglomerate of the overlying Mesoproterozoic Sibley Group. Anisotropy of magnetic susceptibility measurements indicate the Gunflint Formation in the sampling area has not experienced regional dynamic metamorphism. Analyses by variable-field translation balance and X-ray diffraction show that the predominant magnetic mineral is hematite but a small amount of magnetite also is present in some samples. Altogether, 213 Gunflint specimens and 59 Sibley conglomerate specimens were subjected to stepwise thermal demagnetisation and 74 Gunflint specimens to stepwise alternating-frequency demagnetisation. The following components were isolated for the taconites:

• Gunflint magnetite: normal declination D=293.4°, inclination I=30.8°, α₉₅=7.2°, n=21; reverse D=86.7°, I=–54.6°, α₉₅=5.8°, n=29.

• Gunflint hematite: normal D=243.6°, I=23.6°, α₉₅=6.0°, n=11; reverse D=70.3°, I=–51.4°, α₉₅=3.2°, n=79.

• Sibley clasts magnetite: normal D=282.7°, I=33.4°, α₉₅=7.6°, n=20.

• Sibley clasts hematite: normal D=254.5°, I=56.2°, α₉₅=8.4°, n=13; reverse D=110.6°, I=–55.7°, α₉₅=8.3°, n=11.

None of these sets passed the reversal test, with the normal component generally being the shallower. Fold tests were negative or inconclusive and the conglomerate test also was negative. Chert carbonate at one other site appears to have acquired a remanence carried by magnetite (D=97.3°, I=−78.2°, α₉₅=6.3°, n=18) prior to folding related to Keweenawan (1.1 Ga) Logan diabase sill emplacement. Most of the components we identified match components for Keweenawan sills, volcanic rocks, intrusions and baked contact rocks in the Thunder Bay area, indicating that Keweenawan magmatism caused widespread chemical remagnetisation of the Proterozoic country rock in our sampling area. Although others have argued that asymmetry was a feature of the Keweenawan geomagnetic field, the declinations of our Gunflint and Sibley hematite and magnetite components are different, suggesting that the components were acquired at significantly different times. We conclude that the reversal asymmetry shown by our Gunflint and Sibley data may best be ascribed to apparent polar wander during Keweenawan times.     

Estimation of mean trace length of discontinuities

Summary Trace lengths of discontinuities observed on finite exposures are biased due to sampling errors. These errors should be corrected in estimating mean trace length. A technique, which takes into account the sampling errors, is proposed for estimating the mean trace length on infinite, vertical sections from the observations made on finite, rectangular, vertical exposures. The method is applicable to discontinuities whose orientation is described by a probability distribution function. The method requires that the numbers of discontinuities with both ends observed, one end observed, and both ends censored be known. The lengths of observed traces and the density function of trace length are not required. The derivation assumes that midpoints of traces are uniformly distributed in the vertical plane. Also independence between trace length and orientation is assumed. Data on a Pennsylvania shale in Ohio, U. S. A., were used as an example.Notations dip direction - direction of sampling plane - acute angle between dip direction and sampling plane - dip angle - _A apparent dip angle - mean density of trace mid-points per unit area - mean trace length - D diameter of discontinuity - f (.),g (.) probability density function - h height of rectangular window - estimator of mean trace length - m sample size, number of discontinuities intersecting window - m ₀ number of discontinuities intersecting window with both ends censored - m ₂ number of discontinuities intersecting window with both ends observed - n, N expected number of discontinuities intersecting the window - n ₀,N ₀ expected number of discontinuities intersecting the window with both ends censored - n ₂,N ₂ expected number of discontinuities intersecting the window with both ends observed - Pr (.) probability - w width of rectangular window - x trace length