Vertical orthogonal joints are a common feature in shallow crustal rocks. There are several competing theories for their formation despite the ubiquity. We examined the exceptional exposures of ...orthogonal joints in flat-lying Ordovician limestone beds from the Havre-Saint-Pierre Region in Quebec, Canada (north shore of Saint-Lawrence River) to test conceptual models of joint formation in a natural setting. In the region, the spacing of cross-joints is consistently larger than the spacing of systematic joints by a factor of 1.5 approximately. The joint-spacing-to-bed-thickness ratios (s/t) are much larger in these beds (s/t = 4.3 for systematic joints, and 6.4 for cross-joints) than those in higher strained strata along the south shore of the Saint-Lawrence River (s/t = 1), highlighting the effect of tectonic strain in decreasing fracture spacing and block size. The high values of s/t indicate that cross-joint formation was unlikely caused by a switch from compression to tension once a critical s/t ratio for systematic joints was reached (as hypothesized in previous studies). We proposed a new model for the formation of orthogonal joint systems where the principal stress axes locally switch during the formation of systematic fractures. The presence of ladder-shaped orthogonal joints suggests a state of effective stress with σ1∗»0 > σ2∗>σ3∗ and where σ2∗-σ3∗ is within the range of fracture strength variability at the time of fracture. This research provides a new mechanical model for the formation of orthogonal joint systems and cuboidal blocks.
Antigorite, the high‐temperature (HT) form of serpentinite, is believed to play a critical role in various geological processes of subduction zones. We have measured P‐ and S‐wave velocities (Vp and ...Vs), anisotropy and shear‐wave splitting of 17 serpentinite samples containing >90% antigorite at pressures up to 650 MPa. The new results, combined with data for low‐temperature (LT) lizardite and/or chrysolite, reveal distinct effects of LT and HT serpentinization on the seismic properties of mantle rocks. At 600 MPa, Vp = 5.10 and 6.68 km/s, Vs = 2.32 and 3.67 km/s, and Vp/Vs = 2.15 and 1.81 for pure LT and HT serpentinites, respectively. Above the crack‐closure pressure (~150 MPa), the velocity ratio of antigorite serpentinites displays little dependence on pressure or temperature. Serpentine contents within subduction zones and forearc mantle wedges where temperature is >300°C should be at least twice that of previous estimates based on LT serpentinization. The presence of seismic anisotropy, high‐pressure fluids, or partial melt is also needed to interpret HT serpentinized mantle with Vp < 6.68 km/s, Vs < 3.67 km/s, and Vp/Vs > 1.81. The intrinsic anisotropy of the serpentinites (3.8–16.9% with an average value of 10.5% for Vp, and 3.6–18.3% with an average value of 10.4% for Vs) is caused by dislocation creep‐induced lattice‐preferred orientation of antigorite. Three distinct patterns of seismic anisotropy correspond to three types of antigorite fabrics (S‐, L‐, and LS‐tectonites) formed by three categories of strain geometry (i.e., coaxial flattening, coaxial constriction, and simple shear), respectively. Our results are thought to provide a new explanation for various anisotropic patterns of subduction systems observed worldwide.
Key Points
Seismic velocities of antigorite serpentinites
Relationship between seismic anisotropy and antigorite lattice‐preferred orientation
A new explanation for anisotropic patterns of subduction systems
The Chinese Continental Drilling Project (CCSD) has drilled to a depth of 5100 m at Maobei (N34.40, E118.67), Donghai County, Jiangsu Province in the eastern segment of the Dabie‐Sulu ultrahigh ...pressure (UHP) metamorphic terrane. The borehole, which penetrated through all of the high velocity layers and seismic reflectors observed within the uppermost crust on seismic refraction and reflection profiles, reveals the main lithologies to be coesite‐bearing felsic gneisses, metabasic rocks (i.e., amphibolite, retrogressed, and non‐retrogressed eclogites) and ultramafic rocks (i.e., garnet peridotite and serpentinite). P wave velocities, anisotropy, and hysteresis of 31 typical CCSD core samples and 35 representative surface samples collected from the Sulu UHP belt were measured at hydrostatic confining pressures up to 800 MPa. The velocity‐pressure curves can be well described by a four‐parameter exponential equation derived from theory: V(P) = V0 + DP − B0 exp(−kP), where V0 is the projected velocity at zero pressure if pores/cracks were absent; D is the intrinsic pressure derivative of velocity in the linear elastic regime; B0 is the initial velocity drop caused by the presence of pores/cracks at zero pressure; and k is the decay constant of the velocity drop in the nonlinear poro‐elastic regime. The seismic hysteresis is caused by irreversible changes in grain contact, increases in microcrack aspect ratios and reduction of void space during the pressurization‐depressurization cycle. The statistical properties of P wave velocities in the UHP rocks provide an important set of basic information for the interpretation of field seismic data from the root zones of continental convergent orogenic belts and modern and ancient subduction zones.
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•A new expression of the likelihood and an improved ANN speed up Bayesian inference.•First robust identification of the volumetric heat capacity of the ground and grout.•Necessity to ...consider autocorrelation of the residuals is illustrated.•Impact of interpretation model and sampling frequency on robustness is established.•Accuracy is independent of test duration but precision increases for long tests.
Bayesian inference has tremendous potential for thermal response test analysis, as it provides uncertainty metrics that are useful for the design of ground-coupled heat pump systems. The inference process is computationally heavy and has so far been limited to a few thermal parameters and under the unrealistic assumption of residuals’ independence. In this work, a new closed-form expression of the likelihood and an improved artificial neural network are used to speed up Bayesian inference and consider the strong temporal correlation of the residuals. This efficient strategy allowed the robust inference of the joint distribution of five parameters. Using data measured during a real test of 168 h, this work shows that it is possible to robustly identify the volumetric heat capacity of the ground and grout with an uncertainty of 16.3 and 13.8%, a significant improvement. For the specific data used, it is shown that with independence assumption, some parameters are clearly unrealistic, a problem not encountered when the correlation of the residuals is considered. The impact of the interpretation model, of the test duration and of the sampling frequency was also assessed and illustrated by the sizing of a ground heat exchanger. Results reveal that joint identification of some thermal parameters cannot be achieved reliably by the finite line source model, that duration of thermal response tests should be at least 72 h to avoid large uncertainties on the parameters, and that recording temperature every 2 min degrades the identification of the volumetric heat capacity.
Lamé parameter (λ) and shear modulus (μ) are the most important, intrinsic, elastic properties of rocks. The Lamé parameter λ, which relates stresses and strains in perpendicular directions, is ...closely related to the incompressibility and contains a high proportion of information about the resistance to a change in volume caused by a change in pressure. Recent studies have emphasized the roles played by λ in the discrimination of gas sands from carbonates and shale in sedimentary basins and in the seismic reflection of crustal fault zones. Here we analyze the equivalent isotropic elastic data of 475 natural rocks in order to characterize λ values for common types of crystalline rocks in the Earth's crust and upper mantle and their variations with pressure (P), temperature (T), and mineralogical composition. When no partial melting, metamorphic reaction, dehydration, or phase transformation occurs, λ of a crystalline rock as a function of P and T can be described by λ = a + (dλ/dP)P − c exp(− kP) − (dλ/dT)T, where a is the projected λ value at zero pressure if microcracks were fully closed; dλ/dP is the pressure derivative in the linear elastic regime; c is the initial λ drop caused by the presence of microcracks at zero pressure; k is a decay constant of the λ drop in the nonlinear poroelastic regime; and dλ/dT is the temperature derivative. The parameter λ increases nonlinearly and linearly with increasing pressure at low (<∼300 MPa) and high (>∼300 MPa) pressures, respectively. In the regime of high pressures, λ decreases quasi‐linearly with increasing temperature with dλ/dT values in the range of 1–10 × 10−3 GPa/°C. Approaching the α‐β quartz transition temperature, quartzite displays negative λ values. In the λ‐ρ (density) and μ‐λ plots, the main categories of lithology can be clearly distinguished. The ultramafic rocks display systematic decreases in both μ and λ with increasing the degree of serpentinization. Eclogites, mafic rocks (gabbro, diabase, mafic granulite, and mafic gneiss), and felsic rocks (granite, diorite, felsic gneiss, intermediate gneiss, and metasediments) are characterized by high, moderate, and low μ and λ values, respectively. For pyroxene and olivine, both λ and ρ increase, but μ decreases with increasing the Fe/Mg ratios. In the plagioclase series, both λ and μ increases with increasing the anorthite content. Increases in the contents of garnets, sillimanite, rutile, zircon, ilmenite, and spinel result systematically in an increase in rock's λ and μ values. The present results provide improved constraints on the discrimination of composition for crustal and upper mantle rocks in terms of λ and μ.
An improvement to the thermal resistance capacity model (TRCM) used to model borehole heat exchangers is presented. Here, the original model is extended to integrate the thermal capacities of the ...heat carrier fluid and pipe and to better account for the spacing between the pipes. Model results are compared to results provided by numerical models and show very good agreement. It is shown that the improved model brings a significant improvement for short times over the original model, allowing a rapid computation of the temperature response function at virtually any time and distance from a single borehole.
► We improve the original thermal resistance capacity model (TRCM) to model ground heat exchangers. ► The improved model integrates the thermal capacities of the heat carrier fluid and pipes. ► Model results are compared to a numerical models and show very good agreement.
A constructive spectral method is presented to jointly calibrate hydrofacies and hydraulic conductivity to transient pressure heads. The method iteratively constructs Gaussian random fields to model ...the spatial correlation of hydraulic conductivity and hydrofacies using pluriGaussian simulation. Borehole conditioning is done quickly by replacing the slow Gibbs sampler method with an approach that is based on calibrating the underlying Gaussian fields that are subject to inequality constraints. Calibration to transient pressure heads is performed by shallow optimization of the phase vectors of the continuous spectral method. A parameterization technique makes it possible to reduce phase vector optimization from multivariate to univariate. The algorithm is tested on two-dimensional (2D) and 3D synthetic regional aquifers made of three hydrofacies. It reduced the objective function by one order of magnitude in one hundred iterations. The tests on the 2D aquifers indicated that the transient hydraulic heads alone cannot provide much information about hydrofacies. However, combining them with hydrofacies observations from boreholes results in improved hydrofacies identification compared to when only borehole data are used. Similar results were obtained in the 3D aquifer case, although the improvement in aquifer identification was less pronounced. The spectral method presented makes it possible to calibrate complex aquifers to transient heads using a limited number of calls to the flow simulator. Doing so helps to characterize sub-surface heterogeneity and assess the uncertainty and geological risks associated with groundwater flow.
Gibbs sampling is routinely used to sample truncated Gaussian distributions. These distributions naturally occur when associating latent Gaussian fields to category fields obtained by discrete ...simulation methods like multipoint, sequential indicator simulation and object-based simulation. The latent Gaussians are often used in data assimilation and history matching algorithms. When the Gibbs sampling is applied on a large lattice, the computing cost can become prohibitive. The usual practice of using local neighborhoods is unsatisfying as it can diverge and it does not reproduce exactly the desired covariance. A better approach is to use Gaussian Markov Random Fields (GMRF) which enables to compute the conditional distributions at any point without having to compute and invert the full covariance matrix. As the GMRF is locally defined, it allows simultaneous updating of all points that do not share neighbors (coding sets). We propose a new simultaneous Gibbs updating strategy on coding sets that can be efficiently computed by convolution and applied with an acceptance/rejection method in the truncated case. We study empirically the speed of convergence, the effect of choice of boundary conditions, of the correlation range and of GMRF smoothness. We show that the convergence is slower in the Gaussian case on the torus than for the finite case studied in the literature. However, in the truncated Gaussian case, we show that short scale correlation is quickly restored and the conditioning categories at each lattice point imprint the long scale correlation. Hence our approach enables to realistically apply Gibbs sampling on large 2D or 3D lattice with the desired GMRF covariance.
•GMRF template for the 3D case is derived.•Based on coding sets, exact and vastly parallel Gibbs sampling is implemented.•Convergence rate of Gibbs sampler is studied.•New method allows quick simulation of truncated Gaussian by acceptance.•Provide latent Gaussians to represent large discrete fields for history matching.
Mineral resources are typically quantified by estimating the grade–tonnage curve for different resource categories. Statutory resource assessment reports (e.g., NI-43-101), however, do not include a ...measure of uncertainty for the disclosed resources despite the major investments required for mining projects. Although conditional simulation can provide confidence intervals (CIs) for resource estimation, it requires a strong stationarity assumption and depends on the variogram model selected, which is often poorly defined with the available data. In order to avoid these limitations, this research proposes the use and comparison of two machine learning (ML) methods, multiple linear regression and a multilayer neural network, to generate tonnage curves and their CIs directly from the data. The classical variogram modeling step is replaced by the specification of intervals for each parameter of the selected variogram model. The learning is carried out in a perfectly controlled environment using simulations with known variograms. Numerous reference deposits are sampled, and for each one, a series of conditional realizations define the mean tonnage and CI curves. Different statistics computed for the entire data set are used as input to predict the tonnage and CI curves by the ML methods. The results indicate that there are no significant differences between the ML methods. In addition, ML resource predictions outperform those obtained with ordinary kriging, constrained kriging, uniform conditioning and indirect lognormal correction, being surpassed only by the discrete Gaussian model. Nevertheless, these predictors were favored by the use of true variogram models. Moreover, the coverage probabilities of different CIs reach the nominal levels indicating adequate resource uncertainty quantification. Finally, two case studies validate the effectiveness of the proposed approach for tonnage prediction and uncertainty quantification.
This study compared the performance of five variogram-based calibration approaches for five different geological problems. The geostatistical calibration methods studied were the sequential spectral ...turning band method (S-STBM), gradual deformation (GD), iterative spatial resampling (ISR), phase annealing (PA), and fast Fourier transform moving average simulated annealing (FFTMA-SA). The first two problems aimed to produce continuous and categorical simulations with known theoretical distributions. The other two problems were hydrogeological and aimed to calibrate the conductivity field to the pressure heads and travel time between wells. The final problem sought to generate non-Gaussian fields that exhibit spatial directional asymmetry. Two methods, S-STBM and FFTMA-SA, obtained good calibration results for all five problems, with S-STBM being the best overall, particularly for the categorical scenarios. The other methods, GD, ISR, and PA, exhibited a more variable performance. ISR did not properly calibrate simulations for the majority of the problems owing to slow convergence. PA adequately calibrated the five problems, but for the first two, the statistical distributions of the calibrated realizations departed significantly from the theoretical distributions. Similarly, GD exhibited slow convergence for the second problem, which resulted in significant differences compared with the known theoretical distributions. Because the S-STBM constructs the calibrated field directly, it avoids the difficulty encountered by the other calibration methods of having to begin from an unfavorable initial state. The examples clearly illustrate that the choice of the calibration algorithm is significant for some inversion problems.
•A comparative study of five variogram-based inversion methods is carried out.•Calibration to indirect data does not guarantee that the field preserves characteristics of the real field.•Calibration methods that are based on the perturbation of an initial state may face convergence issues.•Some common inversion problems cannot be used alone to assess method performance.•Perturbation type (global, local or constructive) impacts calibration to indirect data.
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