Thin Dyke Research Articles

Macromolecular structural changes in contact metamorphosed inertinite-rich coals from the No. 2 Seam, Witbank Coalfield (South Africa): Insights from petrography, NMR and XRD

The response of inertinite-rich Witbank coals (South Africa) to rapid heating was evaluated using petrography, selected Nuclear Magnetic Resonance (NMR) and X-Ray Diffraction (XRD) structural parameters. A total of thirteen (13) coal samples were collected from the No. 2 Seam; a set of six (6) samples from the western and the eastern sides of a ~ 0.4 m thick dolerite dyke emplaced into the coal seam at 0.25 m intervals. An unaltered coal (Un-C; the 13th sample), collected away from the dyke but within the same seam at the mine, was included for comparison. All 13 coal samples were dominated by inertinite. Semifusinite was most abundant in the samples from the western side of the dyke, whereas the proportion of inertodetrinite was highest in samples from the eastern side. Due to very low vitrinite contents, mean random total reflectance (%RoTmr) was used to compare the maturity of the inertinite-rich coals. A decrease in volatile matter was correlated with an increase in mean random total reflectance (%RoTmr; measured on semifusinite, inertodetrinite, and vitrinite), the latter used as a potential maturity indicator for the thermally altered inertinite-rich coals. Mean random total reflectance rose from a background value of 1.52%RoTmr (for Un-C) to 2.83%RoTmr for the coal sample at the western coal-dyke contact (0.0 m). The corresponding reflectance values for the thermally altered coals from the eastern side were less consistent, decreasing closest to the dyke (1.93%RoTmr for the sample at 0.0 m); this trend is also reflected in the NMR and XRD parameters. Eight (8) samples were selected for the NMR analysis, representative of the maceral composition and maturities of the coals investigated. For Un-C, the fraction of aromatic carbons (fa) was 0.88 (average number of carbons per aromatic cluster (C) = 17), and the interplanar spacing (d002) was 3.48 Å (with a crystallite height of 22.09 Å). For the thermally altered coals from the western side, fa decreased from 0.96 at the coal-dyke contact (C = 26 for sample at 0.0 m) to 0.92 for the sample at 1.25 m from the dyke (C = 20). For samples from the eastern side, fa increased from 0.91 (C = 19 for the sample at 0.25 m) to 0.93 (C = 23 for sample at 0.5 m), before decreasing to 0.89 further from the dyke (C = 18 for sample at 1.25 m). In general, the d002 values for the thermally altered coal samples were larger than for graphite. Similarly, only marginal increases in crystallite heights were observed. Although the dyke induced coal maturation and the resultant increase in fa, the overall lack of graphitic order in the thermally altered coals was ascribed to the limited thermal energy provided by the relatively thin dyke; increased heat input would be required to effect significant structural changes in the inertinite-rich coals. Differences between the two sets of thermally altered coal samples were attributed to the emplacement dynamics of the igneous intrusion, which require further investigation.

Subsoil Characterization for Foundation Stability Using Geophysical and Geotechnical Methods

An Integrated geophysical and geotechnical subsoil characterization of parts of the new stadium complex, Akure, southwestern Nigeria had been carried out with a view to characterize the subsoil materials for stability of proposed engineering foundation. Five (5) magnetic and three (3) dipole-dipole profiling were carried out at station separation of 10 m along the traverses. Twenty one (21) Vertical Electrical Sounding (VES) measurements were made at selected locations along the traverses. A total of five (5) soil samples were collected from a dug pit at a depth of 1.0 m for laboratory analysis. The magnetic profiles delineated characteristic one to two negative peak amplitude anomalies that are typical of thin dipping dyke models (suspected to be fractures, shear zones, faults or geological contacts) along Traverses 1-5. The 2-D geomagnetic section delineated overburden thicknesses ranging from 5 – 15 m along the Traverses. The subsurface geologic units delineated by the geoelectric sections and the 2-D resistivity images consisting of the topsoil, weathered layer, partly weathered/fractured basement and fresh bedrock. Part of the topsoil and the weathered layer are characterized by low resistivity values suggestive of the presence of clay and or weak geomaterials at a depth range of 1 – 4 m within which civil engineering foundation are usually placed. These zones and the fractured/fault zones delineated by the magnetic methods constitute weak geomaterials that are considered to be inimical to civil engineering structures within the study area. Results of geotechnical analysis of soil samples adjudged plasticity indices of samples A, C and D to be of high index and were characterized by high plasticity/compressibility and consequently of low engineering competence. Samples B and E were classified as low-medium plasticity/compressibility, and are rated moderate–high engineering competence. However, it was observed that soil with higher liquid limits or plasticity index have lower electrical resistivity values and hence were adjudged low in engineering foundation competence. Based on the analysis of the results obtained from this study, the engineering foundation suitability of the soil were generally classified as good (B and E), fair (D) and poor (A and C). It can therefore be concluded that the subsoil in the investigated area are generally of low to high civil engineering competence. Keywords: Geophysical; Geotechnical; Subsoil; Competence; Characterization; Foundation, Stability. DOI: 10.7176/JEES/10-6-08 Publication date: June 30 th 2020

Grey wolf optimizer: a new strategy to invert geophysical data sets

ABSTRACTThere is no meta‐heuristic approach best suited for solving all optimization problems making this field of study highly active. This results in enhancing current approaches and proposing new meta‐heuristic algorithms. Out of all meta‐heuristic algorithms, swarm intelligence is preferred as it can preserve information about the search space over the course of iterations and usually has fewer tuning parameters. Grey Wolves, considered as apex predators, motivated us to simulate Grey Wolves in the optimization of geophysical data sets. The grey wolf optimizer is a swarm‐based meta‐heuristic algorithm, inspired by mimicking the social leadership hierarchy and hunting behaviour of Grey Wolves. The leadership hierarchy is simulated by alpha, beta, delta and omega types of wolves. The three main phases of hunting, that is searching, encircling and attacking prey, is implemented to perform the optimization. To evaluate the efficacy of the grey wolf optimizer, we performed inversion on the total gradient of magnetic, gravity and self‐potential anomalies. The results have been compared with the particle swarm optimization technique. Global minimum for all the examples from grey wolf optimizer was obtained with seven wolves in a pack and 2000 iterations. Inversion was initially performed on thin dykes for noise‐free and noise‐corrupted (up to 20% random noise) synthetic data sets. The inversion on a single thin dyke was performed with a different search space. The results demonstrate that, compared with particle swarm optimization, the grey wolf optimizer is less sensitive to search space variations. Inversion of noise‐corrupted data shows that grey wolf optimizer has a better capability in handling noisy data as compared to particle swarm optimization. Practical applicability of the grey wolf optimizer has been demonstrated by adopting four profiles (i.e. surface magnetic, airborne magnetic, gravity and self‐potential) from the published literature. The grey wolf optimizer results show better data fit than the particle swarm optimizer results and match well with borehole data.

Global nonlinear optimization for the interpretation of source parameters from total gradient of gravity and magnetic anomalies caused by thin dyke

An efficient approach to estimate model parameters from total gradient of gravity and magnetic data based on Very Fast simulated Annealing (VFSA) has been presented. This is the first time of applying VFSA in interpreting total gradient of potential field data with a new formulation estimation caused due to isolated causative sources embedded in the subsurface. The model parameters interpreted here are the amplitude coefficient ( k ), exact origin of causative source ( x 0 ) depth ( z 0 ) and the shape factors ( q ). The results of VFSA optimization show that it can uniquely determine all the model parameters when shape factor is constrained. The model parameters estimated by the present method, mostly the shape and depth of the buried structures were found to be in excellent agreement with the actual parameters. The method has also the proficiency of evading highly noisy data points and improves the interpretation results. Study of histogram and cross-plot analysis also suggests the interpretation within the estimated uncertainty. Inversion of noise-free and noisy synthetic data for single structures as well as field data demonstrates the efficacy of the approach. The technique has been warily and effectively applied to real data examples (Leona Anomaly, Senegal for gravity and Pima copper deposit, USA for magnetic) with the presence of ore bodies. The present method can be extremely applicable for mineral exploration or ore bodies of dyke-like structure embedded in the shallow and deeper subsurface. The computation time for the whole process is very short.

Inversion of Source Parameters from Magnetic Anomalies for Mineral/Ore Deposits Exploration Using Global Optimization Technique and Analysis of Uncertainty

Global optimization algorithm using very fast simulated annealing has been used for modeling of magnetic anomaly over various idealized geobodies for mineral/ore deposit investigation. The present technique shows that it can match the observed data very well assuming some simple geometrical bodies such as sphere, horizontal cylinder and thin dyke or sheet. Uncertainty associated with the modeling was also studied. It has been found that the obtained source parameters are strongly identical when all the parameters are optimized. The present study shows that amplitude coefficient depends on the shape factor. The relation between them shows a multimodel-type uncertainty. The shape factor modeled from several VFSA runs shows the different kind of subsurface structure. Constraining the shape factor gives reliable results and analysis of histograms and cross-plots also gives the utmost reliable results, which show a unimodel character. Inversion of synthetic noise-free and noisy data shows the worth of the present work. The present algorithm was also tested in five field case studies for mineral/ore exploration. Computation time for this present work is very minimal.

Effect of host-rock rheology on dyke shape, thickness and magma overpressure

The size and thickness of dykes is of fundamental importance for volcano dynamics because dykes are the primary path for magma transport, and because large numbers of dykes often comprise a major proportion of the volcanic edifice and of the underlying crust. Standard elastic models predict dyke geometry to be elliptic in cross-section for constant overpressure and uniform host-rock properties, whereas observations show that dyke thickness is typically more nearly constant with a sharp taper at the ends. Moreover, the predicted overpressures required to inflate dykes in a purely elastic medium are often significantly higher (>150 MPa and up to 2 GPa) than those estimated by other means (about 1–50 MPa). In this study, we use 2-D finite element models to test whether other host-rock rheologies lead to more realistic dyke shapes and overpressures. We examine three different rheologies, each of which is affected by the presence of the dyke itself: (1) elasticity with reduced moduli in regions of low pressure or tension; (2) elastoplasticity with plastic failure in the high-stress regions surrounding the dyke tips; (3) viscoelasticity with a viscosity decrease due to heating by the dyke. We use rheological parameters obtained from laboratory experiments whenever possible, and assume static conditions for the final dyke shape. We find that all three rheologies tend to make the dyke more rectangular relative to the elliptical dykes of the linearly elastic models. The change in shape is due to enhanced deformation in the high-stress zone surrounding the dyke tip. We also find that the overpressure required to inflate an initially thin dyke to a given thickness is reduced for all three rheologies. The greatest decrease in overpressure by a factor of about 0.1 is observed for the elastoplastic model, and for the viscoelastic model if the dyke intrudes into moderately pre-heated host-rock. We discuss our results with respect to dyke observations from Rum Island (Scotland) and use these as a guide to evaluate our models.

The amplitude and phase of the derivatives of the magnetic anomalies of thin dykes and contacts

If the horizontal and vertical derivatives of the total field magnetic anomalies of thin dykes and contacts (and the magnetic anomaly from a thin dyke) are put into an amplitude-phase form, then this can aid in their interpretation. First, it allows derivatives of fractional order to be calculated analytically; second, estimates of the source dip can be made; and finally, the relationships between local wavenumber and source-distance semi-automatic interpretation methods are clarified. The approach is demonstrated on synthetic data and aeromagnetic data from South Africa.

Inversion of the amplitude of the two-dimensional analytic signal of the magnetic anomaly by the particle swarm optimization technique

SUMMARY Amplitude of the 2-D analytic signal of the magnetic anomaly profile is independent of the directions of the Earth's magnetic field vector and remnant magnetization of the causative source. It exhibits peaks corresponding to the locations of the corners of a causative source, modelled by say a polygon. It also exhibits a peak corresponding to different idealized source geometries related to the structural indices. This amplitude is computed from the first-order horizontal and vertical derivatives of the observed magnetic anomaly and is relatively less noisy than second-order derivatives. The amplitude can also be computed directly from the measured derivatives. Particle swarm optimization (PSO)—a global optimization technique is applied to interpret this amplitude in terms of the horizontal location and depth, constant (related to magnetization) and various source geometries through structural indices. Applicability of the proposed technique is evaluated through the analyses of simulated magnetic anomalies (noise-free and corrupted with 20 per cent random noise) over different types of source geometries, namely, a thin dyke and a contact with high accuracy in parameter estimation. Studies on the choices of search parameter space reveal that a relatively wide search space can be assigned. Practical applicability of the proposed technique has been demonstrated through three magnetic anomaly profiles digitized from published literature. The results of PSO, Euler deconvolution, enhanced local wavenumber and drill hole are comparable. PSO results also seem to be more stable than other techniques.

High‐resolution seismic reflection imaging of a thin, diamondiferous kimberlite dyke

Seismic reflection techniques are, for the first time, used to image a thin, diamondiferous kimberlite dyke from subcrop to depths greater than 1300 m. Geophysical exploration for kimberlite deposits typically involves airborne potential field surveys that are well suited for detecting vertical outcropping pipes but often fail to reveal thin, subhorizontal dykes and sills. Because seismic techniques are especially well suited for mapping structures that have shallow dips and strong impedance contrasts, a feasibility study and seismic reflection survey were undertaken on the diamondiferous Snap Lake dyke (Northwest Territories, Canada) to evaluate the potential for using seismic techniques on these targets. The dyke (average thickness 2–3 m) provides an excellent test site because a drilling program has defined the gross dyke geometry and provides core samples from the kimberlite and host rocks. The feasibility study involved measuring P‐velocity and density of selected cores. Using these data, reflectivity and finite‐difference synthetic seismogram techniques were used to explore the resolution limitations and determine the acquisition parameters for a reflection survey. The seismic survey included two 2D lines designed to obtain comparative data sets from different sources (explosives and vibroseis) and ground types (land or lake‐ice). The explosive‐source land data yielded a superb image of the thin dyke. The vibroseis data, however, detected the dyke only when sources and geophones were on land; the dyke was not imaged beneath the ice due to reverberation and attenuation effects. Correlations are observed between reflection attributes and dyke properties (thickness, structure, and physical properties). The results demonstrate that, in the appropriate situation, seismic methods have great potential for use in kimberlite exploration, subsurface mapping, and detailed imaging for mine development purposes.

A Least-Squares Minimisation Approach to Depth, Index Parameter, and Amplitude Coefficient Determination from Magnetic Anomalies Due to Thin Dykes

We have developed a least-squares approach to determine, successively, the depth, index parameter, and amplitude coefficient of a buried thin dyke, using moving-average residual anomalies obtained from magnetic data using filters of successive graticule spacings. By defining the moving-average residual anomaly value at the origin on the profile, the problem of depth determination is transformed into the problem of solving a nonlinear equation, f(z) = 0. Knowing the depth and applying the least-squares method, the index parameter is determined by solving a nonlinear equation of the form λ(θ) = 0. Finally, knowing the depth and the index parameter, the amplitude coefficient is determined in a least- squares sense using a simple linear equation. In this way, the depth, index parameter, and amplitude coefficient are determined individually from all observed magnetic data. We have developed a procedure for automated interpretation of magnetic anomalies attributable to thin dykes. We apply the method to synthetic data with random errors, complicated regionals, and interference from neighbouring magnetic rocks, and we test it on two field examples from Brazil and Canada.

A study of the self-potential field produced by a polarised inclined sheet in an electrically homogeneous and transversely anisotropic ground

In the present paper, the self-potential (sp) field is studied, which is produced by an inclined sheet (thin dyke) in an electrically homogeneous and transversely anisotropic ground. At first, the mathematical expression for the sp anomaly is deduced, by integration of the formula for the self-potential field produced by a point pole in a transversely anisotropic medium (Skianis & Herntmdez 1999). Then, the behavior of the sp curve is studied, for various angles of schistosity. The whole anomaly may be displaced along the horizontal axis and deformed in terms of amplitude and shape. Particular emphasis is given on the enhancement and suppression of the positive center of the self-potential, which depends on the values and orientations of the schistosity angle of the ground and the dip angle of the inclined sheet. These deformations of the sp anomaly, may introduce significant errors in the calculation of the parameters of the polarized body, if ground anisotropy is not taken into account. Therefore, new methodologies have to be developed, for a reliable quantitative interpretation of self-potential field data. In this paper, a direct interpretation method is proposed, which consists of two steps: In step one, the parameters of the inclined sheet are determined, assuming a homogeneous and isotropic ground. In this stage, any quantitative interpretation method, referred in the international bibliography, may be used. Secondly, the true parameters of the dyke are estimated, by a set of transformations in which the anisotropy coefficient and the schistosity angle are introduced. In order to apply this method, a priori information about ground anisotropy should be available, by dc geoelectrical and geological investigations. The efficiency of the method was tested on a synthetic model. In the first stage, the quantitative interpretation method of Murty & Haricharan 1985 was employed. In the second stage, the calculated parameters of the first step, served as input values of the transformations, and the real parameters of the inclined sheet were estimated. There was a good agreement between the parameter values of the synthetic model and the ones found by the proposed method. The results and conclusions of this paper, may be useful in detecting sulfide mineralization deposits or graphite.

Transient electromagnetic response from a thin dyke in the earth

An electromagnetic solution for a thin tabular conductor in a lossy medium is presented. This is an extension of “Maxwell's theorem.” Both impulsive and time harmonic electric line sources are analyzed. The orientation of the source is parallel to the sheet conductor. This assumption renders the problem two‐dimensional. The solution and associated analytical results have application to geophysical probing. For example, the sheet can model a conducting ore dyke or a fluid‐filled crack in an induction logging application. Transient numerical results are seen to be diagnostic of the conductivity thickness product W = σ2d.

Spectral characteristics of the gravity and magnetic profile data over a geological contact

A simplified frequency domain method is described for the interpretation of gravity, gravity gradient, and vertical, horizontal and total intensity magnetic profile data over a buried geological contact. In this method, the observed data are first transformed from the space to the frequency domain using Fourier transformation. Least square linear regression analyses of the resulting phase spectrum and of the logarithms of modified amplitudes then enable direct estimations of the different parameters of interest, the modifications of the amplitudes being affected by multiplying them with the corresponding frequencies in the case of gravity gradient and the magnetic data and by multiplying them with the squares of corresponding frequencies in the case of gravity data. The use of this method, which is equally effective for interpreting the horizontal gradient of magnetic profile data over a thin dyke of infinite depth extent, is illustrated with the help of theoretical amplitude and phase spectra. The limitations of this method are also discussed.

ON THE ELECTROMAGNETIC RESPONSE OF AN IMPERFECTLY CONDUCTING THIN DYKE

The theoretical electromagnetic response from a thin dyke has been recently treated by Wesley (1958). In his first paper, the dyke was idealized by a perfectly conducting half‐plane, and the source was taken to be a magnetic dipole. The Green’s function he obtains is very simple and is in agreement with an earlier result (Bateman, 1932).

RESPONSE OF THIN DYKE TO OSCILLATING DIPOLE

A dyke of sulfide ore may be geophysically prospected by observing its response to a slowly oscillating magnetic dipole source. To a first approximation the field produced by a thin dyke is given by a dyke of infinite conductivity and vanishing thickness in a vacuum (Wesley, 1958, Geophysics, v. 23, p. 128). In order to identify the ore and to estimate the size of the deposit, it is necessary to consider further approximations involving the conductivity and thickness of the dyke. By a type of analytical continuation an approximation is found which agrees both with the exact solution for a dyke of infinite conductivity and vanishing thickness and with the exact solution (approximated only for ωσ large and also for σ small) for an infinite slab of finite conductivity and nonvanishing thickness, the dyke appearing as an infinite slab when both source and observer are near the dyke but far removed from the edge. The solution is very good provided the dyke is geometrically thin.

AN INCLUSION-BEARING OLIVINE MELILITITE FROM MUKOROB, SOUTH WEST AFRICA

A thin porphyritic dyke, cream-brown in colour, is intruded into Upper Dwyka shales near the kimberlite pipe on Mukorob, South West Africa. Now highly calcitized, the rock was probably an olivine melilitite when fresh. Black ellipsoidal ilmenite-covered altered olivine inclusions give the rock its curious appearance. Other inclusions of rounded replaced olivine and rock types commonly found as cognate xenoliths in kimberlite are scattered throughout the dyke rock. Although the rock is intensely calcitized, it has been possible from the investigation to offer some suggestions concerning the close petrogenetic association of kimberlite and olivine melilitite.