Thin Dike Research Articles

The First Discovery of Archean Dolerite Dikes in the Western Part of the Aldan Shield

Dolerite dikes were studied in the western part of the Aldan terrane, in the middle reaches of the Tokko River. These dolerite dikes form a swarm of submeridional trend about 1 km wide. The dolerites of the thickest dike preserve their primary textural and structural features and mineral composition: plagioclase + pigeonite + augite + titanomagnetite. Dolerite in the chilled margins and central parts of the dike are homogeneous in composition, corresponds to low-Mg tholeiites, has low contents of Ti and other HFSE, with weak enrichment in light REE and small negative Nb anomalies. Sm–Nd isotope data on magmatic minerals of dolerite from the central part of the dike yield a good linear regression in an isochron diagram that gives to an age of 2510 ± 64 Ma, which probably corresponds to the crystallization age of the basalt. Metadolerites in a thin dike retain plagioclase porphyritic structures, but the pyroxenes are completely replaced by amphibole and chlorite. The metadolerites are contrastingly different in low contents of MgO, Cr, and Ni and in higher contents of TiO2, Fe2O3, P2O5, Nb, and all REE. The differences in the composition of the dikes may be explained by the longterm (about 65%) crystallization differentiation of the initial melt and the emplacement of the residual melt from a shallow intermediate magma chamber via opening cracks. Such conditions probably may have existed in tectonically stable intraplate settings. The age of the dolerites of the dike swarm is comparable to that of the anorogenic granites of the Nelyuki complex (~2.4–2.5 Ga), which are widespread in the western part of Aldan granulite–gneiss terrane. Our data bridge some gaps in characteristics of intraplate anorogenic magmatism that occurred in the western Aldan Shield in the Late Archean and marked the final consolidation of a large block of Archean crust in the Chara–Olekma granite–greenstone area.

Minerals and ore deposits exploration using meta-heuristic based optimization on magnetic data

The difficulties in unravelling the tectonic structures, in some cases, prevent the understanding of the ore bodies' geometry, leading to mistakes in mineral exploration, mine planning, evaluation of ore deposits, and even mineral exploitation. For that reason, many geophysical techniques are introduced to reveal the type, dimension, and geometry of these structures. Among them, electric methods, self-potential, electromagnetic, magnetic and gravity methods. Global meta-heuristic technique using Whale Optimization Algorithm (WOA) has been utilized for assessing model parameters from magnetic anomalies due to a thin dike, a dipping dike, and a vertical fault like/shear zone geological structure. These structures are commonly associated with mineralization. This modern algorithm was firstly applied on a free-noise synthetic data and to a noisy data with three different levels of random noise to simulate natural and artificial anomaly disturbances. Good results obtained through the inversion of such synthetic examples prove the validity and applicability of our algorithm. Thereafter, the method is applied to real case studies taken from different ore mineralization resembling different geologic conditions. Data are taken from Canada, United States, Sweden, Peru, India, and Australia. The obtained results revealed good correlation with previous interpretations of these real field examples.

Using the analytic signal amplitude to determine the location and depth of thin dikes from magnetic data

A semiautomatic method to determine the location and depth of thin dykes is introduced. The ratio of analytic signal amplitudes of orders 0 and 1 of the magnetic anomaly from a thin dike was used to give the distance [Formula: see text] to the dike. Local minima of [Formula: see text] gave the depth to the dike, and the position of these minima gave its horizontal location. Because in the method we used just the magnetic field and its first-order derivatives, it was less sensitive to noise than were higher order derivative-based methods. Once the position of the dike has been determined, then its dip and susceptibility-thickness product can be calculated from the analytic signal amplitude, providing that the magnetization vector is known.

Fair function minimization for interpretation of magnetic anomalies due to thin dikes, spheres and faults

Abstract A new method is proposed to interpret magnetic anomalies due to a thin dike, a sphere, and a fault like structure, where depth, horizontal location, effective magnetization intensity and effective magnetization inclination of a buried structure are simultaneously obtained. The proposed method is based on Fair function minimization and also on stochastic optimization modeling. This new technique was firstly tested on a theoretical synthetic data randomly generated by a chosen statistical distribution from a known model with different random noises components. This mathematical simulation shows a very close agreement between the assumed and the estimated parameters. The applicability and validity of this method are thereafter applied to magnetic anomaly data taken from United States, Australia, India, and Brazil. The agreement between the results obtained by the new method and those obtained by other interpretative methods is good and comparable. Moreover, the depth obtained by such a method is found to be in high accordance with that obtained from drilling information.

A New Best-Estimate Methodology for Determining Magnetic Parameters Related to Field Anomalies Produced by Buried Thin Dikes and Horizontal Cylinder-like Structures

A new best estimate methodology is proposed and oriented towards the determination of parameters related to a magnetic field anomaly produced by a simple geometric-shaped model or body such as a thin dike and horizontal cylinder. This approach is mainly based on solving a system of algebraic linear equations for estimating the three model parameters, e.g., the depth to the top (center) of the body (z), the index parameter or the effective magnetization angle (θ) and the amplitude coefficient or the effective magnetization intensity (k). The utility and validity of this method is demonstrated by analyzing two synthetic magnetic anomalies, using simulated data generated from a known model with different random errors components and a known statistical distribution. This approach was also examined and applied to two real field magnetic anomalies from the United States and Brazil. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable. Moreover, the depth obtained by such an approach is found to be in high accordance with that obtained from drilling information. The advantages of such a proposed method over other existing interpretative techniques are clarified, where it can be generalized to be automatically applicable for interpreting other geological structures described by mathematical formulations.

A least‐squares standard deviation method to interpret magnetic anomalies due to thin dikes

We have developed a least‐squares method to determine simultaneously the depth and the horizontal position (origin) of a buried thin dike that extends in both strike direction and down dip (2D) and in which the depth is much greater than the thickness from horizontal gradients obtained numerically from magnetic data using filters of successive window lengths. The method involves using a relationship between the depth and the horizontal position of the source and a combination of windowed observations. The method is based on computing the standard deviation of the depths determined from all horizontal gradient anomalies for each horizontal position. The standard deviation may generally be considered as a criterion for determining the correct depth and the horizontal position of the buried dike. When the correct horizontal position value is used, the standard deviation of the depths is less than the standard deviation using incorrect horizontal position values. This method can be applied to residuals as well as to the observed magnetic data. The method is applied to synthetic examples with and without random errors. The present method was able to provide both the depth and horizontal position of the source accurately. The practical utility of the method is tested on an outcropping dike in Canada.

A Robust Nonlinear Inversion for the Interpretation of Magnetic Anomalies Caused by Faults, Thin Dikes and Spheres Like Structure Using Stochastic Algorithms

A geophysical interpretative method is proposed to depth, amplitude coefficient (effective magnetization intensity), and index parameter (effective magnetization inclination) determination of a buried structure from magnetic field data anomaly due to a fault, a thin dike or a sphere-like structure. The method is based on the nonlinearly constrained mathematical modelling and also on the stochastic optimization approaches. The proposed interpretative method was first tested on a theoretical synthetic model with different random errors, where a very close agreement was obtained between the assumed and the evaluated parameters. The validity of this method was also tested on practical field data taken from United States, Australia, India and Brazil, where available magnetic data existed and were previously analyzed by different interpretative methods. The agreement between the results obtained by our developed method and those obtained by the other geophysical methods is good.

Euler deconvolution of the analytic signal and its application to magnetic interpretation

ABSTRACTEuler deconvolution and the analytic signal are both used for semi‐automatic interpretation of magnetic data. They are used mostly to delineate contacts and obtain rapid source depth estimates. For Euler deconvolution, the quality of the depth estimation depends mainly on the choice of the proper structural index, which is a function of the geometry of the causative bodies. Euler deconvolution applies only to functions that are homogeneous. This is the case for the magnetic field due to contacts, thin dikes and poles. Fortunately, many complex geological structures can be approximated by these simple geometries. In practice, the Euler equation is also solved for a background regional field. For the analytic signal, the model used is generally a contact, although other models, such as a thin dike, can be considered. It can be shown that if a function is homogeneous, its analytic signal is also homogeneous. Deconvolution of the analytic signal is then equivalent to Euler deconvolution of the magnetic field with a background field. However, computation of the analytic signal effectively removes the background field from the data. Consequently, it is possible to solve for both the source location and structural index. Once these parameters are determined, the local dip and the susceptibility contrast can be determined from relationships between the analytic signal and the orthogonal gradients of the magnetic field. The major advantage of this technique is that it allows the automatic identification of the type of source. Implementation of this approach is demonstrated for recent high‐resolution survey data from an Archean granite‐greenstone terrane in northern Ontario, Canada.

Shape and depth solutions from magnetic data using a parametric relationship

We have developed a simple method to simultaneously determine the shape (shape factor) and the depth of a buried structure from magnetic data. The method is similar to Euler deconvolution, but it solves for shape and depth independently. The method involves using a relationship between the shape factor, the depth to the source, and a combination of observations at symmetric points with respect to the coordinate of the source center with a free parameter (graticule spacing). The relationship represents a parametric family of curves. For a fixed free parameter, the depth is determined for each shape factor. The computed depths are plotted against the shape factors representing a continuous monotonically increasing curve. The solution for the shape and depth of the buried structure is read at the common intersection of the parametric curves. The parametric curves method is applied to two theoretical magnetic anomaly profiles due to a thin dike and a horizontal cylinder. The method is also tested on a field example from Brazil. In all cases, the shape and depth solutions obtained are in good agreement with the actual ones.

An iterative least-squares approach to depth determination from residual magnetic anomalies due to thin dikes

We have developed a least-squares approach to depth determination from residual magnetic anomalies due to thin dikes. By defining the zero-anomaly distance x 0 and the anomaly value T(0) at the origin on the profile, the problem of depth determination from magnetic data has been transformed into the problem of finding a solution of a non-linear equation. Procedures are also formulated to estimate the amplitude coefficient and the index parameter. The method is applied to synthetic data with and without random noise. The obtained depth agrees with the model depth within ±4%. The percentage error approaches zero as the sampling interval decreases to 0.25 depths units. Error in the depth parameter due to errors in x 0 and T(0) was also studied through imposing ±1–10% errors on these parameters on a synthetic profile due to a thin dike. The maximum error in depth is ±12%.

Zagami: Product of a two-stage magmatic history

Large specimens of the Zagami shergottite show highly varied grain sizes and mineral abundances on a cm scale and preferred alignment of pyroxene laths. We document the presence of whitlockite and of melt veins and pockets of shock origin. Pyroxene crystals have homogeneous Mg-rich pigeonite and augite cores, overgrown by Fe-rich, zoned pyroxene (mostly pigeonite) rims. Amphibole-bearing magmatic (melt) inclusions occur exclusively in the cores. We conclude that Zagami experienced a twostage crystallization history. The first stage occurred in a deep-seated, slowly cooling magma chamber. There, the homogeneous Mg-rich cores of the pyroxenes crystallized during relatively slow cooling. The deep-seated origin of the cores is also indicated by the presence of amphibole within them, which requires pressures of formation equivalent to crystallization at depths > 7.5 km on Mars. Modest abundance of homogeneous Mg-rich cores (15–20% ) indicates that crystal settling did not play a significant role in this part of the magma chamber. During the second stage, the Mg-rich pyroxenes were entrained into a magma that either intruded to the near-surface and cooled in a relatively thin dike or sill, or extruded to the surface and crystallized in a lava flow > 10 m thick, again without indications for crystal settling. This scenario is suggested by estimates of cooling rates of 0.1–0.5°C/h, based on sizes of the plagioclase (maskelynite) crystals, and of ∼0.02°C/h, based on the width of pyroxene exsolution lamellae ( brearley, 1991). Irregular shapes of the Mg-rich cores result from resorption and possible solid-state diffusion, and the shapes and sizes of the pyroxenes after crystallization of Fe-rich pigeonite rims onto the cores were strongly controlled by the shapes and sizes of the cores. The finer-grained areas of the rock inherited smaller and more numerous Mg-rich pyroxene cores from the first stage than did the coarser-grained areas. Crystallization of both augite and pigeonite cores at depth, but mostly pigeonite rims in the nearsurface environment, may be the result of a phase-boundary shift and expansion of the pigeonite stability field at lower pressures. The estimated depth of the magma chamber for Zagami of >7.5 km and thickness of the putative lava flow of > 10 m are consistent with calculations and observations of volcanic constructs and flows in the Tharsis region of Mars.

Transient electromagnetic responses of high‐contrast prisms in a layered earth

An integral‐equation solution for transient electromagnetic (TEM) scattering by prisms in layered half‐spaces is formulated to provide meaningful results when the prisms are in highly resistive layers. A prism is replaced with an unknown scattering current, which is approximated with pulse and divergence‐free basis functions in the frequency domain. Divergence‐free basis functions model eddy currents that exist in confined bodies in a very resistive host and hence simulate the inductive responses of the prisms. A Galerkin solution for the scattering current is obtained where the dominant charge operator is eliminated from part of the solution by integrating the tensor Green’s function around rectangular paths. After the scattering current is determined, the electric and magnetic fields scattered by the prisms are calculated; and the corresponding TEM responses are obtained by inverse Fourier transformation. The resulting solution provides meaningful results over a wide range of resistivities in layered hosts including the case of free space. The masking effect of a conductive overburden delays and suppresses the three‐dimensional TEM response of a conductor. The overburden response must be removed for the conductor’s response to be fully interpretable. An interpretation of the conductor with free‐space models is a poor approximation when the basement rock is conductive. Instead of an exponential decay at late times, the conductor’s response decays in an inverse power relationship. When the basement resistivity is increased, the conductor exhibits an exponential decay at late times. For a thin dike, the time constant estimated from this decay is identical to that for a thin plate in free space. However, the response of the dike buried beneath the overburden is larger than the response of the dike in free space. This increase in the response of the dike will bias modeling it in free space with thin plates. We have used the solution to gain insight regarding the lateral resolution of two vertical conductors for the fixed‐loop and central‐loop survey configurations. The results suggest that resolution of multiple conductors is very poor in a fixed‐loop survey; but in a central‐loop survey, the resolution is much better, provided the data are interpreted at early times. At later times, multiple conductors may not be resolvable and interpretational ambiguities could arise.

Rapid gravity interpretation by nomograms — A discussion

Pal (1983) presented a set of nomograms for interpreting gravity fields due to some two-dimensional models (thin dike, geological contact and thick dike) under the assumption that the depth to the bottom is infinite for all models. Raising a discussion on this paper, Rambabu and Atchuta Rao (1985) pointed out the mathematical fallacies, rightly questioning the validity of Pal’s (1983 ) nomograms. I have the following additional comments to make. Taking the example of a thin dike, Pal’s (1983) study can be more clearly expanded in the following steps. (i) The expression for gravity field dg( x)~ due to a thin dike is available in the literature. (ii) The limit of dg( n) t as H, the depth to the bottom tends to infinity, is infinity as the author himself admits with the remark that it is “practically inconceivable” (Pal, 1985, p.284). (iii) The Fourier transform ( FT ) of dg (x) t is derived. Comment. Unlike the author’s notation I discriminate by denoting the frequency domain function as &j (co) t. (iv) The limit of s( w) t as H+ co is obtained. I denote this as a, (m) t. (v) The inverse FT of Zg, (co) t is obtained. Comment. As I show later this step is not possible mathematically. Assuming it is I call the resulting space domain function as dg, ( x) t which, in the author’s notation is dg( x), (Pal, 1983, eq. 5d). (vi) The author constructs nomograms based on dg, (x) t which according to him is the desired expression for the gravity field as H+co. Comment. In essence acccording to the author, a well behaved, continuous and continuously differentiable function like Ag (x) t has two distinctly different limits as H+ca One is the well known infinity (see step ii) and the other is the author’s round about result Ag, ( x) t (or Ag ( LX) t of eq. 5d of Pal, 1983 ) . The above absurdity is due to the lack of mathematical rigour in step (v) . To elaborate, consider the vertical thin dike model. The gravity field is given by:

Active tectonic and magmatic processes beneath Long Valley Caldera, eastern California: An overview

Geological, chronological, and structural studies of the Long Valley‐Mono/Inyo Craters area document a long history of related volcanic eruptions and earthquakes controlled by regional extensional tectonics of the Basin and Range province. This activity has persisted for hundreds of thousands of years and is likely to continue. The Long Valley magma chamber had a volume approaching 3000 km3 prior to its climatic caldera‐forming eruption 0.7 m.y. ago but has been reduced to less than a third of this volume by cooling, eruption, and crystallization. Seismic evidence indicates that the main mass of the present Long Valley magma chamber is about 10 km in diameter and that its roof is 8–10 km deep with smaller cupolas as shallow as 4–5 km. Although a chamber of this size is probably capable of producing an eruption approaching 30 km3 of lava, the record over the past 0.5 m.y. suggests that eruptions of 1 km3 or less are far more likely. Models proposed for the current ground uplift and seismicity within the caldera require inflation of 0.1–0.2 km3 by additional magma since mid‐1979, and some models suggest that inflation was accompanied by injection of a thin dike or dikes (probably of silicic magma) into the ring fracture zone beneath the south moat. Several of the M 5.8–6.2 earthquakes that occurred in the region beginning in 1978 had non‐double‐couple focal mechanisms. Whether these unusual mechanisms indicate injection of mafic (low‐viscosity) magma at midcrustal depths in the Sierra Nevada block south of the caldera remains debatable. Studies of calderas of various ages throughout the world indicate that episodes of unrest are relatively common and do not invariably culminate in eruptions. Although current unrest is concentrated in the south moat of Long Valley caldera, the Inyo/Mono Craters probably hold a greater potential for producing an eruption in the foreseeable future. The Inyo/Mono Craters have erupted at 500‐year intervals over the past 2000–3000 years, whereas the Long Valley magma chamber has erupted at about 200,000‐year intervals over the past 700,000 years. In either case, a major earthquake near the caldera could strongly influence the course of volcanic activity.

Hilbert transform in the interpretation of magnetic anomalies of various components due to a thin infinite dike

The Hilbert transformH(x) applicable to vertical (ΔZ), horizontal (ΔH), and total (ΔT) magnetic anomalies due to a thin dike of infinite depth extent is derived from the generalised expression of magnetic effectF(x). The depth and dip of the dike is extracted by a simple procedure making use ofF(x) andH(x). A modified version of the amplitude of the analytic signal is given to locate the origin. The abscissa of the point of intersection ofF(x) and the discrete Hilbert transformH(1.Δx) directly yields the depth to the top. An example for each case is considered theoretically to illustrate the process. Applicability of the method is examined on the vertical component of the well-known magnetic anomaly at Kiirunavaara in northern Sweden, originally described by Von Carlheim Gyllenskjold, as well as on total magnetic anomaly of Bensons Mines, U.S.A.

Werner deconvolution for automated magnetic interpretation and its refinement using Marquardt’s inverse modeling

We present a deconvolution for automated magnetic interpretation based on Werner’s (1953) simplified thin‐dike assumption which leads to the linearization of complex nonlinear magnetic problems. The usefulness of the method is expanded by the fact that the horizontal gradient of the total field caused by the edge of a thick interface body is equivalent to the total field from a thin dike. Statistical decision, numerical iteration, and a seven‐point operator are used to improve approximations of susceptibility, dip, depth, and horizontal location of the source. Marquardt’s nonlinear least‐squares method for inverse modeling is then used to refine automatically the first approximation provided by the deconvolution. Synthetic and real total‐field data are used to demonstrate the process.

Interpretation of magnetic anomalies due to dikes: The complex gradient method

A method to interpret the magnetic anomaly due to a dipping dike using the resultant of the horizontal and vertical gradients of the anomaly is suggested. The resultant of both the gradients is a vector quantity and is defined as the “complex gradient.” A few characteristic points defined on the amplitude and phase plots of the complex gradient are used to solve for the parameters of the dike. For a dike uniformly magnetized in the earth’s magnetic field, the amplitude plot is independent of [Formula: see text], the index parameter, which depends upon the strike and dip of the dike and the magnetic inclination of the area. The phase plot of the complex gradient is an antisymmetric curve with an offset value equal to [Formula: see text]. For a dike whose half‐width is greater than its depth of burial, two maxima at equal distances on either side of a minimum value appear on the amplitude plot. For a dike whose half‐width is equal to or less than its depth of burial, the amplitude plot is a bell‐shaped symmetric curve with its maximum appearing directly over the origin. In the case of a thin dike, the amplitude function falls off to half its maximum value at the same point on the abscissa where the phase function reaches, i.e., [Formula: see text]. A combined analysis of the amplitude and phase plots of the complex gradient yields all the parameters of the dike. The method is applicable for the magnetic anomaly in either the total, vertical, or horizontal field. A field example is included to show the applicability of the method.

Relationship of magnetic anomalies due to subsurface features and the interpretation of sloping contacts

A study of the magnetic anomalies produced by sloping geologic contacts, thin dikes, and horizontal cylinders has revealed that a single relationship exists among the magnetic anomalies created by them. The magnetic anomaly due to a horizontal cylinder, the first horizontal derivative of the magnetic anomaly due to a thin dike, and the second horizontal derivative of the magnetic anomaly due to a sloping contact are found to be identical in shape. Gay (1963, 1965) presented standard curves to interpret the magnetic anomalies over long tabular bodies (1963) and long horizontal cylinders (1965). It is shown here that the same curves can also be used to interpret the total, vertical and horizontal magnetic anomalies due to sloping geologic contacts.

Heat flow anomaly associated with dike intrusion, 2

An investigation reported by Horai (1974) is continued. A special case of the steady state temperature field associated with dike intrusion is studied, taking into account an infinite vertical downward extension of the isotherm of rectangular shape approximating the dike. The considered case represents a problem of two-dimensional steady state thermal conduction. The technique of conformal mapping used is identical to the method employed by Horai (1974). The characteristics of surface heat flow associated with an infinitesimal thin dike of certain temperature with the considered extension are shown in a graph.

Note on datolite and other minerals in a contact-altered limestone at Chapel quarry, near Kirkcaldy, Fife

The Chapel, or Charlestown Main, Limestone horizon lies in the Lower Limestone Group of the Carboniferous Limestone Series. At Chapel quarry the limestone is underlain by a thick sill of quartz-dolerite. The contact, however, is not exposed but probably lies only a few feet below the quarry floor. Other intrusions are seen in the vicinity: a very thin dike of decomposed basalt, which connects with a small ‘float’ of white trap, cuts the limestone about 30 yards north-eastwards of the point where the quarry crosses the Chapel road, and a small sill of olivine-dolerite or teschenite occurs at a horizon about 100 feet above the top of the limestone. In the quarry the limestone is about 60 feet thick. The contact-alteration described in this paper is most evident near the base of the limestone face and its extension laterally in the quarry has no relation to the outcrop of the thin dike. The alteration is therefore considered to be essentially connected with the underlying, unexposed, sill of quartz-dolerite, and, as will be shown ih the following pages, has been effected by the action of hot solutions rather than by thermal reconstruction.