D. Atchuta Rao

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 θF, 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 -θF. 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 appe...

Quantitative interpretation of self-potential anomalies due to two-dimensional sheet-like bodies

A method for quantitative interpretation of self‐potential anomalies due to a two‐dimensional sheet of finite depth extent is proposed. In the case of an inclined sheet, positions and amplitudes of the maximum, minimum, and zero‐anomaly points are picked and then the origin is located on the horizontal gradient curve using the template of Rao et al (1965). The parameters of the sheet may be evaluated either geometrically or by using some analytical relations among the characteristic distances. When the sheet is vertical, the parameters may be evaluated using the positions of half and three‐quarter peak amplitudes.

A Fourier transform method for the interpretation of self-potential anomalies due to two-dimensional inclined sheets of finite depth extent

The self-potential anomaly due to a two-dimensional inclined sheets of finite depth extent has been analysed in the frequency domain using the Fourier transform. Expression for the Fourier amplitude and phase spectra are derived. The Fourier amplitude and phase spectra are analysed so as to evaluate the parameters of the sheet. Application of this method on two anomalies (synthetic and field data) has given good results.

A rapid graphical method for the interpretation of the self-potential anomaly over a two-dimensional inclined sheet of finite depth extent

The inclined sheet is an important model for interpreting self‐potential (SP) anomalies over elongated ore deposits. Many techniques (Roy and Chowdhurry, 1959; Meiser, 1962; Paul, 1965; Atchuta Rao et al., 1982; Atchuta Rao and Ram Babu, 1983; Murty and Haricharan, 1985) have been proposed for interpreting SP anomalies over this model. We propose a simple graphical procedure for locating the upper and lower edges of an inclined sheet of infinite strike extent from its SP anomaly V(x) using a few characteristics points including Vmax, Vmin, and V0. The amplitude ratio R=Vmin/Vmax, is shown to vary with θ, the dip of the sheet, making it possible to estimate θ. The two edges of the sheet are equidistant from the abscissa of V0, the zero potential point. The sheet, when extrapolated onto the line of observation, meets the x‐axis at a point where V(x)=Vmax+Vmin. From these characteristic features of V(x), the sheet can be located easily using the simple geometrical construction presented below.

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.

On the half‐slope and straight‐slope methods of basement depth determination

Although a great variety of interpretation techniques for basement depth determination has been developed during the past two or three decades, the half‐slope and straight‐slope methods are still popular due to their simplicity and general reliability in manual interpretation and are widely used in oil exploration work (Nettleton, 1976). The half‐slope and straight‐slope rules are derived for a particular set of geologic/geophysical conditions and care should be taken in applying them in a more general way. For example, the half‐slope method of Peters (1949) was derived for magnetic anomalies over vertical dikes with vertical polarization. The straight‐slope method uses the horizontal projection of the straight‐line part of the steepest gradient at the inflection point on the anomaly curve as the depth estimator. This rule is purely empirical because mathematically there is no straightline part on the anomaly curve. Vacquier et al. (1951) made an exhaustive study of the straight‐slope method and presented...

Crustal structure associated with Gondwana graben across the Narmada-Son lineament in India: An inference from aeromagnetics

Abstract Aeromagnetic data over an 80-km-wide belt along the ENE-trending Narmada-Son lineament (NSL), starting from Baroda in the west and continuing to the south of Jabalpur in the east, has been studied to understand the structural and tectonic framework of the region. The area is covered by generally E-W-trending steeply dipping and folded Archean phyllites and quartzites as basement, with Bijawars (Upper Precambrian), upper Vindhyans (Upper Proterozoic), and Gondwanas (Upper Carboniferous) overlying them. Overlapping them all are the Deccan trap (Cretaceous-Eocene) flows. Aeromagnetic linements and their disposition and pattern in this region suggest major dislocations in the crust. The region around Hoshangabad, which is the intersection point of the NSL and the northwestern extension of the Godavari lineament, appears to have been intensely disturbed. Spectral analysis of aeromagnetic profiles across the NSL belt brought out a deep magnetic interface within crust at depths varying from 4 km to about 20 km below the surface, perhaps corresponding to the discontinuity characterized by the interface of granitic and basaltic rocks. There is a significant downwarping of this interface under the Hoshangabad region, suggesting that this is perhaps related to the evolution of the Gondwana basin structure in this area. This warping of the magnetic interface may be a reflection of the crustal flexuring and rift faulting. Elsewhere in the world, concentrations of carbonatite complexes and dike swarms are known to occur in areas of crustal flexuring and rift faulting. The occurrence of carbonatite complexes in this region (e.g. at Amba Dongar and Barwaha, and dike swarms in the Dadiapada region) gives credence to the present inferences from the aeromagnetic study.

Nomograms for rapid evaluation of magnetic anomalies over long tabular bodies

The magnetic anomaly due to a long tabular body usually consists of a maximum and a minimum. The distances and the amplitudes of the maximum and the minimum, when defined in dimensionless quantities, may be used as characteristics of the source. In this paper, a method based on the positions of the maximum and the minimum on the magnetic anomaly due to a long tabular body has been presented. Characteristic ratios,D andA involving the distances and amplitudes of the maximum and the minimum points on the anomaly curve are defined. Nomograms showing the variations ofD andA with the parameters of (1) the dike and (2) the vertical fault models are presented. The parameters of the causative source are evaluated from the two ratiosD andA and the nomograms, using some simple analytical relations presented here. From the nomograms, it is observed that (a) for a thick dike,A is always greater thanD, (b)A=D for a thin sheet and (c) for a vertical fault,A is always less thanD. Thus from the characteristic ratiosD andA it is possible to evaluate the source parameters and also to distinguish whether the source is a dike, sheet or a vertical fault. The method is fast and is applicable for the magnetic anomalies either in total, vertical or horizontal component. The method has been applied on two field examples and the results are found to be in close agreement with those obtained by using other methods. A simple method of locating the origin on the anomaly curve is included. The limitations of the method are also discussed.

Inversion of Gravity and Magnetic Anomalies over Some Bodies of Simple Geometric Shape

The general expression for gravity and magnetic anomalies over thin sheets and sloping contacts may be expressed as a polynomial of the formFx2+C1Fx+C2F+C3x3+C4x2+C5x+C6. The initial parameters of the source are obtained from the coefficientsC1, C2,..., C6 which may be solved by inverting a 6×6 matrix. The initial parameters are modified by successive iteration process using the difference formula until the root mean square error between the observed and calculated anomalies is a minimum. The regional background which may be in the form of a polynomial is estimated by the computer itself. This method is applied on a number of field anomalies and is found to yield reliable estimates of depth and other parameters of the source.The general expression for gravity and magnetic anomalies over thin sheets and sloping contacts may be expressed as a polynomial of the formFx2+C1Fx+C2F+C3x3+C4x2+C5x+C6. The initial parameters of the source are obtained from the coefficientsC1, C2,..., C6 which may be solved by inverting a 6×6 matrix. The initial parameters are modified by successive iteration process using the difference formula until the root mean square error between the observed and calculated anomalies is a minimum. The regional background which may be in the form of a polynomial is estimated by the computer itself. This method is applied on a number of field anomalies and is found to yield reliable estimates of depth and other parameters of the source.

A comparative study of the relation figures of magnetic anomalies due to two-dimensional dike and vertical step models

Magnetic anomalies in vertical and horizontal components, when plotted one against the other in polar form, result in a curve called the relation figure (Werner, 1953). In this paper, a comparative study of the relation figures of magnetic anomalies due to two‐dimensional (2-D) dike and vertical step models is made. The relation figures for these two models are found to be ellipses with different properties. The tangent at the origin to the ellipse is parallel to the major axis of the ellipse for the dike model, whereas it is perpendicular to the major axis for the vertical step. This property may be used to distinguish whether the source is a dike or a vertical step. For both of the models, the angle made by the axis of symmetry of the ellipse with the coordinate axis is equal to θ, the combined magnetic angle. The ratio between the lengths of the major and minor axes of the ellipse is directly related to the width‐to‐depth ratio of the dike or the bottom‐to‐top depth ratio of the vertical step. A few ch...