C. Visweswara Rao

Forward modeling: gravity anomalies of two-dimensional bodies of arbitrary shape with hyperbolic and parabolic density functions

Abstract Computer programs in FORTRAN 77 to compute the gravity anomaly of a two-dimensional (2-D) body of irregular cross section with hyperbolic and parabolic variations in density contrast are developed and presented. The gravity anomaly of San Jacinto Graben, California, using a hyperbolic function and that of Los Angeles Basin, California, using a parabolic function, are computed and compared with respective observed anomalies.

TWO METHODS FOR COMPUTER INTERPRETATION OF MAGNETIC ANOMALIES OF DIKES

Two computer‐oriented methods are presented in this paper for interpreting the magnetic anomalies of a dipping dike. In the first method, horizontal derivatives of the observed magnetic anomalies are calculated which define a single linear equation of the type X4G+C1X3G+C2X2G+C3XG+C4G+C5X2+C6X+C7=0, where G is the horizontal gradient of the anomaly, and X is the distance of the gradient measured from any convenient point in the profile. Seven normal equations are derived and the coefficients C1 to C7 are solved from which the various parameters (Figure 1 of the body are obtained as D=-C1/4, T=[(C7+DC6)2-C4C52]2DC5, Z=-(D2+T2)-(C7+DC6)C5, and Q=tan-1B/A. In the second method, the method of iteration, the magnitudes and positions of the maximum and minimum anomaly points are located in the profile, and the approximate parameters of the dike are computed from these shape characteristics. The resulting anomalies are then calculated and compared with the observed data. The errors at each point of observation a...

A computer program for interpreting vertical magnetic anomalies of spheres and horizontal cylinders

SummaryA common computer program for the interpretation of vertical magnetic anomalies of spheres and horizontal cylinders has been developed. The input consists of the observed anomalies noted against their distances measured from an arbitrary point in the profile and a code number for each model. The program is written so that the positions and magnitudes of the maximum and minimum anomalies are located and their ratios and signs are used to define the initial parameters of the model under consideration. The errors resulting from these approximate values are derived and are solved for the increments to be given to the initial values. The process is repeated until the sum of the squares of the errors is less than 0.25% of the sum of the squares of the observed anomalies. The method has been tested on various theoretical examples and the results justify the validity of the programme.

A gradient method for interpreting magnetic anomalies due to horizontal circular cylinders, infinite dykes and vertical steps

A new method of interpreting magnetic anomalies of arbitrarily-magnetised horizontal circular cylinders, dipping dykes and vertical steps is presented. The method makes use of both horizontal and vertical gradients of the magnetic field of the model under consideration, rather than the observed magnetic anomaly. Vertical and horizontal gradients are calculated from the observed anomalies, and plotted one against the other to find out the locus of tip of the resultant gradient vector. This locus is a symmetrical curve for each of the three models mentioned above. The properties of these curves are used to deduce the various parameters of these models and the direction of magnetisation.

Parabolic density function in sedimentary basin modelling

For modelling sedimentary basins of large thickness from their gravity anomalies, the concept of parabolic density function which explains the variation of true density contrast of the sediments with depth in such basins is introduced inBotts (1960) procedure. The analytical expression the gravity anomaly of a two-dimensional vertical prism with parabolic density contrast needed to estimate the gravity effect of the basin in modelling procedure is derived in a closed form. Two profiles of gravity anomalies, one across San Jacinto Graben, California and the other across Tucson basin, Arizona where the density of sediments is found to vary with depth are interpreted.

Gravity modelling of an interface above which the density contrast decreases hyperbolically with depth

Abstract An interpretational procedure for determining the depth of an interface underlying sediments whose density contrast decreases hyperbolically with depth is developed. The approximate depth of the interface at each gravity station is calculated by using the gravity formula of an infinite slab with a hyperbolic density contrast. Based on these depth values, the sediment—basement interface is replaced by an n -sided polygon. Its gravity anomaly is computed by using the formula of Visweswara Rao et al. (1994). These depth values are refined using the procedure of Bott (1960).

A direct method of interpreting gravity and magnetic anomalies: The case of a horizontal cylinder

SummaryA new method of interpreting the gravity and magnetic anomalies is introduced with special reference to the magnetic anomalies of a horizontal cylinder. The method consists of calculating the functions of the anomaly and its distance from an arbitrary point. These form a simple linear equation with coefficients related to the parameters defining the body. Since each observation forms a separate linear equation, the required normal equations are formed by the method of least squares and solved for the coefficients and hence for the various parameters defining the target. The discussion here is confined to the vertical magnetic anomalies. The application of the method to horizontal and total field anomalies of two dimensional bodies is also outlined.

Characteristic curves for interpreting gravity anomalies of vertical cylinders and horizontal circular discs

Characteristic curves for the complete interpretation of a wide range of parameters of a vertical cylinder and a horizontal circular disc are presented. It is established that the distance of the inflexion point on the gravity profile of a vertical cylinder from the point of maximum anomaly [i.e. the origin] is approximately equal to the radius of the vertical cylinder, thus enabling one to demarcate the boundary of the vertical cylinder directly from the contour map based on the cluster of contours. Two gravity profiles, one across an anomalous zone in central Alberta, Canada and the other over Borsad area, India are interpreted by the curves presented and the results are shown.

Anticlines and synclines with hyperbolic density contrast and their gravity inversion

Abstract Gravity anomaly expressions of symmetrical anticlines and synclines with a hyperbolic density contrast are derived. We developed an inversion procedure for these two models making use of a non-linear Marquardt optimisation technique. The partial derivatives required in the inversion may be evaluated either numerically or analytically with little difference in the time of convergence of the solution, though analytical partial derivatives are very lengthy.

A direct method for interpreting magnetic anomalies—the case of a horizontal circular cylinder

A new method is introduced here to interpret the magnetic anomalies with special reference to vertical magnetic anomalies of a horizontal circular cylinder. The parameters of the cylinder are found to be related toV, ∂V/∂x and∂V/∂z at the origin of the cylinder. HereV is the observed anomaly,∂V/∂x and∂V/∂z are its horizontal and vertical derivatives respectively. The origin may be located working out an equality,viz.,3(∂V/∂z)2=2V∂2V/∂z2 which is true only at the origin. Thus, once the cylinder is located,V, ∂V/∂x and∂V/∂z at its origin can be determined and hence its parameters. The procedure is illustrated with a theoretical example.