I. V. Radhakrishna Murthy

Gravity anomalies of two-dimensional bodies of irregular cross-section with density contrast varying with depth

The line-integral method of Hubbert (1948) is extended to obtain the gravity anomalies of two-dimensional bodies of arbitrary cross-sections with density contrast varying linearly with depth. The cross-section is replaced by an N-sided polygon. The coordinates of two vertices of any given side are used to determine the associated contribution to the gravity anomaly. The gravity contribution of each side is then summed to yield the total gravity effect. The case where density contrast varies exponentially with depth is also considered. This technique is used to obtain the structure of the San Jacinto Graben, California, where sediments filling the graben have an exponential increase in density with depth.

Interpretation of self-potential anomalies of some simple geometric bodies

SummaryAn entirely new procedure for interpreting selfpotential anomalies of spheres, rods and dipping sheets is presented. The anomaly of a sphere is divided into two parts — the anomaly of odd symmetry and the anomaly of even symmetry — from which the depth can be obtained by fitting them with the master curves. The self-potential anomalies of a finite rod are transformed to the anomalies of a veritcal sheet, for which standard curves are presented. The case of a sheet was divided into three parts; (a) finite line of poles; (b) infinite double line of poles and (c) finite double line of poles. For the first case logarithmic curves were prepared and presented; by their comparison with the field profile, different parameters can be obtained. In the second case, a geometrical construction is provided to obtain the various values. In the third case, the anomalies of finite sheet (finite double line of poles) are transformed into those due to an infinite double line of poles for interpretation.

The density difference and generalized programs for two- and three-dimensional gravity modeling

Abstract Computer programs developed to model flat-topped bodies cannot accommodate models with a flat bottom, without a modification in the program. The concept of density difference is introduced and used to construct computer programs that can model gravity anomalies of any body—flat topped, flat bottomed, or undulating. The density difference is the density of the material lying below the interface minus the density of the material above. The suggested schemes determine the initial depths to the interface based on the Bouguer slab formula and improve them iteratively based on the differences between the observed and calculated anomalies. Two generalized computer programs in FORTRAN 77 for modeling two- and three-dimensional structures are presented.

Paleocene on-spreading-axis hotspot volcanism along the Ninetyeast Ridge: An interaction between the Kerguelen hotspot and the Wharton spreading center

Investigations of three plausible tectonic settings of the Kerguelen hotspot relative to the Wharton spreading center evoke the on-spreading-axis hotspot volcanism of Paleocene (60-54 Ma) age along the Ninetyeast Ridge. The hypothesis is consistent with magnetic lineations and abandoned spreading centers of the eastern Indian Ocean and seismic structure and radiometric dates of the Ninetyeast Ridge. Furthermore, it is supported by the occurrence of oceanic andesites at Deep Sea Drilling Project (DSDP) Site 214, isotopically heterogeneous basalts at Ocean Drilling Program (ODP) Site 757 of approximately the same age (59-58 Ma) at both sites. Intermix basalts generated by plume-mid-ocean ridge (MOR) interaction, exist between 11° and 17°S along the Ninetyeast Ridge. A comparison of age profile along the Ninetyeast Ridge between ODP Sites 758 (82 Ma) and 756 (43 Ma) with similarly aged oceanic crust in the Central Indian Basin and Wharton Basin reveals the existence of extra oceanic crust spanning 11° latitude beneath the Ninetyeast Ridge. The extra crust is attributed to the transfer of lithospheric blocks from the Antarctic plate to the Indian plate through a series of southward ridge jumps at about 65, 54 and 42 Ma. Emplacement of volcanic rocks on the extra crust resulted from rapid northward motion (absolute) of the Indian plate. The Ninetyeast Ridge was originated when the spreading centers of the Wharton Ridge were absolutely moving northward with respect to a relatively stationary Kerguelen hotspot with multiple southward ridge jumps. In the process, the spreading center coincided with the Kerguelen hotspot and took place on-spreading-axis volcanism along the Ninetyeast Ridge.

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...

Inversion of gravity anomalies of three-dimensional density interfaces

Abstract An inversion scheme to trace three-dimensional density interfaces from their gridded gravity anomalies is developed. The scheme requires the gravity anomaly values, profile and station spacings as the input, besides densities of the underlying and overlying materials and the mean or undisturbed depth to the interface. The scheme calculates the initial values of the depths to the interface below the internal grid points, and modifies them iteratively until a best fit is achieved between the observed and calculated anomaly values. The gravity anomalies of the density interface are generated by equating the material below the interface to a series of juxtaposing rectangular blocks, one centered below each of the internal gridded anomaly points. It is assumed that the interface flattens out to its undisturbed depth well ahead of the boundaries of the sampled area. The values of initial thicknesses of the prisms are calculated by equating the anomaly at a station to the algebraic sum of products of vertical gradients of gravity effects of the prisms and their thicknesses. The differences between the observed and calculated anomalies are then used to improve the thicknesses of the prisms by equating these differences to the algebraic sum of the products of the vertical gradients of gravity effects of prisms and increments to their thicknesses. The computer program, named GRAV3DIN coded in FORTRAN 77 and used to invert gravity anomalies of three-dimensional density interfaces, is presented.

Gravity anomalies and crustal structure of the Bay of Bengal

Abstract The Bengal Fan is covered afresh by systematic geological and geophysical investigations by National Institute of Oceanography (NIO), India and a detailed free-air gravity map of the fan is prepared. The map shows two strong gravity lows – one corresponding to the continental shelf and the other to the 85°E Ridge. The Ninetyeast Ridge is brought out as a gravity high. The anomalies are inverted to determine the anomaly-producing interfaces, which suggest that the 85°E Ridge anomaly could not be explained by an isolated geophysical model invoking a negative density contrast for the ridge material. The 85°E Ridge anomaly and several other isolated gravity lows are attributed mostly to the depression-like structures in the Moho. Each depression of the Moho is associated with a basement high. The depression beneath the 85°E Ridge is about 6 km deep from the regional Moho boundary, which is at variance to the earlier results. It is suggested that the depressions may possibly have developed due to the surface volcanic loads emplaced on already evolved oceanic crust of the Bay of Bengal.

A new method of interpreting self-potential anomalies of two-dimensional inclined sheets

A new method of interpreting self-potential anomalies of inclined sheet-like bodies of infinite strike length is presented in this study. In contrast to conventional schemes, the method does not explicitly make use of the magnitudes of the anomaly values during inversion. But, positions of a pair of points, at which the anomaly values differ from each other by a constant magnitude, are selected to construct some linear equations. The coefficients of these equations are functions of the model parameters, and hence the latter are solved from these coefficients. The method can be extended to gravity and magnetic anomalies of various models of simple geometry.

Gravity anomalies of a vertical cylinder of polygonal cross-section and their inversion

The equation for the gravity anomaly of a vertical cylinder with a polygonal cross-section is derived. An algorithm for inverting the gravity anomalies of the model is developed and the related software, coded in FORTRAN 77, is presented in the program GPCYLNIN. The input to the computer consists of anomaly values, their distance coordinates, and initial values of horizontal coordinates of the edges of the cylinder. Initial values of density contrast and coefficients defining linear regional gradient are generated by the computer. Then all initial parameters of the model are revised iteratively, based on an optimization technique.

Automatic inversion of self-potential anomalies of sheet-like bodies

Abstract A computer program in FORTRAN 77 is presented to invert the self-potential anomalies of sheet-like bodies. The program needs as input only the self-potential anomalies and their distances measured from an arbitrary reference in the profile and does not require the initial estimates of the body parameters of the model as in classical inversion techniques. The program measures the maximum and minimum anomalies, scales a few characteristic distances, calculates the initial values of the body parameters and improves them iteratively until a best fit is obtained between the observed and calculated anomalies.