The computation of gravitational vector field of variable-density bodies has been attracting much attention in high precision gravity investigation. In forward and inverse gravity modeling, a 3-D rectangular prism, as a simple building block, is commonly used to approximate 3-D variable-density bodies with irregular shape. In this paper, we first model the density of a rectangular prism using an arbitrary-order polynomial function of depth, and derive the closed-form expressions for computing the vertical and horizontal components of the gravitational vector field of a 3-D rectangular prism with the polynomial density variation. Then, we extend the polynomial density function of depth to a linear combination of three arbitrary-order polynomial functions in x-, y- and z-directions, and derive the analytical expressions of the gravitational vector field of a 3-D rectangular prism with such more general density function. The analytic expressions are numerically validated and compared with other existing methods. It is shown that the new expressions are far superior to the common method based on the stack of a collection of uniform subprisms in computational efficiency. In addition, the numerical error of the expressions is analysed and the results show that the expressions are available for practical applications.

We have developed a generalized solution for computing the gravity anomalies of 3D irregular-mass bodies with complicated density-contrast variation. The 3D irregular-shaped bodies can be approximated flexibly by a collection of finite-juxtaposed right-rectangular prisms. The complicated density-contrast variation of each prism can be well-represented by a depth-dependent polynomial function. A novel analytic solution of gravity anomalies due to a right-rectangular prism with an arbitrary order of polynomial density-contrast function of depth is then derived. The solution is singularity free in the upper half-space over the prism, and its singularity in the lower half-space containing the prism is resolved by assigning their limit values to the singular terms. The numerical stability of the solution is also evaluated through numerical tests. Hence, the solution can be used to compute the gravity anomalies of 3D irregular bodies with variable density contrasts without singularities when computation points are within the numerical stability range. Based on synthetic models with variable density contrast, our solution is validated by using other solutions in the literature. We also simulated the gravity anomalies of the Los Angeles basin and compared them with the observed anomalies and with those computed using the analytic solutions of other workers. These tests confirm the accuracy and efficiency of our analytic solution.

Summary. We propose a new ray tracing technique in a 3-D heterogeneous isotropic media based on bilinear traveltime interpolation and the wave front group marc

Inversion of residual gravity anomalies is an important geophysical technique for depicting subsurface density contrasts, for example, for mineral deposits. We have expressed subsurface density variations using depth-variable polynomial functions and developed the polynomial coefficient inversion (PCI) method, which is an alternative method for mapping subsurface density distributions by inverting the coefficients of density-contrast functions. PCI enables the linear inversion of density variations without vertically subdividing the subsurface. Synthetic tests indicate that PCI combines polynomial functions and multiple constraints to highlight the anomalous masses through an iterative process with appropriate weighting parameters. We apply our method to a local investigation of banded iron formation (BIF) deposits in the Hebei Province, North China. The inversion results depict the approximate distribution of the subsurface density contrasts to identify the stratigraphic boundaries of different lithologies and BIF-favorable zones, thus implying that local iron-rich ore bodies may be located at the syncline axis or dip along the faults. The successful application of PCI for the BIF deposits indicates that this method is a promising strategy for density mapping.