Complex polynomials for the computation of 2D gravity anomalies

Abstract

We present an efficient algorithm using a complex variables formulation for the computation of the gravity effect of 2D polygonal bodies having densities varying both laterally and with depth. The first derivatives of the gravity effect are also provided in order to enable the computation of the Jacobian matrix, which is necessary for linear inverse gravity problems. A geophysical example based on numerical assumptions about the density contrast on a well‐studied basin area shows the applicability of the algorithm.

A Comparative Study on Two Different Methods for Calculating Gravity Effect of an Uneven Layer: Application to Computation of Bouguer Gravity Anomaly in the East Vietnam Sea and Adjacent Areas

“…The methods can generally be divided into two main groups, namely the space ________ domain methods, and the frequency domain methods. Numerous methods have been developed to calculate gravity anomaly of 2D structures in the space domain [11][12][13][14][15][16]. Some authors (e.g.…”

Gravity inversion of 2D bedrock topography for heterogeneous sedimentary basins based on line integral and maximum difference reduction methods

“…1999b). These inversion methods are then extended to include heterogeneous cases where the density contrast varies with depth linearly (Reamer and Ferguson 1989), quadratically (Bhaskara Rao 1986), exponentially (Chai and Hinze 1988; Bhaskara Rao and Mohan Rao 1999), as a polynomial function of horizontal and vertical positions (Oliva and Ravazzoli 1997; Zhou 2010), hyperbolically (Rao et al . 1994; Silva, Costa and Barbosa 2006; Silva et al .…”

“…To obtain a stable and convergent inversion solution, a smoothness constraint is usually superimposed for homogeneous sedimentary basins (Bott 1960;Parker 1973;Oldenburg 1974;Pilkington and Crossley 1986;Leão et al 1996;Medeiros 1997, 1999a;Barbosa et al 1999b). These inversion methods are then extended to include heterogeneous cases where the density contrast varies with depth linearly (Reamer and Ferguson 1989), quadratically (Bhaskara Rao 1986), exponentially (Chai and Hinze 1988;Bhaskara Rao and Mohan Rao 1999), as a polynomial function of horizontal and vertical positions (Oliva and Ravazzoli 1997;Zhou 2010), hyperbolically (Rao et al 1994;Silva, Costa and Barbosa 2006;Silva et al 2010), or parabolically (Chakravarthi and Sundararajan 2004) with smoothness constraint imposed.…”