Gravity interpretation of sedimentary basins with hyperbolic density contrast¹

Abstract

The variation in the density of sediments with depth in a sedimentary basin can be represented by a hyperbolic function. Gravity anomaly expressions for a 2D vertical prism and an asymmetric trapezium with a hyperbolic density distribution are derived in a closed form. These are used in inverting the gravity anomaly of a sedimentary basin with variable density. Firstly, the basin is viewed as a series of prisms juxtaposed with each other. The initial thickness of each prism is obtained from the gravity anomaly at its centre, based on the gravity anomaly of an infinite slab with a hyperbolic density contrast. These thicknesses are improved, based on the differences between the observed and the calculated anomalies. For an improved rate of convergence of the solution, these thicknesses may alternatively be refined using the well-known ridge regression technique. Secondly, the basin is approximated by an asymmetric trapezium and its anomalies are inverted for the parameters of the trapezium using the ridge regression. Since this approximation serves to oversimplify the floor of the basin, it must be used only when the sediment-basement interface has minor undulations. The results of a hypothetical case and two field cases (the San Jacinto Graben, California and the Godavari Graben, southern India) are presented. In both field cases, the interpreted depths are comparable with the real ones, proving the validity of the assumption of a hyperbolic density distribution of the sediments in the two basins considered.

Application of particle swarm optimization for gravity inversion of 2.5-D sedimentary basins using variable density contrast

“…Several authors have developed 2-D/2.5-D local optimization techniques over the 2-D/2.5-D sedimentary basin (Annecchione et al, 2001;Barbosa et al, 1999;Bhattacharya and Navolio, 1975;Gadirov et. al, 2016;Litinsky, 1989;Morgan and Grant, 1963;Murthy et al, 1988;Murthyan and Rao, 1989;Rao, 1994;Won and Bavis, 1987) to interpret gravity anomalies with constant density function. In many publications over 3-D gravity field computation with an approximation of geological bodies by 3-D polygonal horizontal prism has been applied (Eppelbaum and Khesin, 2004;Khesin et al 1996).…”

3D gravity interface inversion constrained by a few points and its GPU acceleration

“…The other is the variable density-contrast model, which is the density contrast of sedimentary changes with depth and/or horizontal position partly as a result of compaction. The variable density-contrast models include exponential decay model (Cordell, 1973;Chai and Hinze, 1988;Litinsky, 1989;Chappell and Kusznir, 2008), hyperbolic decay model (Litinsky, 1989;Silva et al, 2006;Rao and Pramanik et al, 1994), linear model (Murthy and Rao, 1979;Pokanka,1998;Hansen, 1999;Holstein, 2003), quadratic model (Rao, 1986;Rao et al,1990;Garcia-Abdeslem et al, 2005), parabolic model Sundararajan, 2004), polynomial model( Guspi,1990;Zhang et al, 2001). However, inclusion of variable density contrast in the interface inversion obviously introduces substantial complication in gravity modelling, thus inevitably increasing the computational burden.…”

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.…”