Fast finite-element calculation of gravity anomaly in complex geological regions

Abstract

S U M M A R YForward computation of the gravity anomaly of a density model is often a necessary step in modelling the subsurface density of a region. For geologically complex regions, this step may be computationally demanding and become the bottleneck in gravity inversion. We present a fast finite-element method (FFEM) for solving boundary value problems of the gravitational field in forward computation of gravity anomaly in complex geological regions. Testing against analytical solutions show that the method is more accurate than the classical integration method in cases where density in the material body is highly heterogeneous. At the same time, FFEM is more efficient than the integration method by a factor between s/100 and s/10, where s is the number of stations at which gravity anomalies are computed. Since s is usually much greater than 10-100 in 3-D gravity inversion in geologically complex regions, FFEM may be significantly more efficient in gravity modelling of such regions. We illustrate the utility of this method by calculating the gravity anomalies in central Taiwan.

Optimal, scalable forward models for computing gravity anomalies

“…The second approximate boundary condition we considered was introduced by Cai & Wang (2005) and consists of approximating the far-field gravitational attraction on a finite-sized domain . The far-field gravity is approximated according to…”

“…In Cai & Wang (2005), a finiteelement (FE) method was used to obtain the solution to the Poisson equation. They favoured the FE method over the finite-difference method as the former allowed more geometric freedom in meshing the density anomalies and the formulation easily permitted a variable density field within each voxel.…”

Modelling of ground deformation and gravity fields using finite element method: an application to Etna volcano

“…Subsurface displacement fields caused by pressure sources necessarily alter the density distribution of the medium that in turn affects the gravity field. The gravity anomaly δ g , related to the mass redistribution, can be calculated by solving the following Poisson's differential equation for the gravitational potential ø g using appropriate boundary conditions (Cai & Wang 2005): where G denotes the universal gravitational constant and Δρ( x , y , z ) is the change in the density distribution. Generally, the total gravity change at a benchmark on the ground surface associated with pressure source changes is given by: where δ g 0 represents the ‘free air’ gravity change accompanying the uplift of the observation site.…”

“…Subsurface displacement fields caused by pressure sources necessarily alter the density distribution of the medium that in turn affects the gravity field. The gravity anomaly δg, related to the mass redistribution, can be calculated by solving the following Poisson's differential equation for the gravitational potential ø g using appropriate boundary conditions (Cai & Wang 2005):…”

An alternative method for density variation modeling of the crust based on 3-D gravity inversion

“…to find the density of the source masses from the given gravity field functionals, such as norm of the gravity vector (from gravimetry), gravity vector (from the inertial systems or astronomical observations plus gravimetry), gravity potential (from geodetic leveling), on or above the surface of the earth, is of particular interest for geoscience studies. For this reason extensive contributions are made in this respect that as recent examples we refer to Welford et al (2010), Aitken (2010), Schreiber et al (2010), Kimbell et al (2010), Welford and Hall (2007), Jacoby et al (2007), Camacho et al (2007), Ebbing et al (2007), Bosch et al (2006), Strykowski et al (2005), Tiberi et al (2005), Pinto et al (2005), Jacoby and Çavşak (2005), Cai and Wang (2005), Kaban et al (2004), Wang et al (2004), Widiwijayanti et al (2004), Çavşak et al (2002), Koslovskaya et al (2004), Rivero et al (2002), , Silva et al (2001Silva et al ( , 2002Silva et al ( , 2007, Tondi et al (2000).…”