Interpretation of Gravity Data Measured by Topography

Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study

“…Previously, the authors developed such a software implementation based on the original algorithm [10] for an ellipsoidal model of a section of the Earth's crust and demonstrated its speed and accuracy in comparison to Gauss-Legendre cubature formulas. Then, the algorithm was generalized to solve a forward problem on the topography (given by a height map) [2]. Next, the described inverse problem algorithm was tested on synthetic models, which made it possible to evaluate characteristics such as the convergence rate, the calculation time, and the dependence of the solution morphology on the values of the tuning parameters.…”

“…The "classical" approximation of this stage (for a "flat" model) can be called the calculation of the correction for the influence of the intermediate plane-parallel layer, which is included in the Bouguer correction [1]. The values of errors in the field (arising when introducing a correction for topography) significantly exceed the resolution of modern gravimeters [2]. A number of authors have studied the problem of correction for the Earth's spherical shape in the results of gravimetric data inversion for the creation of density models.…”

“…To obtain a more accurate result of the inversion, we need to use gravity data measured directly on the topography, without recalculation to an auxiliary reference surface. In [2], the authors proposed the algorithm of forward problem solving (parallelized for graphics processing units-GPUs) for real topography using the irregular grids of the density model and field. The algorithm is based on the concise closed form of the gravitational field of a polyhedron.…”

Computationally Effective Gravity Inversion Allows for High-Resolution Regional Density Modeling of Earth's Crust with the Inclusion of the Topography Layer

“…In [Martyshko et al, 2020] we've presented an example of calculating the gravitational field on the topography surface for a practical model, taking into account the Earth's sphericity. The introduction of the complex-shaped surfaces (such as the topography) to the model does not affect the performance of calculations.…”

“…Direct calculation of the gravitational field from an object of complex shape, such as a section of the Earth's crust, which bounded by the surface of the topography above and by the surface of an ellipsoid below, is a computationally difficult task. In [Martyshko et al, 2020], we proposed a computationally efficient method for solving the direct problem, the computational complexity of which does not depend on the geometric shape of the gravitating object (only on its discretization size). The method is a variant finite element method (FEM), based on the approximation of the elements of the partition with polyhedrons.…”