Vredefort impact site modelling through inhomogeneous depth weighted inversion.

We are showing an application of the 3D self-constrained depth weighted inversion of the inhomogeneous gravity field (Vitale and Fedi, 2020) of the Vredefort impact site.

This method is based on two steps, the first being the search in the 3D domain of the homogenous degree of the field, and the second being the inversion of the data using a power-law weighting function with a 3D variable exponent. It does not involve directly data at different altitudes, but it is heavily conditioned by a multiscale search of the homogeneity degree.

The main difference between this inversion approach and the one proposed by Li and Oldenburg algorithm (1996) and Cella and Fedi (2012) is therefore about the depth weighting function, whose exponent is a constant through the whole space in the original Li and Oldenburg and Cella and Fedi approaches, while it is a 3D function in the method which we will discuss here.

The model volume of the area reaches 20 km in depth, while along x and y its extension is respectively 41 by 63 km. The trend at low and middle altitudes of the estimated β related to the main structures is fitting the expectations because the results relate to two main structures, which are geometrically different: the core is like a spheroid body (β ≈ 3) and the distal rings are like horizontal pipes or dykes (1 < β < 2).

With a homogeneous depth weighting function, we recover a smooth solution and both the main sources, the main core and the rings of the impact, are still visible at the bottom of the model (20 km). This is not in agreement with the result by Henkel and Reimold (1996, 1998), which, based on gravity and magnetic inversion supported by seismic data, proposed a model where the bottom of the rings is around 10 km and the density contrast effect due to the core structure loses its effectiveness around 15 km.

Instead, using an inhomogeneous depth weighting function (figure 28) we can retrieve information regarding the position at depth of both core and distal ring structures that better fits the above model. In fact, the bottom of the distal ring structure, that should be around 10 km according to Henkel and Reimold (1996, 1998), is recovered very well using an inhomogeneous depth weighting function, while in the homogeneous case we saw that the interpreted structure was still visible at large depths.

In addition, also the core structure is shallower compared to the homogeneous approach and seems more reliable if we compare it with the model of Henkel and Reimold (1996, 1998).

Instead, the inhomogeneous approach presented in this paper leads naturally us to a better solution because it takes into account during the same inversion process of the inhomogeneous nature of the structural index within the entire domain.