3D gravity data inversion constrained by bounding interval ADMM regularization : Application to density distribution reconstruction of the Pyrenees chain lithosphere.

Gravity inversion methods are able to recover density distributions in the Earth but they need to be strongly constrained using a variety of prior information. Here, we aim at inverting gravity data anomalies constrained by existing geological and density information on orogenic areas such as the Pyrenees where many geological and geophysical studies have been conducted for geophysical exploration purposes and fluid resources recovering of economic interest.

To perform such inversion, we aim at constraining gravity inversions using covariance matrix defined as an interval distribution of possible density values. This covariance-like matrix is obtained by computing the probability of impact of lithological density variations on gravity residuals. Instead of using a Monte Carlo-like approach to sample density values in each rock unit, which may be too computationally expensive (in terms of number of forward calculations, memory and disk storage of all data needed for the probabilistic analysis), we calculate a series of probabilistic metrics associated to different combinations of density variations. For this, we select representative model variations and use partial plane experiment-based probabilistic method approach to estimate the impact of density variations on gravity data misfit. This drastically reduces the number of calculations and requires only a few tens of forward problems evaluations (instead of hundreds or thousands with Monte Carlo-like approach). Based on the impact of each prior lithological density variation, intervals of density variations can thus be estimated for each rock unit. This approach allows to define at low cost all these intervals, which can be interpreted as a reduced covariance matrix. For inversion using these intervals as constraints, we use an initial a priori density model obtained from a prior Vp model obtained by seismic teleseismic time-arrival inversion. To reconcile the so-obtained density model with gravity data, we perform gravity inversion constrained by bounded density intervals estimated from the probabilistic approach we propose. A dynamic Alternate Direction Multipliers Method regularization approach is used to constrain the inversion over such variation intervals. This allows us to obtain inverted models consistent with the geological structures modelled in the area and gravity data.

We apply this inversion technique to the whole Pyrenees chain (southwest Europe) at a 2 km resolution and on a smaller zoomed 1 km resolution area constrained by outer information (density, ADMM variation intervals, …) provided by the 2km coarser inverted model. This way, new geological features can be inferred in the collisional intraplate Iberian-Eurasian region, in the axial zone and basement, and also at depth until the upper mantle. Besides, strong excesses of mass in the northern part and strong negative density contrasts in the south of the Pyrenees are appearing and increasing with depth when compared to previous prior models.