Brittle Deformation in the Neoproterozoic Basement of Southeast Brazil: Traces of Intraplate Cenozoic Tectonics

The basement of southeast Brazil is traditionally interpreted as the result of Neoproterozoic and early Paleozoic orogenic cycles. Wide regions of the Atlantic Plateau (southeast Brazil) are characterized by rocks and tectonic structures of Precambrian age. According to the classical literature, these regions have not been affected by tectonics since the Miocene, despite the fact that they rest close to Cenozoic basins, which have suffered recent tectonic deformation. The objective of this research is to evaluate the role of neotectonics in the Atlantic Plateau. This task is accomplished through a multiscalar approach which includes lineament domain analysis from regionally sized digital elevation models and structural geology field surveys. Lineaments are automatically detected and statistically analyzed. Azimuthal analyses of data on faults and fractures by a polynomial Gaussian fit enables the identification of the main structural trends. Fault-slip direct inversion by means of the original Monte Carlo approach allows one to compute the multiple paleostresses that produced the measured fault population. The results show the presence of a principal ENE–WSW lineament domain, related to an old shear zone possibly reactivated since the Miocene. One of the paleostresses computed from fault-slip inversion is in agreement with the neotectonic stress-field proposed by other authors.

APPLICATIONS OF TWO NON-CENTRAL HYPERGEOMETRIC DISTRIBUTIONS OF BIASED SAMPLING STATISTICAL MODELS

Statistical models of biased sampling of two non-central hypergeometric distributions Wallenius' and Fisher's distribution has been extensively used in the literature, however, not many of the logic of hypergeometric distribution have been investigated by different techniques. This research work examined the procedure of the two non-central hypergeometric distributions and investigates the statistical properties which includes the mean and variance that were obtained. The parameters of the distribution were estimated using the direct inversion method of hyper simulation of biased urn model in the environment of R statistical software, with varying odd ratios (w) and group sizes (mi). It was discovered that the two non - central hypergeometric are approximately equal in mean, variance and coefficient of variation and differ as odds ratios (w) becomes higher and differ from the central hypergeometric distribution with ω = 1. Furthermore, in univariate situation we observed that Fisher distribution at (ω = 0.2, 0.5, 0.7, 0.9) is more consistent than Wallenius distribution, although central hypergeometric is more consistent than any of them. Also, in multinomial situation, it was observed that Fisher distribution is more consistent at (ω = 0.2, 0.5), Wallenius distribution at (ω = 0.7, 0.9) and central hypergeometric at (ω = 0.2)

Approaches to improve the robustness of the Comparison Model Method for the inverse problem of groundwater hydrology

<p>Indirect inversion approaches are widely used in Geosciences, and in particular also for the identification of the hydraulic properties of aquifers. Nevertheless, their application requires a substantial number of model evaluation (forward problem) runs, a task that for complex problems can be computationally intensive. Reducing this computational burden is an active research topic, and many solutions, including the use of hybrid optimization methods, the use of physical proxies or again machine-learning tools <span>allow to avoid</span> considering the full physics of the problem when running a numerical implementation of the forward problem.</p><p>Direct inversion approaches represent computationally frugal alternatives to indirect approaches, because in general they require a smaller number of runs of the forward problem. The classical drawbacks of these methods can be alleviated by some implementation approaches and in particular by using multiple sets of data, when available.</p><p>This work is an effort to improve the robustness of the Comparison Model Method (CMM), a direct inversion approach aimed at the identification of the hydraulic transmissivity of a confined aquifer. The robustness of the CMM is here ameliorated by (i) improving the parameterization required to handle small hydraulic gradients; (ii) investigating the role of different criteria aimed at merging multiple data-sets corresponding to different flow conditions.</p><p>On a synthetic case study, it is demonstrated that correcting a small percentage of the small hydraulic gradients (about 10%) allows to obtain reliable results, and that a criteria based on the geometric mean is adequate to merge the results coming from multiple data-sets. In addition, the use of multiple-data sets allows to noticeably improve the robustness of the CMM when the input data are affected by noise.</p><p>All the tests are performed by using open source and widely <span>used</span> tools like the USGS Modflow6 and its Python interface flopy to foster the application of the <span>CMM. The scripts and corresponding package</span>, named <em>cmmpy</em>, is available on the Python Package Index (PyPI) and on bitbucket at the following address: https://bitbucket.org/alecomunian/cmmpy.</p>

Direct inversion of circulation from tracer measurements – Part 2: Sensitivity studies and model recovery tests

The direct inversion of the 2D continuity equation allows for the inference of the effective meridional transport of trace gases in the middle stratosphere. This method exploits the information given by both the displacement of patterns in measured trace gas distributions and the approximate balance between sinks and horizontal as well as vertical advection. Model recovery tests show that with the current setup of the algorithm, this method reliably reproduces the circulation patterns in the entire analysis domain from 6 to 66 km altitude. Due to the regularization of the inversion, velocities above about 30 km are more likely under- than overestimated. This is explained by the fact that the measured trace gas distributions at higher altitudes generally contain less information and that the regularization of the inversion pushes results towards 0. Weaker regularization would in some cases allow a more accurate recovery of the velocity fields, but there is a price to pay in that the risk of convergence failure increases. No instance was found where the algorithm generated artificial patterns not present in the reference fields. Most information on effective velocities above 50 km is included in measurements of CH4, CO, H2O, and N2O, while CFC-11, HCFC-22, and CFC-12 constrain the inversion most efficiently in the middle stratosphere. H2O is a particularly important tracer in the upper troposphere or lower stratosphere. SF6 and CCl4 generally contain less information but still contribute to the reduction in the estimated uncertainties. With these tests, the reliability of the method has been established.

Direct inversion of surface wave dispersion data with multiple-grid parameterizations and its application to a dense array in Chao Lake, eastern China

Summary The direct surface wave tomography has become an efficient tool in imaging three-dimensional (3-D) shallow Earth structure. However, some fundamental problems still exist in selecting the grids to parameterize the model space. This study proposes to implement a model parameterization approach with multiple grids to the direct surface wave tomography. These multiple grids represent several overlapping collocated grids with the same or different grid spacings, such as staggered grids, multiscale grids, and multiscale-staggered grids. At each iteration, direct inversion is applied to each individual set of collocated grids to invert for the shear-wave velocity (Vs) model; the models are then projected onto a set of predefined base grids (usually the finest grids) using 3-D B-spline interpolation. At the end of each iteration, we average the Vs models of all sets of collocated grids to obtain the average 3-D Vs model, which is then used as the initial model for the next iteration. The properties of this approach are explored by applying it to a newly deployed dense array in Chao Lake (CL), eastern China. Synthetic and field data tests demonstrate that the method using multiple grids recovers anomaly patterns better than that using the individual set of collocated grids, though it does not necessarily achieve the smallest traveltime residual. We then obtain a high-resolution 3-D shallow crustal Vs model beneath the CL. The 3-D Vs model reveals two prominent features: (1) a stripe-like structural pattern of velocity variations, where the Hefei basin and eastern CL display low-velocity anomalies while the Tanlu fault zone (TFZ), Zhangbaling uplift, and Yinping mountain present high-velocity anomalies; (2) north-shifted low-velocity anomalies beneath the eastern CL as depths go shallow. The shallow Vs features are consistent well with the local geological units and topography. We suggest that the two main features could be associated with the multistage tectonic activities of the Tanlu fault. The multiple-grid scheme proposed in this study could be conveniently extended to other 3-D direct inversion approaches in the near future.

Solving Coupled Cluster Equations by the Newton Krylov Method

We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.