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The continental margin of southeast Brazil is elevated. Onshore Tertiary basins and Late Cretaceous/Paleogene intrusions are good evidence for post breakup tectono‐magmatic activity. To constrain the impact of post‐rift reactivation on the geological history of the area, we carried out a new thermochronological study. Apatite fission track ages range from 60.7 ± 1.9 Ma to 129.3 ± 4.3 Ma, mean track lengths from 11.41 ± 0.23 μm to 14.31 ± 0.24 μm and a subset of the (U‐Th)/He ages range from 45.1 ± 1.5 to 122.4 ± 2.5 Ma. Results of inverse thermal history modeling generally support the conclusions from an earlier study for a Late Cretaceous phase of cooling. Around the onshore Taubaté Basin, for a limited number of samples, the first detectable period of cooling occurred during the Early Tertiary. The inferred thermal histories for many samples also imply subsequent reheating followed by Neogene cooling. Given the uncertainty of the inversion results, we did deterministic forward modeling to assess the range of possibilities of this Tertiary part of the thermal history. The evidence for reheating seems to be robust around the Taubaté Basin, but elsewhere the data cannot discriminate between this and a less complex thermal history. However, forward modeling results and geological information support the conclusion that the whole area underwent cooling during the Neogene. The synchronicity of the cooling phases with Andean tectonics and those in NE Brazil leads us to assume a plate‐wide compressional stress that reactivated inherited structures. The present‐day topographic relief of the margin reflects a contribution from post‐breakup reactivation and uplift. Key Points New (U‐Th)/He and AFT data from southeast Brazil Results imply polyphased post‐rift tectonic reactivation Passive margins are not passive

Residual terrain modelling (RTM) plays a key role for short-scale gravity modelling in physical geodesy, e.g. for interpolation of observed gravity and augmentation of global geopotential models (GGMs). However, approximation errors encountered in RTM computation schemes are little investigated. The goal of the present paper is to examine widely used classical RTM techniques in order to provide insights into RTM-specific approximation errors and the resulting RTM accuracy. This is achieved by introducing a new, independent RTM technique as baseline that relies on the combination of (1) a full-scale global numerical integration in the spatial domain and (2) ultra-high-degree spectral forward modelling. The global integration provides the full gravity signal of the complete (detailed) topography, and the spectral modelling that of the RTM reference topography. As a main benefit, the RTM baseline technique inherently solves the “non-harmonicity problem” encountered in classical RTM techniques for points inside the reference topography. The new technique is utilized in a closed-loop type testing regime for in-depth examination of four variants of classical RTM techniques used in the literature which are all affected by one or two types of RTM-specific approximation errors. These are errors due to the (1) harmonic correction (HC) needed for points located inside the reference topography, (2) mass simplification, (3) vertical computation point inconsistency, and (4) neglect of terrain correction (TC) of the reference topography. For the Himalaya Mountains and the European Alps, and a degree-2160 reference topography, RTM approximation errors are quantified. As key finding, approximation errors associated with the standard HC (4πGρHPRTM) may reach amplitudes of ~ 10 mGal for points located deep inside the reference topography. We further show that the popular RTM approximation (2πGρHPRTM-TC) suffers from severe errors that may reach ~ 90 mGal amplitudes in rugged terrain. As a general conclusion, the RTM baseline technique allows inspecting present and future RTM techniques down to the sub-mGal level, thus improving our understanding of technique characteristics and errors. We expect the insights to be useful for future RTM applications, e.g. in geoid modelling using remove–compute–restore techniques, and in the development of new GGMs or high-resolution augmentations thereof.

During the last few years, the determination of high-resolution global gravity field has gained momentum due to high-accuracy satellite-derived observations and development of forward gravity modelling. Forward modelling computes the global gravitational field from mass distribution sources instead of actual gravity measurements and helps improving and complementing the medium to high-frequency components of the global gravity field models. In this study, we approximate the global gravity potential of the Earth’s upper crust based on ellipsoidal approximation and a mass layer concept. Such an approach has an advantage of spectral methods and also avoids possible instabilities due to the use of a sequence of thin ellipsoidal shells. Lateral density within these volumetric shells bounded by confocal lower and upper shell ellipsoids is used in the computation of the ellipsoidal harmonic coefficients which are then transformed into spherical harmonic coefficients on the Earth’s surface in the final step. The main outcome of this research is a spectral representation of the gravitatioal potential of the Earth’s upper crust, computed up to degree and order 3660 in terms of spherical harmonic coefficients (ROLI_EllApprox_SphN_3660). We evaluate our methodology by comparing this model with other similar forward models in the literature which show sub-cm agreement in terms of geoid undulations. Finally, EIGEN-6C4 is augmented by ROLI_EllApprox_SphN_3660 and the gravity field functionals computed from the expanded model which has about 5 km half-wavelength spatial resolution are compared w.r.t. ground-truth data in different regions worldwide. Our investigations show that the contribution of the topographic model increases the agreement up to ~ 20% in the gravity value comparisons.

The Gravity Recovery and Climate Experiment (GRACE) mission and its successor, GRACE Follow‐On (GFO), effectively monitor terrestrial water storage anomaly (TWSA). However, their constrained spatial resolution imposes limitations, with leakage and attenuation potentially impacting the accuracy of regional TWSA. While GRACE/GFO observations capture the ongoing TWSA decline in the Middle East due to excessive groundwater extraction, the nearby Caspian Sea's long‐term water loss, combined with the seasonal signals from the coastal sea, complicate accurate TWSA estimation through signal attenuation and leakage. To address these issues, we propose a combined approach, that is, independent component analysis (ICA)‐based forward modeling (IFM), to discern and isolate the leakage effect and improve the recovery of TWSA signal. We demonstrate the impact of signal attenuation and leakage through simulation, and validate the effectiveness of IFM. This method is also confirmed through steric‐corrected altimetry estimates in the Caspian Sea, Red Sea, and Persian Gulf, and further validated in Greenland and Victoria Lake. Our results show considerable leakage in GRACE/GFO TWSA estimates for Saudi Arabia and Iran. Leakage from the Red Sea and Persian Gulf introduces a 28.6% bias in Saudi Arabia's TWSA trend, while leakage from the Caspian Sea results in a 36.4% bias in Iran. After IFM recovery, the TWSA decline rates for Saudi Arabia, Iraq, and Iran are 11.48 ± 0.32, 3.56 ± 0.44, and 7.75 ± 0.45 km3/yr, respectively. This study demonstrates the effectiveness of IFM in deriving refined TWSA signal, providing valuable insights for water resource management in arid regions.

Building energy performance (BEP) is an ongoing point of reflection among researchers and practitioners. The importance of buildings as one of the largest activators in climate change mitigation was illustrated recently at the United Nations Framework Convention on Climate Change 21st Conference of the Parties (COP21). Continuous technological improvements make it necessary to revise the methodology for energy calculations in buildings, as has recently happened with the new international standard ISO 52016-1 on Energy Performance of Buildings. In this area, there is a growing need for advanced tools like building energy models (BEMs). BEMs should play an important role in this process, but until now there has no been international consensus on how these models should reconcile the gap between measurement and simulated data in order to make them more reliable and affordable. Our proposal is a new generation of models that reconcile the traditional data-driven (inverse) modelling and law-driven (forward) modelling in a single type that we have called law-data-driven models. This achievement has greatly simplified past methodologies, and is a step forward in the search for a standard in the process of calibrating a building energy model.

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods, PINNs have several advantages, for example their ability to provide mesh-free solutions of differential equations and their ability to carry out forward and inverse modelling within the same optimisation problem. Whilst promising, a key limitation to date is that PINNs have struggled to accurately and efficiently solve problems with large domains and/or multi-scale solutions, which is crucial for their real-world application. Multiple significant and related factors contribute to this issue, including the increasing complexity of the underlying PINN optimisation problem as the problem size grows and the spectral bias of neural networks. In this work, we propose a new, scalable approach for solving large problems relating to differential equations called finite basis physics-informed neural networks (FBPINNs) . FBPINNs are inspired by classical finite element methods, where the solution of the differential equation is expressed as the sum of a finite set of basis functions with compact support. In FBPINNs, neural networks are used to learn these basis functions, which are defined over small, overlapping subdomains. FBINNs are designed to address the spectral bias of neural networks by using separate input normalisation over each subdomain and reduce the complexity of the underlying optimisation problem by using many smaller neural networks in a parallel divide-and-conquer approach. Our numerical experiments show that FBPINNs are effective in solving both small and larger, multi-scale problems, outperforming standard PINNs in both accuracy and computational resources required, potentially paving the way to the application of PINNs on large, real-world problems.

Deep learning has become the dominant approach in artificial intelligence to solve complex data-driven problems. Originally applied almost exclusively in computer-science areas such as image analysis and nature language processing, deep learning has rapidly entered a wide variety of scientific fields including physics, chemistry and material science. Very recently, deep neural networks have been introduced in the field of nanophotonics as a powerful way of obtaining the nonlinear mapping between the topology and composition of arbitrary nanophotonic structures and their associated functional properties. In this paper, we have discussed the recent progress in the application of deep learning to the inverse design of nanophotonic devices, mainly focusing on the three existing learning paradigms of supervised-, unsupervised-, and reinforcement learning. Deep learning forward modelling i.e. how artificial intelligence learns how to solve Maxwell’s equations, is also discussed, along with an outlook of this rapidly evolving research area.

The currently available global geopotential models and the global elevation and bathymetry data allow modelling the topography-corrected and bathymetry stripped reference gravity field to a very high spectral resolution (up to degree 2160 of spherical harmonics) using methods for a spherical harmonic analysis and synthesis of the gravity field. When modelling the topography-corrected and crust-density-contrast stripped reference gravity field, additional stripping corrections are applied due to the ice, sediment and other major known density contrasts within the Earth's crust. The currently available data of global crustal density structures have, however, a very low resolution and accuracy. The compilation of the global crust density contrast stripped gravity field is thus limited to a low spectral resolution, typically up to degree 180 of spherical harmonics. In this study we derive the expressions used in forward modelling of the bathymetry-generated gravitational field quantities and the corresponding bathymetric stripping corrections to gravity field quantities by means of the spherical bathymetric (ocean bottom depth) functions. The expressions for the potential and its radial derivative are formulated for the adopted constant (average) ocean saltwater density contrast and for the spherical approximation of the geoid surface. These newly derived expressions are utilized in numerical examples to compute the gravitational potential and attraction generated by the ocean density contrast. The computation is realized globally on a 1 x 1 arc-deg geographical grid at the Earth's surface.

We present and compare four types of the isostatic gravity disturbances compiled at sea level over the world oceans and marginal seas. These isostatic gravity disturbances are computed by applying the Airy–Heiskanen (AH), Pratt–Hayford (PH) and Vening Meinesz–Moritz (VMM) isostatic models. In addition, we compute the complete crust-stripped (CCS) isostatic gravity disturbances which are defined based on a principle of minimizing their spatial correlation with the Moho geometry. We demonstrate that each applied compensation scheme yields a distinctive spatial pattern in the resulting isostatic marine gravity field. The AH isostatic gravity disturbances provide the smoothest gravity field (by means of their standard deviation). The AH and VMM isostatic gravity disturbances have very similar spatial patterns due to the fact that the same isostatic principle is applied in both these definitions expect for assuming a local (in the former) instead of a global (in the latter) compensation mechanism. The PH isostatic gravity disturbances are highly spatially correlated with the ocean-floor relief. The CCS isostatic gravity disturbances reveal a signature of the ocean-floor spreading characterized by an increasing density of the oceanic lithosphere with age.

There are numerous applications in geodesy and other geo-sciences in which the gravitational potential effect or other functions of the potential are computed by forward modelling from a given mass distribution. Different volume discretisations, e.g. prisms, tesseroids or mass layers are used. In order to control the numerical realisation of the forward calculation in the practical application, e.g. in reduction tasks, these evaluation programs should be verified against rigorous analytical solutions. In this contribution, a closed analytical solution for the potential of an ellipsoidal shell as a test body is presented. Furthermore, we derive the respective closed formulae for the gravity vector and the gravity gradient tensor. Program implementations of the tesseroid approach are compared on the basis of this ellipsoidal mass arrangement. For the practical usage, fast-converging expansions in spherical harmonics are provided in addition. The derivation of the formulae is based on a closed solution of the potential of a homogeneous ellipsoid for computation points situated on the rotation axis, which then is extended to the external space.