dataesr/scientific-paragraphs-categorization huggingface dataset:
Tectonic mapping We have examined and built upon previous tectonic map databases  2, 3  to produce a global map of potential shortening structures to use as a methodological tool for our global grabens survey. Our mapping was undertaken to improve the accuracy of linework and because previous databases either did not have end-of-mission data products available at the time of completion 2 or did not map all compressional tectonic structures 3. To produce a global map of shortening structures at the highest resolution and completeness, we used the latest available data products to map all resolvable structures at a constant 1:500,000 drafting scale. We recognize and interpret all thrust fault-related structures on the basis of their morphology. Positive relief landforms with a recognizable break in slope are interpreted as surface-breaking thrust faults (lobate scarps), with a steep escarpment representing the leading edge and vergence of the underlying thrust.
Graben survey For the global grabens survey, we first selected all NAC frames 150 m pixel -1 or better that intersected any of the potential shortening structures in our database. To do this, we used a combination of Java Mission Planning and Analysis for Remote Sensing  53  and ArcGIS Pro to first query and then filter the 93,408 NAC frames of which 25,489 intersected the tectonic structures that we mapped. We then downloaded and processed the intersecting images in ISIS3 where spacecraft and camera information, radiometric calibration, map projection and photometric corrections were made so that the images could be analysed in ArcGIS. On a quadrangle-by-quadrangle basis, we inspected all the NAC images for each of the tectonic structures in context, superposed on the basemap. We identified grabens on the basis of their morphology: linear to sublinear mostly flat-floored depressions bounded on two sides by parallel to subparallel escarpments, sometimes found either side of horsts, raised fault-bounded blocks that share an escarpment with an adjacent graben or grabens.
A positive emission angle is used in this expression when the spacecraft has taken the image of the surface while looking towards the Sun, and a negative one is used when the Sun is behind the spacecraft  21. When possible, multiple shadow measurements were taken along the length of the graben, and then the calculated depths were averaged for a final depth result. This was performed to obtain the most robust average depth measurement for each of the grabens. The estimated error for each shadow measurement has been calculated and is found in Supplementary Data 3. The percentage of error per shadow measurement length can be applied to the calculated depth. For ~96% of shadow-length measurements, an error percentage between 0 and 10% has been calculated. With only ~4% ≥10% error, it is unlikely that measurement error has affected our estimates of depth.
Acknowledgements B. M. was funded by the  UK Research and Innovation (UKRI) Science and Technology Facilities Council  ( ST/T506321/1 ) and the  Open University 's https://doi. org /10. 1038/s41561-023-01281-5 Strategic Research Area in Space. While this work was being completed, D. A. R. , M. R. B. and J. W. were funded on the  PLANMAP  project. This project has received funding from the  European Union 's  Horizon 2020 research and innovation programme  under grant agreement no. 776276. J. W. acknowledges support from the  European Space Agency (ESA)  as an  ESA Research Fellow  received during the write-up of this work. S. J. C. is grateful for the support of the  French Space Agency ,  CNES , for her BepiColombo-related work. Thanks are also given to the  Royal Astronomical Society (RAS).
Data availability The MESSENGER data used in this article are available from NASA's Planetary Data System (PDS) Geosciences Node (https://pds-geosciences. wustl. edu/) and the Cartography and Imaging Sciences Node (https:// pds-imaging. jpl. nasa. gov/). The datasets produced as part of this study are available in Supplementary Data 1-3 and via Figshare at https://doi. org/10. 21954/ou. rd. 24167700. v1 (ref. 56 ).
Extended Data Fig. 3 | Examples of grabens 3. a, Lance Rupes (H08) certain & probable (EN1014677849M), b, Pelagia Rupes (H09) certain (MDIS HIW tile), c, Providencia Rupes (H09) certain & probable (EN1015944874M), d, Antares Rupes (H09) certain (MDIS HIW tile), e, Unnamed Rupes (H09) certain (MDIS HIW tile), f, Vejas Rupes (H03) certain (EN0212502528M overlain on MDIS global BDR mosaic). Credit: MESSENGER images from NASA/JHUAPL/CIW.
ACKNOWLEDGMENTS The authors thank  R. Russo  for useful discussions during the development of this work. P. R. acknowledges the hospitality and the stimulating environment of the  Institut des Hautes Etudes Scientifiques. The present research was partly supported by the " 2021 Balzan Prize for Gravitation : Physical and Astrophysical Aspects" , awarded to  Thibault Damour. P. R. acknowledges support by the  Fondazione Della Riccia , A. A. 2021/2022. P. R. is supported by the  Italian Minister of University and Research (MUR)  via the  PRIN 2020KB33TP , Multimessenger astronomy in the  Einstein Telescope Era  (METE). L. M. T. is supported by  STFC , the  School of Physics and Astronomy at the University of Birmingham , and the  Birmingham Institute for Gravitational Wave Astronomy. G. P. is very grateful for support from a  Royal Society University Research  Fellowship  URF\R1\221500  and  RF\ERE\221015 , and gratefully acknowledges support from an  NVIDIA Academic Hardware Grant.
Accurately mapping the evolving bathymetry under energetic wave breaking is challenging, yet critical for improving our understanding of sandy beach morphodynamics. Though remote sensing is one of the most promising opportunities for reaching this goal, existing depth-inversion algorithms using linear approaches face major theoretical and/or technical issues in the surf zone, limiting their accuracy over this region. Here, we present a new depth-inversion approach relying on Boussinesq theory for quantifying nonlinear dispersion effects in nearshore waves. Using high-resolution datasets collected in the laboratory under diverse wave conditions and beach morphologies, we demonstrate that this approach results in enhanced levels of accuracy in the surf zone (errors typically within 10%) and presents a major improvement over linear methods.
, 2011; Bergamasco et al. , 2017)  have seen major developments over the last decade and now allow the collection of accurate measurements of the sea-surface elevation in nearshore areas. By making information on wave heights directly accessible, these technologies offer the potential to substantially improve bathymetry inversion in the surf zone and right up to the shoreline. However, a universal nonlinear dispersion relation for shoaling and breaking waves is still lacking (for the most recent review refer:  Catalán & Haller, 2008). Here, we describe a new depthinversion method that relies on the stochastic Boussinesq theory of  Herbers et al. (2002)  to quantify nonlinear frequency and amplitude dispersion effects within both the shoaling and breaking wave regions. The new approach utilises high-resolution datasets of free surface elevation and is designed so that it can be applied in the field with any technology collecting such data (e.
Experimental Datasets The new Boussinesq depth-inversion approach is developed then evaluated using high-resolution surface elevation datasets collected in the laboratory. Here, the objective is to mimic under controlled conditions the field situation in which similar datasets can now be routinely collected using existing remote-sensing technologies. Though lidars presently offer the most robust and practical solution for collecting highly-resolved surface elevation data in the field, the approach presented is applicable to any technology capable of collecting such data (e. g. , stereo imagery systems). We consider three specific series of experiments, which covered a relatively wide range of wave conditions and beach morphologies. The experiments of van  Noorloos (2003)  were performed over a 1:35 planar beach in the 40 m-long wave flume at Delft University of Technology (Fig.
Assessment of the Boussinesq Theory for Estimating Nearshore Wave Dispersive Properties Prior to testing the new nonlinear depth-inversion approach, we first assess the capacity of the Boussinesq theory (Eq. 2) to predict the dispersive properties of irregular waves in both shoaling and breaking conditions. the shoaling region and surf zone (15-20% differences for both datasets). For the barred case, these differences reach 25% above the sandbar, where wave breaking is most intense (x = 9 -10 m, see Fig 2l). Fig. 3  shows that the accuracy of the Boussinesq theory extends across the whole range of frequencies [0. 7ω p ; 2. 5ω p ], which is consistent with the results of  Herbers et al. (2002)  and  Martins, Bonneton, Lannes, and Michallet (2021). Two examples taken from the shoaling region close to the breaking point (U r ∼ 1) and in the surf zone (U r ∼ 2.
The development of this new method was motivated by the recent widespread collection of high-resolution free surface elevation datasets by lidar scanners in the field (e. g. ,  Brodie et al. , 2015; Martins et al. , 2018; Fiedler et al. , 2021). Lidar scanners have the unique feature that they directly measure both surf zone processes and the subaerial section of sandy beaches. In combination with the proposed nonlinear depth-inversion procedure, these sensors open a whole new range of possibilities for continuous monitoring of the morphological evolution of sandy beaches extending from the nearshore to the dunes.
Cross-spectra are here computed using Welch's method and Hann-windowed blocks of 128 seconds, which were overlapping by 75%. This results in each spectral estimate having approximately 51, 71 and 30 equivalent degrees of freedom for the datasets of van Noorloos (  2003 ), GLOBEX and  Michallet et al. (2011) , respectively, while a spectral resolution of 0. 0078 Hz is retrieved in all cases. Let E and B denote the spectral and bispectral densities of the free surface elevation signal ζ, respectively. The energy spectra E is here given by: E(ω) = 2 E [A(ω) A * (ω)] , (6) The bispectrum of ζ is here computed following  Kim and Powers (1979)  as: B( ω 1 , ω 2 ) = E [A(ω 1 ) A(ω 2 ) A * (ω 1 + ω 2 )] , (7) Both energy spectra and bispectra of ζ are computed using 128 s blocks overlapping by 75%.
Fig. S1  gathers the results of this sensitivity analysis performed at the two locations corresponding to shoaling and breaking situations used in the manuscript. For each level of signal-to-noise ratio (SNR), the analysis was repeated 200 times, and results are shown in terms of deviation from the measured mean water depth value h obs : δ h = (h-h obs )/h obs ×100. The development of the present depth-inversion methodology was motivated and designed for future use in the field using highly-resolved free surface elevation datasets. At the moment, lidar scanners offer the most robust and promising solution, but the new depth-inversion approach can be applied to any technology capable of collecting high-resolution free surface elevation datasets (e. g. , stereo-video imagery). Though this might vary between field deployments and lidar scanner models, the systematic noise in lidar data does not generally exceed a few centimeters, which is 1-2 orders of magnitude lower than the amplitude of incident waves typically measured in the field  (Brodie et al.
Acknowledgments Kévin Martins  greatly acknowledges the financial support from the  European Union 's  Horizon 2020 research and innovation program  under the  Marie Sk lodowska-Curie Grant Agreement 887867  (lidBathy) that has enabled him to work with his Australian collaborators. We warmly thank  Ap van Dongeren  and  Hervé Michallet  for providing the raw data for the experiments described in van Noorloos (2003) and Michallet et al. (2011), respectively. The  GLOBEX  project was supported by the  European Community's Seventh Framework Programme  through the  Hydralab IV  project, EC Contract  261520. Continuous discussions over the past few years with David Lannes on Boussinesq models and methods to predict the dispersive properties of incident wave fields are greatly appreciated.
Digital Image Correlation Overhead, time-lapse photographs of the deforming models were acquired at 1-minute intervals. We used a DSLR camera (18 megapixels, Canon EOS 550D) fitted with a 35. 0 mm fixed lens and mounted ∼1. 3 m above the model basement. With a field of view of approximately 562 × 842 mm, the image resolution was approximately 3 pixels/mm. To calculate horizontal displacements, velocities, and strains of the model surface, the time-lapse photographs were processed with the StrainMaster2D module of the commercially available digital image correlation (DIC) software DaVis by LaVision  (Adam et al. , 2005). This software uses a fast-Fourier transform approach to locate and track peaks in pixel amplitudes from one image to the next in the time-lapse series. DaVis also enables the use of an adaptive multi-pass correlation to improve the precision and spatial resolution of the displacement vector field.
3 (van Wyk de Vries and Matela, 1998); and (iii) a combination of positively-sloped and horizontal lines at B/D ∼ 2 and B/D = 0. 3  (Borgia et al. , 2000). Our more extensive dataset shows that spreading and sagging domains are separated by a gradual, negatively-sloped zone of hybrid behavior in D/H -B/H space. Moreover, the B/D ratio is not as critical a control as previously thought, since we show that models with the same B/D ratio can exhibit either spreading or sagging. The hybrid deformation style is also a new finding here. A distinctive characteristic of the hybrid deformation style is that the maximum cumulative horizontal displacement can occur in the basement rather than on the cone flank. This behavior is seen also in past numerical model simulations of volcano-basement interactions that were interpreted to result in 'basement extrusion' (van Wyk de Vries and Matela, 1998), and in a recent combined analog and numerical study of the geodetic behavior of Vesuvius  (De Matteo et al.
Acknowledgements This manuscript greatly benefited from the comments of four anonymous reviewers and editor  C. Petrone. We acknowledge  O. Galland and Beanhive  for fruitful discussions, and  M. Rosenau  for access to the DaVis software. During this work EPH received financial support from  University College Dublin ,  GFZ-Potsdam , the  European Regional Development Fund project AGEO -Platform for Atlantic Geohazards  (Grant code:  EAPA_884/2018 ) and the  Irish Centre for Research in Applied Geosciences  (iCRAGgrant code:  13/RC/2092_P2 ). SP was supported by an Aspirant PhD grant from  FWO-Flanders  ( 2014-2019 ), and since 2021 by  ULAM postdoctoral scholarship  ( PPN/ULM/2020/1/00067 ) from the  Polish National Agency for Academic Exchange (NAWA)  and project  2020/37/K/ST10/02447  from the  Norwegian Financial Mechanism   2014-2021  (  NCN Poland ).
The observation area is 8 AM-4 PM local time in the daytime 0 • -90 • N, and the LIR observations are assimilated twice a day. This observation area is based on the previous OSSE performed for Akatsuki LIR in  Sugimoto et al. (2022b). While  Sugimoto et al. (2022b)  covers the equatorial region, the observation area is shifted to the northern hemisphere in this Table  2  shows the total number of observation data per day for the LIR and P1P2P3 (RO) experimental cases. In the P1P2P3 case, 28 observation data are obtained in the vertical direction per an observation point. Since RO observations are performed 24. 8 times a day, the total number of observation data per day is 24. 8 × 28 = 694. 4. In the LIR case, the observation data in the daytime 8 AM-4 PM local time (31 points) and 0 • -90 • N (49 points) can be obtained in the horizontal direction.
Acknowledgments This study was conducted under the joint research project of the Earth Simulator Center with title "High resolution general circulation simulation of Venus and Mars atmosphere using AFES". The work is partly supported by  MEXT | Japan Society for the Promotion of Science (JSPS)  grants  JP19H01971 ,  JP19H05605 ,  JP20K04064. This study was supported by  GSC (Global Science Campus) of JST (Japan Science and Technology Agency ). Work performed by  C. Ao  was carried out at the  Jet Propulsion Laboratory, California Institute of Technology , under a contract with the  National Aeronautics and Space Administration. Results from the simulation experiments performed in this paper are available at Mendeley Data (https://doi. org/10. 17632/cg8nxtkf94. 4).
For the homogenous debris https://doi. org/10. 5194/egusphere-2023-2766 Preprint. Discussion started: 27 November 2023 c Author(s) 2023. CC BY 4. 0 License. case they highlight the importance of equal vertical spacings between thermistors to reduce truncation errors, and show that if unequal spacing cannot be avoided, the Bayesian method outperforms that of  Conway and Rasmussen (2000). As expected, for the two layer debris case they demonstrate that the model versions accommodating this structure outperform model versions forced to solve for a single layer. They limit their multi-layer analysis to the case of three data points within the debris layer and explore the impact of the sampled spacing and ratio of thermal diffusivity above and below the central point. Based on theory and the analysis presented in these two papers, the new or modified methods appear to offer advances on the method of  Conway and Rasmussen (2000) , but further analysis with a wider selection of datasets would help establish the robustness of the improvement.
, 2015)  of the daily mean debris layer temperature is only fulfilled for perfectly idealized datasets. A glacier's debris layer is at a steady state when the debris layer's 185 temperature decreases linearly towards the debris-ice interface. In the model, we can also select and de-selected errors and uncertainties to investigate their effect. To account for the fact that measurement devices do not have a double float accuracy as does our model, we can discretize the data to correspond with the measurement uncertainty of 0. 1 to 0. 4 °C. This is the uncertainty range of thermistors most commonly used in the field. Also, the vertical field deployment of the thermistors is not as exact as in our model. We accounted for that by using a Gaussian random error to displace the values by a Gaussian width of 0.
235 we add a temperature discretization from 0. 1 to 0. 4 °C since these are the discretizations of the thermistors used to create our datasets. We again sample over the thermistor spacings but only focus on the region not affected by the truncation error (Fig. 9 ). Because we added temperature uncertainty, it now makes a difference how we sample the thermistor spacings. One can either start at the top -so from the surface layer -and increase the ∆x from there. Alternatively, one starts in the middle of the debris layer and selects ∆x symmetrically. The third option is to start at the debris-ice interface and go up from there with increasing measurement uncertainty. For small values of ∆x the relative error spikes and exponentially decreases for larger values of ∆x. The averaging method produces different but similar results.
Furthermore, they stated "the top sensor should be placed approximately at the middle of the debris layer" and our analysis indicates that while it is true, that thermistors too close to the surface produce large truncation errors, the same is valid for too deep thermistors as the temperature gradient is to small relative to the thermistor precision. Finally, in addition to all these measurement setup related errors, non-conductive processes within the debris layer (e. g. rain, phase changes) would distort the results. This must be evaluated on a case-by-case basis using meteorological data and closely evaluating the vertical temperature measurements in the debris layer and the corresponding gradient functions  Petersen et al. (2022). All of this makes it challenging to interpret the results correctly leaving considerable room for error, especially since the datasets often lack relevant meta-and meteorological data.
Debris layer depth: Minimum of 40 cm but ideally deeper (e. g. 100 cm). The maximum depth is limited by the thermistor precision and temperature gradients in the debris layer. This can be simulated beforehand. Thermistor installation and recovery: Thermistors have to be carefully extracted at the end of the measurement period to make sure the thermistors haven't moved in the debris while deployed. However, in case the thermistors moved, it might be necessary to omit this dataset. Therefore mounting thermistors to a thermally insulated rod or set of rods eliminates this potential error source.
Acknowledgements We thank  Monique Gentric  and  Marion Delattre  ( LOG laboratory ) for the financial/administrative management and the technical support of this project, respectively, and the  Department of Earth Sciences of the University of Lille  for its support. Thanks to  Ivan Jovovic  ( Biogéosciences Lab, University of Dijon ) for the isotope composition determination. Thanks to our referees for their useful review, thanks to  Abderrazak El Albani  for his constant support.
Apparent polar wander paths (APWPs) calculated from paleomagnetic data describe the motion of tectonic plates relative to the Earth's rotation axis through geological time, providing a quantitative paleogeographic framework for studying the evolution of Earth's interior, surface, and atmosphere. Previous APWPs were typically calculated from collections of paleomagnetic poles, with each pole computed from collections of paleomagnetic sites, and each site representing a spot reading of the paleomagnetic field. It was recently shown that the choice of how sites are distributed over poles strongly determines the confidence region around APWPs and possibly the APWP itself, and that the number of paleomagnetic data used to compute a single paleomagnetic pole varies widely and is essentially arbitrary.
Here, we use a recently proposed method to overcome this problem and provide a new global APWP for the last 320 million years that is calculated from simulated site-level paleomagnetic data instead of from paleopoles, in which spatial and temporal uncertainties of the original datasets are incorporated. We provide an updated global paleomagnetic database scrutinized against quantitative, stringent quality criteria, and use an updated global plate motion model. The new global APWP follows the same trend as the most recent pole-based APWP but has smaller uncertainties. This demonstrates that the first-order geometry of the global APWP is robust and reproducible. Moreover, we find that previously identified peaks in APW rate disappear when calculating the APWP from site-level data and correcting for a temporal bias in the underlying data.
Finally, we show that a higher-resolution global APWP frame may be determined for time intervals with high data density, but that this is not yet feasible for the entire 320-0 Ma time span. Calculating polar wander from site-level data provides opportunities to significantly improve the quality and resolution of the global APWP by collecting large and well-dated paleomagnetic datasets from stable plate interiors, which may contribute to solving detailed Earth scientific problems that rely on a paleomagnetic reference frame.