dataesr/scientific-paragraphs-categorization huggingface dataset:
All implicit surface modelling techniques involve finding a combination of weighted basis functions that fit the geological observations. There are two main approaches used for implicit surface modelling: (1) data-supported approaches where the basis functions are estimated at the data points  (Calcagno et al. , 2008a; Cowan et al. , 2003; Gonçalves et al. , 2017; Hillier et al. , 2014; Lajaunie et al. , 1997)  and Published by Copernicus Publications on behalf of the European Geosciences Union. L. Grose et al. :  LoopStructural 1. 0: time-aware geological modelling (2) discrete interpolation where the basis functions are located on a predefined support  (Caumon et al. , 2013; Frank et al. , 2007; Irakarama et al. , 2018; Renaudeau et al. , 2019). The algorithms are often linked to commercial software, e.
g. Leapfrog 1  , 3D GeoModeller 2 and Gocad-SKUA 3. These packages will usually only provide one algorithm for interpolation, making it difficult to compare different interpolation schemes. The algorithms are also usually black box algorithms with limited ability to change algorithm parameters, with no understanding of how the algorithm is implemented. A recent open-source Python library, Gempy (de la  Varga et al. , 2019) , implements the dual co-kriging implicit interpolation algorithm  (Lajaunie et al. , 1997)  using a high performance computational library. In this contribution we introduce the open-source Loop-Structural, a 3D geological modelling Python library based on the incremental contributions of  Laurent et al. (2016)  and  Grose et al. (2017 Grose et al. ( , 2018 Grose et al.
( , 2019)). LoopStructural is a new geological modelling engine developed within the Loop 4 consortium  (Ailleres et al. , 2018). The core modelling library within LoopStructural depends on scipy  (Virtanen et al. , 2020) , numpy  (Van Der Walt et al. , 2011)  and pandas (pandas development team, 2020), the core scientific Python libraries. A visualisation module uses LavaVu  (Kaluza et al. , 2020) , a minimal OpenGL visualisation package allowing for models to be visualised within a Jupyter notebook environment. LoopStructural has been written using an object-oriented program design with class structures designed to allow for powerful inheritance and modularity. The design of Loop-Structural allows development and research into geological modelling methods to be easily performed without having to rewrite boiler plate code for interpolation algorithms, visualisation and model interaction.
LoopStructural is a modelling package allowing for multiple stratigraphic groups, faults, folds and unconformities to be represented using implicit surfaces. Different interpolation algorithms can be used for interpolating these surfaces with the ability to mix and match interpolation algorithms depending on the surface type being modelled. LoopStructural has native implementation of discrete implicit modelling using a piecewise linear interpolation on a tetrahedral mesh  (Caumon et al. , 2013; Frank et al. , 2007; Mallet, 2014 Mallet, , 2002)) , finite-difference interpolation on a Cartesian grid  (Irakarama et al. , 2018; Renaudeau et al. , 2018) , fold interpolation using tetrahedral meshes  (Laurent et al. , 2016)  and an interface to a generalised radial basis interpolation  (Hillier et al.
, 2014). This paper begins with a background analysis of 3D modelling methods and the algorithms used in implicit modelling, with an overview of the mathematical and geological backgrounds used in our implementation. A detailed overview of the specifics of the implementation can be found on (http:// loop3d. github. io/LoopStructural, last access: 15 June 2021). To demonstrate the versatility of LoopStructural and to provide a user guide we include four case studies in this paper with corresponding Jupyter notebooks. The first case study is a synthetic example interpolating two planar surfaces where the height of one surface has been perturbed to simulate uncertainty in the surface location. In this example we use the LoopStructural API to compare three different interpolation codes and investigate the parameters and how they are affected by noise.
The second example is a synthetic refolded type 3 interference pattern from  Laurent et al. (2016) , where we apply the time-aware discrete fold interpolation method described by  Laurent et al. (2016)  for modelling the refolded folds. In the third case study LoopStructural is applied to a real dataset from the Flinders Ranges in South Australia, where the dataset has been prepared using the pre-processing module of the Loop workflow map2loop  (Jessell et al. , 2021). In the fourth and final case study we use map2loop to augment an input dataset for a model in the Hamersley region in Western Australia. We generate 10 unique models, demonstrating the range of possible geometries when perturbing the fault geometry.
The joint posterior distribution of the fold parameters (Fourier series coefficients, fold wavelength and a misfit parameter) are sampled using Bayesian inference. This allows multiple fold geometries to be explored without perturbing the datasets. LoopStructural does not provide a direct probabilistic interface; however, it is possible to define a probabilistic representation of the fold geometry curves and add this into the modelling workflow. An example using the Python library emcee (Foreman-Mackey et al. , 2013) is provided in the LoopStructural documentation.
Loop structural design LoopStructural is written using Python 3. 6+, using numpy data structures and operations. The design of LoopStructural follows an object-oriented architecture with multiple levels Geosci. Model Dev. , 14, 3915-3937, 2021 https://doi. org/10. 5194/gmd-14-3915-2021 of inheritance. Object-oriented design allows for LoopStructural to be used as a development platform for 3D geological modelling, where new features can be added without needing to implement boiler plate code. There are five submodules that can be imported into a Python environment: 1. core contains the core modelling functionalities and the management of the geological concepts. 2. interpolation contains the various interpolation code and supports used to build scalar fields. 3. datasets contains the test and reference datasets.
Model output LoopStructural includes a number of helper functions for evaluating the GeologicalModel on an array of coordinates within the model. The following functions can be called from a GeologicalModel as shown in the code below. -To evaluate the lithology value at a location the function evaluate_model(xyz) returns a numpy array containing the integer ID of the stratigraphy that was specified in the stratigraphic column. -To evaluate the value of a GeologicalFeature at a location within the model the function evalu-ate_feature_value(feature_name,xyz) returns the value of the scalar field that represents the geological feature. -To evaluate the gradient of a GeologicalFeature the eval-uate_feature_gradient(feature_name,xyz) can be called. Triangulated surfaces can be extracted from a Geologi-calFeature within LoopStructural and exported into common mesh formats, e.
Model visualisation LoopStructural has three different visualisation tools that can be accessed from the LoopStructural. visualisation module: 1. LavaVuModelViewer. LavaVu  (Kaluza et al. , 2020 ) is a visualisation module that provides interactive visualisation. We use LavaVu for visualising triangulated surfaces representing the geological interfaces as well as the scalar field representing the implicit function. The creation and manipulation of LavaVu objects is wrapped by the LavaVuModelViewer class which provides an interface to the GeologicalModel. This is an interactive (and static) 3D visualisation using LavaVu. 2. MapView. This is a 2D visualisation (cross section, map) using matplotlib  (Hunter, 2007)  that can create a 5 https://www. paraview. org/, last access: 15 June 2021 geological map from the resulting geological model.
Integration with map2loop In the final examples we use map2loop  (Jessell et al. , 2021)  as a pre-processor to generate an input dataset from regional geological survey maps, the national stratigraphic database and a global digital elevation model. map2loop creates a set of augmented data files that can be used to build a geological model in LoopStructural. The class method (Ge-ologicalModel. from_map2loop_directory(m2l_directory, **kwargs)) creates an instance of a GeologicalModel from a root map2loop output directory. We will demonstrate the interface between map2loop and LoopStructural with two case studies (1) from the Flinders Ranges in South Australia and (2) from the Hamersley region in Western Australia. The first case study demonstrates the interface between map2loop and LoopStructural for a large regional model.
The second case study shows how the conceptual model used to generate the input dataset can be varied. The first example uses a small study area from South Australia using the Geological Survey of South Australia's open-access datasets (GSSA, 2020). The model area covers approximately 85 km by 53 km within the Finders Ranges in South Australia. The stratigraphic units within this area are shown in Fig. 13a , and the outcropping geology is shown in the geological map (Fig. 13b ); the patches of the map https://doi. org/10. 5194/gmd-14-3915-2021 Geosci. Model Dev. , 14, 3915-3937, 2021    14  where the surface represents the base of a stratigraphic group and are coloured using the stratigraphic column (Fig. 13a ). The faults in the model are interpolated using a Cartesian grid with 50 000 elements and are interpolated using the finite-difference interpolator, and the interpolation matrix is solved using the pyamg algorithmic multigrid solver  (Olson and Schroder, 2018).
Stratigraphy is interpolated using a finer mesh with 500 000 elements using the finite-difference interpolator and also using pyamg. Using a workstation laptop with an i7 processor and 32gb of RAM the data processing using map2loop takes approximately 1 min, building the implicit model takes approximately 8 min and the rendering of the surfaces on a (200 × 200 × 100) Cartesian grid takes 3 min. The intersection of the solid geological model and the map surface is shown in Fig. 13c , allowing for a comparison with the input dataset. The geological model has interpolated the geological packages underneath the surficial deposits. In the second example we use map2loop to process a small area of the Turner Syncline in the Hamersley region in Western Australia using data provided by the Geological Survey of Western Australia (GSWA) (2016).
Discussion LoopStructural is the 3D geological modelling module for Loop, a new open-source 3D probabilistic geological and geophysical modelling platform. LoopStructural integrates the relative timing of geological features into the description of the model elements using a time-aware modelling approach where the model is built by adding geological features in the reverse order from which they occur. This is necessary for capturing the complexities of complex structural geometries, for this approach is used for modelling refolded folds (Fig. 12 ). In a similar way faults are added backwards in time; this means that the displacements of the faults are applied to the model prior to interpolating the faulted surface. As a result, the fault displacements and overprinting relationships are internally consistent.
, 2017; Laurent et al. , 2016)  and a finite-difference interpolator, minimising the second derivative as a regularisation constraint  (Irakarama et al. , 2018). In Fig. 8  we showed that choosing the regularisation weight is somewhat dependent on the quality of the input dataset. For this reason, varying the regularisation weight and interpolation approach should be a common step in implicit modelling workflows. The current implementation of the piecewise linear interpolation uses a tetrahedral mesh that is derived from a Cartesian grid. A more sophisticated mesh generated from an external mesh generation code could be integrated into LoopStructural by overwriting the tetrahedral mesh class with a custom class. Within the LoopStructural architecture alternative regularisation constraints could easily be incorporated.
By incorporating the geological concepts into the geological modelling algorithms, these conceptual uncertainties can be integrated into a probabilistic definition of the geological model. Currently, LoopStructural does not have a probabilistic interface; however, all parameters relating to geological structures (topological ordering, fold geometries, fault displacement and geometries) are accessible from the GeologicalModel class functions. In Fig. 14 , map2loop  (Jessell et al. , 2021)  generates an augmented dataset from the open-access geological survey databases (stratigraphic database, DTM, geology shapefiles, structural lines and structural observations). In this example, the total time from data processing to model rendering was approximately 10 min. Using discrete implicit modelling means that the complexity of the model is defined by the resolution of the support, rather than the number of observations.
Conclusions In this contribution we have introduced LoopStructural, a new open-source Python library for implicit 3D geological modelling. The key features of LoopStructural are as follows: implicit 3D geological modelling algorithms using discrete interpolation, implementation of structural geology of folds and faults using structural frames, a direct link to map2loop for automated 3D geological modelling, an object-oriented software design allowing for easy development and extension of the 3D modelling algorithms. LoopStructural uses a time-aware modelling approach where relative timing between different geological features (folding, faulting and stratigraphy features) allows for complex overprinting relationships to be incorporated into the implicit geological models. Folds and faults are encoded using structural frames, a curvilinear coordinate system that is oriented with the geometry of the major structural feature of the deformational event.
Acknowledgements. This research has performed as part of the  Loop  project, a  OneGeology initiative  funded by the  Australian Research Council  and supported by  Monash University ; the  University of Western Australia ;  Geoscience Australia ; the  Geological Surveys of Western Australia, Northern Territory ,  South Australia  and New South Wales; the  Research for Integrative Numerical Geology; Universite de Lorraine ;  RWTH Aachen; Geological Survey of Canada ;  British Geological Survey ; and  Bureau de Recherches Géòlogiques et Minières and Auscope. The work has also been supported by the  Mineral Exploration Cooperative Research Centre , whose activities are funded by the  Australian Government's Cooperative Research Centre Programme. This is MinEx  CRC Document 2021/41. The source data used in the final example were provided by  Geological Survey of South Australia, Geological Survey of Western Australia and Geoscience Australia.
Code and data availability. LoopStructural is a free open-source Python library licensed under the Massachusetts Institute of Technology (MIT) license. It is currently hosted on https:// github. com/Loop3d/LoopStructural (last access: 15 June 2021) the version associated with the publication can be found https://doi. org/10. 5281/zenodo. 4649536 (Grose et al. , 2021b). Documentation is available within the package and is hosted on https://loop3d. github. io/LoopStructural (last access: 15 June 2021). Jupyter notebooks used for the examples in this paper are available on https://github. com/lachlangrose/loopstructural_paper_ examples (last access: 15 June 2021) and can also be found https://doi. org/10. 5281/zenodo. 4677735 (Grose, 2021).
Dans l'ensemble, les coûts économiques ont été estimés à 9,8 milliards de dollars entre 1960 et 2020, dont 8,9 milliards de dollars de coûts potentiels. Les coûts potentiels étaient principalement liés aux coûts extrapolés du ouaouaron d'Amérique Lithobates catesbeianus, du cerisier noir Prunus serotina et de deux mammifères: le rat musqué Ondatra zibethicus et le vison d'Amérique Neovison vison. Les coûts observés étaient attribuables à un large éventail de taxons et principalement associés aux dépenses liées au contrôle et aux dommages ou pertes affectant les ressources humaines. Nous avons identifié une augmentation considérable des coûts au cours du temps, avec des coûts supérieurs aux estimations réalisées précédemment. Il est important de noter que sur les 2249 espèces exotiques et 181 espèces envahissantes signalées en Allemagne, seules 28 espèces ont des coûts économiques reportés dans la base de données considérée.
Using the literature-based data on the economic costs of invasive species compiled in the InvaCost database  (Diagne et al. 2020) , we synthesise and describe the costs of invasions for the German economy. Our study is more comprehensive in presenting economic costs inferred from invasions than previous assessments at the national level (see, for example,  Reinhardt et al. 2003). Indeed, data included in this database are more rigorous and complete, with rich ancillary information allowing a more detailed examination of the origin of costs and methodologies used in primary studies. Moreover, the database compiled cost information using a standardised and annualised currency, enhancing comparisons among data sources within and beyond the country. Focusing on the period of 1960-2020 in Germany, we asked: (i) what is the economic cost of biological invasions in that country; (ii) which taxonomic groups cause the highest economic costs, which economic sectors are most impacted and how amounts are distributed between damage and management costs; (iii) what proportion of costs are from highly reliable sources (i.
Data collection To determine the cost of invasions on the German economy, we used data from the InvaCost database  (2,419 entries; Diagne et al. 2020)  on the published economic costs of biological invasions globally, enabling comprehensive quantification of costs associated with invasive species at various spatio-temporal scales. The data in InvaCost were collected following a series of literature searches using the Web of Science platform (https://webofknowledge. com/), Google Scholar database (https://scholar. google. com/), the Google search engine (https://www. google. com/) and all of the retrieved costs were converted to a common, up-to-date currency (2017 USD; World Bank 2019; Suppl. material 1). The InvaCost database has been recently complemented with data from non-English literature (5,212 entries;  Angulo et al.
2021a ) and additional data from English sources (ca. 2,300 entries; Ballesteros-Mejia et al. 2020). Potential duplicates were also carefully checked and removed from the database. The resulting complete In-vaCost database (version 3. 0) is available and detailed elsewhere (https://figshare. com/s/ c88d2e0dbe7b3e8a4edc). Following our data processing (see below), we extracted 71 entries for Germany for the purpose of our analyses (Suppl. material 2). The estimated period for reported costs varied considerably, spanning periods of several months to several years. For the purpose of the analysis and in order to obtain comparable invasion costs, we considered all costs for a period of less than a year as annual costs and re-calculated costs covering several years on an annual basis. That is, costs spanning several years were divided equally amongst those years, so as to not inflate costs artificially.
Equally, costs covering a time period of under one year were not increased in value to span that entire year, to remain conservative. This was performed using the "expandYearlyCosts" function of the 'invacost' package version 0. 3-4  (Leroy et al. 2020 ) in R version 4. 0. 2 (R Core Team 2020). In using this function, we estimated average annual costs represented in the InvaCost database. Deriving the total cumulative cost of invasions over time requires consideration of the probable duration time of each cost occurrence. The duration consisted of the number of years between the probable starting and ending years of the costs reported by each publication included in the InvaCost database. When information was missing for the starting year, we conservatively considered the publication year of the original reference.
Economic cost descriptors Based on the 71 entries found for invasive species in Germany, the InvaCost database contained 194 annualised cost estimates distributed across twenty taxonomic orders and twenty-eight species, amounting to a total of US$ 9. 77 billion or € 8. 14 billion (2017 value). Of all the reported costs, 36. 60% of the entries (n = 71) and 91. 50% of the total cost (US$ 8. 94 billion) were potential (Fig. 1 ). These were mostly driven  by extrapolations considering Amphibia (Lithobates catesbeianus; US$ 6. 04 billion; n = 1), Magnoliopsida (mostly constituted by Prunus serotina; US$ 1. 32 billion; n = 2), Mammalia (multiple species; US$ 0. 93 billion; n = 4) and Insecta (multiple species; US$ 0. 25 billion; n = 5). The majority of the costs were deemed to be highly reliable (Fig.
However, publications in German mostly referred to the costs reported by  Reinhardt et al. (2003) , while adding only a few additional cost estimations (see, for instance,  Pehl et al. 2003; AELF 2008; Arndt 2009 ). In contrast, similar studies for economically-comparable countries yielded many more (unexpanded) cost records. For example, InvaCost data for Spain (2384 entries,  Angulo et al. 2021b ), France (595 entries, Renault et al. 2021 ) and the UK (353 entries,  Cuthbert et al. 2021a ) highlight the data deficiency in Germany (71 entries). Several supranational lists of potentially invasive species exist for Germany; specifically, the Global Invasive Species Database (GISD; De Poorter and Browne 2005) currently lists 181 invasive species in Germany and the Global Register of Introduced and Invasive Species (GRIIS;  Pagad et al.
2018 ) lists 2,249 introduced and invasive species, of which 48 are known to have negative impacts. These numbers contrast markedly with the 28 species in our dataset, which highlights a considerable mismatch between species present and studies or management efforts reporting economic costs. For example, non-native fish species listed in the German Blacklist  (Essl et al. 2011)  were missing entirely, indicating a profound lack of cost information. Alien fish species, in particular, are known to be very costly in other regions, such as North America  (Haubrock et al. 2021b ). Other regional studies of the InvaCost database have similarly found that the number of species with recorded costs represent a very small percentage of known alien species. For example, costs evaluations were missing for over 90% of alien species in the UK  (Cuthbert et al.
By comparison, similar national studies found a high predominance of agricultural costs in Argentina  (Duboscq-Carra et al. 2021 ), Brazil (Adelino et al. 2021) , the UK  (Cuthbert et al. 2021a) , Australia  (Bradshaw et al. 2021 ) and the USA  (Crystal-Ornelas et al. 2021) , showing that the low costs recorded for Germany might be due to further data deficiency. Another interesting example of data deficiency is Ambrosia artemisiifolia (common ragweed), an allergenic plant known for its impact on human health  (Essl et al. 2015) , whose monetary impact on the EU was recently extrapolated at EUR€ 7. 4 billion annually  (Schaffner et al. 2020). The InvaCost database lists four "observed" cost entries totalling EUR€ 117. 14 million for A. artemisiifolia in Germany for the period until 2020. The cost estimated in  Schaffner et al.