Computers & Geosciences最新文献

{"title":"Distance Transform Loss: Boundary-aware segmentation of seismic data","authors":"Rafael Henrique Vareto ,&nbsp;Ricardo Szczerbacki ,&nbsp;Luiz A. Lima ,&nbsp;Pedro O.S. Vaz-de-Melo ,&nbsp;William Robson Schwartz","doi":"10.1016/j.cageo.2025.106061","DOIUrl":"10.1016/j.cageo.2025.106061","url":null,"abstract":"<div><div>The segmentation of seismic data is a challenging exercise given the complexity and high variability of subsurface sources. This arduous task is effective in the identification of geological features, including facies classification, fault detection, and horizon interpretation. As a result, this work introduces a new cost function entitled Distance Transform Loss (DTL) that punishes deep networks when class boundaries are misclassified in exchange for more accurate contour delineations, an important aspect in the geological field. DTL consists of four key steps: contour detection, distance transform mapping, pixel-wise multiplication, and the summation of all grid elements. We conduct a comprehensive evaluation of deep convolutional architectures using publicly available seismic datasets, demonstrating that the proposed approach consistently enhances semantic segmentation performance. The results highlight DTL as a robust and architecture-agnostic loss function, capable of addressing class imbalance and boundary delineation challenges that commonly arise in seismic interpretation tasks.</div></div>","PeriodicalId":55221,"journal":{"name":"Computers & Geosciences","volume":"207 ","pages":"Article 106061"},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A mixture of experts model for shallow crustal earthquake ground motion prediction in Japan","authors":"Zifa Wang ,&nbsp;Jinfeng Dai ,&nbsp;Dengke Zhao ,&nbsp;Xiangying Wang ,&nbsp;Jianming Wang ,&nbsp;Zhaoyan Li ,&nbsp;Yongcheng Feng ,&nbsp;Zhaodong Wang","doi":"10.1016/j.cageo.2025.106095","DOIUrl":"10.1016/j.cageo.2025.106095","url":null,"abstract":"<div><div>Ground motion prediction is central to earthquake engineering and disaster assessment, but traditional ground motion prediction models (GMPMs) struggle to capture the complex nature of seismic wave propagation. GMPMs based on a single machine learning algorithm also exhibit unsatisfactory performance when handling high-dimensional nonlinear relationships and large datasets. This study proposes a novel ground motion prediction model, MoE-XGB, which combines the Mixture of Experts (MoE) architecture with the XGBoost algorithm. Through a gating network, it dynamically assigns weights to adaptively handle the heterogeneity of earthquake data. The model innovatively integrates latitude and longitude features of stations and seismic sources, primarily acting as proxies for relative positions between stations and epicenters. The model was trained and validated using a strong-motion database of shallow crustal earthquakes in Japan and tested for cross-regional generalization with a New Zealand earthquake dataset. Results show that the MoE-XGB model, trained on a 1997<strong>–</strong>2019 strong-motion dataset, improves the mean squared error (MSE) by 39.2 %, reduces the standard deviation by 22.0 %, and increases the correlation coefficient by 4.8 % compared to the XGBoost-SC model, which is a regression model based on XGBoost and specifically designed for predicting seismic motions in the shallow crust region (SC). The inclusion of latitude and longitude features, primarily acting as proxies for relative positions between stations and epicenters, significantly enhances prediction accuracy. Cross-regional testing in New Zealand confirms the model's robust generalization to earthquake events in other regions. By efficiently integrating spatial features and a dynamic expert mechanism, the MoE-XGB model provides a high-precision, highly generalizable solution for ground motion prediction.</div></div>","PeriodicalId":55221,"journal":{"name":"Computers & Geosciences","volume":"208 ","pages":"Article 106095"},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A comparative study of data- and image- domain LSRTM under velocity–impedance parametrization","authors":"Pengliang Yang,&nbsp;Zhengyu Ji","doi":"10.1016/j.cageo.2025.106091","DOIUrl":"10.1016/j.cageo.2025.106091","url":null,"abstract":"<div><div>Least-squares reverse time migration (LSRTM) is one of the classic seismic imaging methods to reconstruct model perturbations within a known reference medium. It can be computed in either data or image domain using different methods by solving a linear inverse problem, whereas a careful comparison analysis of them is lacking in the literature. In this article, we present a comparative study for multiparameter LSRTM in data- and image- domain in the framework of SMIwiz open software. Different from conventional LSRTM for recovering only velocity perturbation with variable density, we focus on simultaneous reconstruction of velocity and impedance perturbations after logarithmic scaling, using the first-order velocity–pressure formulation of acoustic wave equation. The first 3D data-domain LSRTM example has been performed to validate our implementation, involving expensive repetition of Born modeling and migration over a number of iterations. As a more cost-effective alternative, the image-domain LSRTM is implemented using point spread function (PSF) and nonstationary deblurring filter. Dramatic distinctions between data and image domain methods are discovered with 2D Marmousi test: (1) The data-domain multiparameter inversion provides much better reconstruction of reflectivity images than image-domain approaches, thanks to the complete use of Hessian in Krylov space; (2) The poor multiparameter image-domain inversion highlights the limitation of incomplete Hessian sampling and strong parameter crosstalks, making it difficult to work in practice; (3) In contrast, monoparameter image-domain inversion for seismic impedance is found to work well. These observations have been further validated on Viking Graben Line 12 dataset.</div></div>","PeriodicalId":55221,"journal":{"name":"Computers & Geosciences","volume":"208 ","pages":"Article 106091"},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An interpretable causal variational autoencoder for geochemical anomalies recognition by regarding ore-controlling factors","authors":"Fan Ni,&nbsp;Yihui Xiong","doi":"10.1016/j.cageo.2025.106090","DOIUrl":"10.1016/j.cageo.2025.106090","url":null,"abstract":"<div><div>Conventional approaches for identifying geochemical anomalies often overlook the causal relationships between geological ore-controlling factors (e.g., fault, granite, and strata) and mineralization. This ignoration can lead to a lack of interpretability and robustness of the deep learning based geochemical anomaly identification methods. This study presents an interpretable causal variational autoencoder, which integrates structural causal models (SCM) with variational autoencoders (VAE) to address this issue. The interpretable causal VAE explicitly defines the causal relationships between geological factors that control mineralization and geochemical elements by utilizing a directed acyclic graph (DAG) and assessing causal effects through counterfactual reasoning. The model employs a semi-supervised training methodology, combining a limited number of labeled samples that reflect established geological control relationships with a large dataset of unlabeled data. Throughout the training process, it continuously updates both the causal graph structure and model parameters through data-driven causal discovery. Experimental results from geochemical datasets in the Nanling region in South China indicate that interpretable causal VAE significantly improves the accuracy of geochemical anomaly identification compared to traditional methods; for example, it necessitates the identification of only 14 % of high anomaly areas to capture all known deposits. Additionally, interpretable causal VAE enhances the geological interpretability of the model's results by clarifying the causal mechanisms through which geological ore-controlling factors affect element enrichment and depletion. This research highlights the considerable potential of merging deep learning and causality with geological knowledge derived from mineral system, thereby providing a novel tool for geochemical exploration.</div></div>","PeriodicalId":55221,"journal":{"name":"Computers & Geosciences","volume":"208 ","pages":"Article 106090"},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PRT-DeepONet: Geometry-aware neural operator for efficient prediction of pore-scale concentration fields","authors":"Yehoon Kim ,&nbsp;Ho-rim Kim ,&nbsp;Heewon Jung","doi":"10.1016/j.cageo.2025.106098","DOIUrl":"10.1016/j.cageo.2025.106098","url":null,"abstract":"<div><div>The computational challenge of predicting reactive transport in heterogeneous porous media originates from resolving complex pore-scale geometries and sharp concentration gradients near solid-fluid interfaces. This study introduces PRT-DeepONet (Pore-scale Reaction Transport Deep Operator Network), a geometry-aware neural operator that predicts local concentration fields in porous media with linear and nonlinear reactions. The architecture comprises two branch networks—a CNN branch for encoding the spatial patterns of binary porous media and an FNN branch for extracting parametric controls in partial differential equations—and a trunk network augmented with a geodesic distance function. This geodesic encoding addresses the inherent limitation of convolutional neural networks in maintaining geometric fidelity at solid-fluid interfaces by providing explicit transport pathway information absent in conventional architectures. PRT-DeepONet was trained on lattice Boltzmann simulations spanning various Péclet and Damköhler numbers, encompassing diffusion-to advection-dominated transport and slow to fast reaction kinetics. For steady-state predictions, PRT-DeepONet achieves an average RMSE below 0.04 while preserving complex grain geometries that baseline models fail to capture, with computational speedups of 3–5 orders of magnitude—reducing simulation times from minutes to milliseconds. The architecture successfully extends to transient problems, accurately predicting temporal concentration evolution for both reversible sorption and Monod kinetics. PRT-DeepONet demonstrates robust interpolation for unseen parametric conditions and time points, with performance improving with denser sampling of training data. These capabilities position PRT-DeepONet as an efficient tool for subsurface applications requiring rapid evaluation of reactive transport, including groundwater contamination assessment, CO₂ sequestration modeling, and nuclear waste disposal safety analysis.</div></div>","PeriodicalId":55221,"journal":{"name":"Computers & Geosciences","volume":"208 ","pages":"Article 106098"},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Raising the bar: Deep learning on comprehensive database sets new benchmark for automated fission-track detection","authors":"Samuel C. Boone ,&nbsp;Ling Chung ,&nbsp;Noel Faux ,&nbsp;Usha Nattala ,&nbsp;Thomas Church ,&nbsp;Chenghao Jiang ,&nbsp;Malcolm McMillan ,&nbsp;Sean Jones ,&nbsp;David Liu ,&nbsp;Han Jiang ,&nbsp;Kris Ehinger ,&nbsp;Tom Drummond ,&nbsp;Barry Kohn ,&nbsp;Andrew Gleadow","doi":"10.1016/j.cageo.2025.106096","DOIUrl":"10.1016/j.cageo.2025.106096","url":null,"abstract":"<div><div>Apatite fission-track (FT) thermochronology is widely used for constraining the thermal evolution of crustal rocks. However, manual FT identification is time-intensive and subjective. Although recent AI-based approaches have shown promise, performance often declines for complex, natural samples due to limited and overly idealised training data.</div><div>We introduce two open-access convolutional neural networks (CNNs) for automatic detection of surface-intersecting FTs in apatite and mica. The first, <em>HALtracks 2D</em>, uses paired reflected- and transmitted-light surface images, while <em>HALtracks 3D</em> incorporates an additional 3D stack of transmitted light images. <em>HALtracks 2D</em> exhibits mean accuracies (94.2–91.6 %) that are as good or better than both <em>HALtracks 3D</em> and all previous FT algorithms across a broad range of apatite fission track densities (up to 8.54 × 10⁶ tracks/cm²) on expert-curated reference data. This improvement is due to a comprehensive training dataset comprising a wider range of track densities and etch-pit morphologies.</div><div>Unexpectedly, <em>HALtracks3D</em> performed worse (91.5–80.1 %), likely because reflected-light information—critical for recognising track openings—became underrepresented among multiple transmitted-light inputs during CNN training. At very high track densities (&gt;8.54 × 10⁶ tracks/cm²) pushing the analytical boundaries of optical fission-track counting, <em>Coincidence Mapping</em> (Gleadow et al., 2009) remains more accurate than <em>HALtracks 2D</em>. Thermochronologists might therefore consider utilising a combination of automated fission-track algorithms depending on FT density.</div><div>Future work could expand the open-access training dataset to include a broader range of apatite FT specimens, and increased metadata for targeted CNN training on spurious features such as surface imperfections and dislocations, which are misidentified as fission tracks by existing algorithms. The open-access testing dataset presented here provides a benchmark for evaluating future FT algorithms.</div><div>Nevertheless, HALtracks 2D's enhanced accuracy brings apatite FT analysis significantly closer to full automation, with the potential to mitigate observer bias, reduce inter-laboratory variability, and broaden the accessibility of the technique to the wider geoscience community.</div></div>","PeriodicalId":55221,"journal":{"name":"Computers & Geosciences","volume":"208 ","pages":"Article 106096"},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Diffusion models for multivariate subsurface generation and efficient probabilistic inversion","authors":"Roberto Miele,&nbsp;Niklas Linde","doi":"10.1016/j.cageo.2025.106076","DOIUrl":"10.1016/j.cageo.2025.106076","url":null,"abstract":"<div><div>Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate that diffusion models enhance multivariate modeling capabilities compared to variational autoencoders and generative adversarial networks. In diffusion modeling, the generative process involves a comparatively large number of generative steps with update rules that can be modified to account for conditioning data. We propose different corrections to the popular Diffusion Posterior Sampling approach by Chung et al. (2023). In particular, we introduce a likelihood approximation accounting for the noise-contamination that is inherent in diffusion modeling. We assess performance in a multivariate geological scenario involving facies and correlated acoustic impedances. Conditional modeling is demonstrated using both local hard data (well logs) and nonlinear geophysics (fullstack seismic data). Our tests show significantly improved statistical robustness, enhanced sampling of the posterior probability density function and reduced computational costs, compared to the original approach. The method can be used with both hard and indirect conditioning data, individually or simultaneously. As the inversion is included within the diffusion process, it is faster than other methods requiring an outer-loop around the generative model, such as Markov chain Monte Carlo.</div></div>","PeriodicalId":55221,"journal":{"name":"Computers & Geosciences","volume":"207 ","pages":"Article 106076"},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SeismoDual: A dual-domain deep learning framework for robust seismic phase picking","authors":"Kuan-Wei Tang,&nbsp;Kuan-Yu Chen","doi":"10.1016/j.cageo.2025.106080","DOIUrl":"10.1016/j.cageo.2025.106080","url":null,"abstract":"<div><div>We present SeismoDual, a dual-domain deep learning framework for robust seismic phase picking that integrates both time-domain waveforms and time–frequency spectrograms. Unlike conventional pickers or recent deep learning-based models that usually operate solely in the time domain, SeismoDual captures complementary temporal and spectral features, enhancing resilience to strong background noise and low-SNR conditions. The framework adopts a Conformer-based encoder for both local and long-range time-domain modeling, a meticulous design encoder for distilling and encapsulating time–frequency information into feature representations, and a domain-aware decoder for effective fusion of heterogeneous seismic features. Extensive experiments on three benchmark datasets – STEAD, INSTANCE, and CWA – demonstrate SeismoDual’s superior accuracy and generalization capability across diverse scenarios. Compared to advanced methods, including PhaseNet, EQTransformer, and RED-PAN, SeismoDual achieves consistently higher F1 scores, particularly under challenging noise and sensor variability, highlighting its potential for operational deployment in real-time seismic monitoring. Furthermore, we integrate SeismoDual into a real-time earthquake early warning system and demonstrate its capability to reduce false picks significantly while maintaining low latency.</div></div>","PeriodicalId":55221,"journal":{"name":"Computers & Geosciences","volume":"207 ","pages":"Article 106080"},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Three-dimensional inversion method based on multi-source fused physical information networks for leachate distribution in landfills","authors":"Xiaochen Sun ,&nbsp;Ya Xu ,&nbsp;Changxin Nai ,&nbsp;Jingcai Liu","doi":"10.1016/j.cageo.2025.106077","DOIUrl":"10.1016/j.cageo.2025.106077","url":null,"abstract":"<div><div>Groundwater pollution caused by high-concentration harmful leachate leakage from landfills has become a global environmental problem. The combined observation of multi-source geophysical data can offer a more comprehensive and multi-faceted view of underground conditions. With improved detection capability, the quantity and diversity of multi-source data pose significant challenges to landfill leachate imaging. With rapid development of deep learning, a novel approach can be realized for the fusion inversion of multi-source geophysical data. However, predictions from purely data-driven deep learning models can be physically inconsistent or unreliable, leading to poor generalization performance of network models. We propose a fusion neural network, PI-FusNet, based on physical information, to characterize leachate distribution in landfills by fusing resistivity and self-potential data. PI-FusNet designs a loss function that incorporates electric field partial differential loss in addition to traditional mean square error loss. This ensures that the network follows the distribution pattern of data samples while conforming to the physical law described by the partial differential equation. Consequently, resistivity and self-potential data obtained from different observation methods converge into the same electric field space. In numerical simulations, PI-FusNet performed better on evaluation metrics than the pure data-driven network and the smooth model, with the lowest RMSE (0.1054) and MAE (0.3775) and the highest SSIM (0.9276) and UIQI (82.8266). Therefore, it is evident that PI-FusNet can accurately characterize the distribution of pollutants, whether in single or multiple contaminated areas. Field verification demonstrates that PI-FusNet can more accurately reconstruct the diffusion and distribution process of leachate in soil.</div></div>","PeriodicalId":55221,"journal":{"name":"Computers & Geosciences","volume":"207 ","pages":"Article 106077"},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An effective deep domain adaptation approach for least squares migration","authors":"Wenjun Ni ,&nbsp;Shaoyong Liu ,&nbsp;Zhikang Zhou ,&nbsp;Hanming Gu ,&nbsp;Bin Zhang","doi":"10.1016/j.cageo.2025.106081","DOIUrl":"10.1016/j.cageo.2025.106081","url":null,"abstract":"<div><div>Seismic migration is an essential process in geophysical exploration for precisely imaging subsurface structures. Traditional image-domain least-squares migration (ID-LSM) is an effective tool for enhancing resolution; but it is often limited by high computational costs and its reliance on linear Point Spread Function (PSF) deconvolution, which struggles to capture complex nonlinear imaging effects. To address these limitations, deep learning (DL) provides a powerful framework capable of learning the complex, nonlinear mapping between conventional migration image to high-resolution reflectivity models. However, a critical defect of standard DL methods is their poor generalization: networks trained exclusively on synthetic data (source domain) often fail to generalize to field data (target domain) owing to inherent feature discrepancies. To bridge this domain gap, we propose a novel domain-adaptive mage-domain least-squares migration (DA-ID-LSM) approach. The proposed method employs a U-Net-based convolutional neural network combined with a Maximum Mean Discrepancy (MMD) loss function to minimize the distribution gap between the source and target domains, thereby enabling the model to learn domain-invariant features and generalize effectively. Numerical experiments on both synthetic and field datasets demonstrate that the proposed DA-ID-LSM approach outperforms conventional methods. It achieves improved resolution and enhanced lateral continuity. The incorporation of the MMD constraint notably improves imaging resolution and robustness without compromising training stability.</div></div>","PeriodicalId":55221,"journal":{"name":"Computers & Geosciences","volume":"207 ","pages":"Article 106081"},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145617889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}