Pub Date : 2023-11-13DOI: 10.1007/s11004-023-10117-2
Jianhuan Gong, Gang Chen, Jiawen Bian, Zhuofan Wang
{"title":"Reconstruction of GPS Coordinate Time Series Based on Low-Rank Hankel Matrix Recovery","authors":"Jianhuan Gong, Gang Chen, Jiawen Bian, Zhuofan Wang","doi":"10.1007/s11004-023-10117-2","DOIUrl":"https://doi.org/10.1007/s11004-023-10117-2","url":null,"abstract":"","PeriodicalId":51117,"journal":{"name":"Mathematical Geosciences","volume":"63 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136282012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-06DOI: 10.1007/s11004-023-10102-9
Amílcar Soares, Rúben Nunes, Paulo Salvadoretti, João Felipe Costa, Teresa Martins, Mario Santos, Leonardo Azevedo
Abstract Pore pressure prediction is fundamental when drilling deep and geologically complex reservoirs. Even in relatively well-characterized hydrocarbon reservoir fields, with a considerable number of drilled wells, when located in challenging geological environments, poor prediction of abnormal pore pressure might result in catastrophic events that can cause harm to human lives and infrastructures. To better quantify drilling risks, the uncertainty associated with the pore pressure prediction should be integrated within the geo-modelling workflow. Leveraging a challenging real case from the Brazilian pre-salt, the work presented herein proposes a seismic-driven gradient pore pressure modelling workflow, which combines machine learning and geostatistical co-simulation to predict high-resolution gradient pore pressure volumes. First, existing angle-dependent seismic reflection data are inverted for P- and S-wave velocity and density. Then, K-nearest neighbor is used to create a regression model between pore pressure gradient and P- and S-wave velocity, density and depth based on the well log information. The trained model is applied to predict a three-dimensional gradient pore pressure model from the models obtained from geostatistical seismic inversion. This gradient pore pressure model is a smooth representation of the highly variable subsurface and is used as secondary variable in stochastic sequential co-simulation with joint probability distributions to generate multiple high-resolution realizations of gradient pore pressure. The ensemble of co-simulated models can be used to assess the spatial uncertainty about the gradient pore pressure predictions. The results of the application example show the ability of the method to reproduce the spatial patterns observed in the seismic data and to reproduce existing gradient pore pressure well logs at two blind well locations, which were not used to condition the gradient pore pressure predictions.
{"title":"Pore Pressure Uncertainty Characterization Coupling Machine Learning and Geostatistical Modelling","authors":"Amílcar Soares, Rúben Nunes, Paulo Salvadoretti, João Felipe Costa, Teresa Martins, Mario Santos, Leonardo Azevedo","doi":"10.1007/s11004-023-10102-9","DOIUrl":"https://doi.org/10.1007/s11004-023-10102-9","url":null,"abstract":"Abstract Pore pressure prediction is fundamental when drilling deep and geologically complex reservoirs. Even in relatively well-characterized hydrocarbon reservoir fields, with a considerable number of drilled wells, when located in challenging geological environments, poor prediction of abnormal pore pressure might result in catastrophic events that can cause harm to human lives and infrastructures. To better quantify drilling risks, the uncertainty associated with the pore pressure prediction should be integrated within the geo-modelling workflow. Leveraging a challenging real case from the Brazilian pre-salt, the work presented herein proposes a seismic-driven gradient pore pressure modelling workflow, which combines machine learning and geostatistical co-simulation to predict high-resolution gradient pore pressure volumes. First, existing angle-dependent seismic reflection data are inverted for P- and S-wave velocity and density. Then, K-nearest neighbor is used to create a regression model between pore pressure gradient and P- and S-wave velocity, density and depth based on the well log information. The trained model is applied to predict a three-dimensional gradient pore pressure model from the models obtained from geostatistical seismic inversion. This gradient pore pressure model is a smooth representation of the highly variable subsurface and is used as secondary variable in stochastic sequential co-simulation with joint probability distributions to generate multiple high-resolution realizations of gradient pore pressure. The ensemble of co-simulated models can be used to assess the spatial uncertainty about the gradient pore pressure predictions. The results of the application example show the ability of the method to reproduce the spatial patterns observed in the seismic data and to reproduce existing gradient pore pressure well logs at two blind well locations, which were not used to condition the gradient pore pressure predictions.","PeriodicalId":51117,"journal":{"name":"Mathematical Geosciences","volume":"70 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135679751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-06DOI: 10.1007/s11004-023-10110-9
Mehmet Onur Dogan
{"title":"Extended Multiple Interacting Continua (E-MINC) Model Improvement with a K-Means Clustering Algorithm Based on an Equi-dimensional Discrete Fracture Matrix (ED-DFM) Model","authors":"Mehmet Onur Dogan","doi":"10.1007/s11004-023-10110-9","DOIUrl":"https://doi.org/10.1007/s11004-023-10110-9","url":null,"abstract":"","PeriodicalId":51117,"journal":{"name":"Mathematical Geosciences","volume":"217 2‐3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135679940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.1007/s11004-023-10109-2
Michele Nguyen, Almut E. D. Veraart, Benoit Taisne, Chiou Ting Tan, David Lallemant
Abstract Extreme events such as natural and economic disasters leave lasting impacts on society and motivate the analysis of extremes from data. While classical statistical tools based on Gaussian distributions focus on average behaviour and can lead to persistent biases when estimating extremes, extreme value theory (EVT) provides the mathematical foundations to accurately characterise extremes. This motivates the development of extreme value models for extreme event forecasting. In this paper, a dynamic extreme value model is proposed for forecasting volcanic eruptions. This is inspired by one recently introduced for financial risk forecasting with high-frequency data. Using a case study of the Piton de la Fournaise volcano, it is shown that the modelling framework is widely applicable, flexible and holds strong promise for natural hazard forecasting. The value of using EVT-informed thresholds to identify and model extreme events is shown through forecast performance, and considerations to account for the range of observed events are discussed.
自然灾害和经济灾害等极端事件对社会产生了持久的影响，促使人们从数据中分析极端事件。虽然基于高斯分布的经典统计工具关注的是平均行为，在估计极值时可能导致持续的偏差，但极值理论(EVT)提供了准确表征极值的数学基础。这促使了极端事件预测极值模型的发展。本文提出了一种预测火山喷发的动态极值模型。这是受到最近引入的一种利用高频数据进行金融风险预测的启发。通过对Piton de la Fournaise火山的实例研究表明，该模型框架具有广泛的适用性和灵活性，在自然灾害预测中具有很强的应用前景。通过预测性能显示了使用evt通知阈值来识别和模拟极端事件的价值，并讨论了考虑观察到的事件范围的考虑因素。
{"title":"A Dynamic Extreme Value Model with Application to Volcanic Eruption Forecasting","authors":"Michele Nguyen, Almut E. D. Veraart, Benoit Taisne, Chiou Ting Tan, David Lallemant","doi":"10.1007/s11004-023-10109-2","DOIUrl":"https://doi.org/10.1007/s11004-023-10109-2","url":null,"abstract":"Abstract Extreme events such as natural and economic disasters leave lasting impacts on society and motivate the analysis of extremes from data. While classical statistical tools based on Gaussian distributions focus on average behaviour and can lead to persistent biases when estimating extremes, extreme value theory (EVT) provides the mathematical foundations to accurately characterise extremes. This motivates the development of extreme value models for extreme event forecasting. In this paper, a dynamic extreme value model is proposed for forecasting volcanic eruptions. This is inspired by one recently introduced for financial risk forecasting with high-frequency data. Using a case study of the Piton de la Fournaise volcano, it is shown that the modelling framework is widely applicable, flexible and holds strong promise for natural hazard forecasting. The value of using EVT-informed thresholds to identify and model extreme events is shown through forecast performance, and considerations to account for the range of observed events are discussed.","PeriodicalId":51117,"journal":{"name":"Mathematical Geosciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136022623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-14DOI: 10.1007/s11004-023-10105-6
Zhice Fang, Yi Wang, Cees van Westen, Luigi Lombardo
{"title":"Space–Time Landslide Susceptibility Modeling Based on Data-Driven Methods","authors":"Zhice Fang, Yi Wang, Cees van Westen, Luigi Lombardo","doi":"10.1007/s11004-023-10105-6","DOIUrl":"https://doi.org/10.1007/s11004-023-10105-6","url":null,"abstract":"","PeriodicalId":51117,"journal":{"name":"Mathematical Geosciences","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135803360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1007/s11004-023-10104-7
Peter A. Dowd, Eulogio Pardo-Igúzquiza
Abstract In this expository review paper, we show that co-kriging, a widely used geostatistical multivariate optimal linear estimator, has a diverse range of extensions that we have collected and illustrated to show the potential of this spatial interpolator. In the context of spatial stochastic processes, this paper covers scenarios including increasing the spatial resolution of a spatial variable (downscaling), solving inverse problems, estimating directional derivatives, and spatial interpolation taking boundary conditions into account. All these spatial interpolators are optimal linear estimators in the sense of being unbiased and minimising the variance of the estimation error.
{"title":"The Many Forms of Co-kriging: A Diversity of Multivariate Spatial Estimators","authors":"Peter A. Dowd, Eulogio Pardo-Igúzquiza","doi":"10.1007/s11004-023-10104-7","DOIUrl":"https://doi.org/10.1007/s11004-023-10104-7","url":null,"abstract":"Abstract In this expository review paper, we show that co-kriging, a widely used geostatistical multivariate optimal linear estimator, has a diverse range of extensions that we have collected and illustrated to show the potential of this spatial interpolator. In the context of spatial stochastic processes, this paper covers scenarios including increasing the spatial resolution of a spatial variable (downscaling), solving inverse problems, estimating directional derivatives, and spatial interpolation taking boundary conditions into account. All these spatial interpolators are optimal linear estimators in the sense of being unbiased and minimising the variance of the estimation error.","PeriodicalId":51117,"journal":{"name":"Mathematical Geosciences","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136013532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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