{"title":"Gravity Degree-Depth Relations for High-Order Disturbing Potential Gradients","authors":"Xiao-Le Deng,Nico Sneeuw,Dimitrios Tsoulis","doi":"10.1007/s10712-026-09962-7","DOIUrl":"https://doi.org/10.1007/s10712-026-09962-7","url":null,"abstract":"Abstract The degree-depth relation links the spherical harmonic degree to an operational depth scale for gravity signals. Previous studies have primarily examined the degree-depth relation for the gravity anomaly, the vertical component of the gravitational vector, and the gravity disturbance. However, degree-depth relations for other high-order radial disturbing potential gradients, such as the second- and third-order radial derivatives of the disturbing potential, remain unestablished. This study reviews existing degree-depth relations and their applications in modeling and spectral-scale interpretation of observed gravity signals. degree-depth relations are derived for the components of the second- and third-order radial derivatives of the disturbing potential. Furthermore, the general degree-depth relation for the s th-order ( $$s ge 1$$ s ≥ 1 ) radial disturbing potential gradients is established. Numerical results show that, for all degree-depth relations, operational depths decrease as spherical harmonic degrees increase, and vice versa. Results further indicate that distinct degree-depth relations should be applied to the corresponding orders of radial disturbing potential gradients. The derived degree-depth relations offer a self-consistent set of bounds for spectral-filtering choices when working with high-order radial gradients in geodesy, geophysics, and planetary sciences.","PeriodicalId":49458,"journal":{"name":"Surveys in Geophysics","volume":"14 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149209681","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":"Seismic Structure and Geodynamics of the Philippine Sea Plate and its Surrounding Subduction Zones","authors":"Dapeng Zhao,Jianke Fan,Genti Toyokuni,Motoya Suzuki,Ryo Tsunashima","doi":"10.1007/s10712-026-09966-3","DOIUrl":"https://doi.org/10.1007/s10712-026-09966-3","url":null,"abstract":"","PeriodicalId":49458,"journal":{"name":"Surveys in Geophysics","volume":"24 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149091104","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}
Manuel Arias,Shungudzemwoyo P. Garaba,Dany Ghafari,Samantha Lavender
{"title":"The UN SDG14.1.1b Plastic Debris Density Sub-Indicator From Earth Observation: Progress, Challenges and Perspectives in International Waters","authors":"Manuel Arias,Shungudzemwoyo P. Garaba,Dany Ghafari,Samantha Lavender","doi":"10.1007/s10712-026-09963-6","DOIUrl":"https://doi.org/10.1007/s10712-026-09963-6","url":null,"abstract":"","PeriodicalId":49458,"journal":{"name":"Surveys in Geophysics","volume":"25 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149091106","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":"Uncertainties of GRACE/GRACE-FO Satellite Gravimetry Data and Thereof Derived Products","authors":"Adrian Jäggi,Andreas Güntner,Ulrich Meyer,Alejandro Blazquez,Benedikt Soja,Frank Flechtner,Felix Landerer,Christoph Dahle,Christopher McCullough,Tamara Bandikova,Torsten Mayer-Gürr,Felix Öhlinger,Henryk Dobslaw,Eva Boergens,Junyang Gou,Roland Pail,Hugo Lecomte,David Wiese,Martin Lasser,Ehsan Sharifi","doi":"10.1007/s10712-026-09959-2","DOIUrl":"https://doi.org/10.1007/s10712-026-09959-2","url":null,"abstract":"Abstract Inter-satellite ranging by space gravimetry missions, such as from the Gravity Recovery And Climate Experiment (GRACE) mission and its successor mission GRACE Follow-On, has been established to observe mass variations in the Earth system from space globally. A complex processing chain is needed to invert the instrument data (Level-1) of space gravimetry missions into global gravity field products, either represented as a spherical harmonic series expansion (Level-2) or further processed gridded products dedicated to use for various scientific applications (Level-3), and combine them with products from other remote sensing satellite missions or assimilate them into geophysical process models (Level-4). The complexity arises from the need to use multiple background models and apply numerous corrections. Consequently, providing uncertainties for the various products is challenging. Not only is inter-satellite ranging data needed in this processing chain, but also other satellite observations, such as GPS, and geophysical background models, e.g., for de-aliasing of high-frequency signals or signal separation in the Level-3 data sets. These observations and model data sets are contributing with their specific uncertainties to the overall uncertainty budget of the final gravity fields. As long as the uncertainties of the models cannot be fully accounted for, a formal uncertainty propagation remains insufficient. Thus, an empirical error assessment remains the only reliable way of uncertainty assessment at the moment. Finally, a further source of error is signal leakage, which is related to the signal attenuation at satellite altitude and may be aggravated by spatial filtering of the Level-3 products. A comprehensive review of the current status of the uncertainty modeling of mass variation products through the whole processing chain is missing and thus is addressed in this article.","PeriodicalId":49458,"journal":{"name":"Surveys in Geophysics","volume":"23 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149050112","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":"On Energy and Density of Jovian Lightning","authors":"Kateřina Rosická,Ondřej Santolík,Ivana Kolmašová","doi":"10.1007/s10712-026-09964-5","DOIUrl":"https://doi.org/10.1007/s10712-026-09964-5","url":null,"abstract":"","PeriodicalId":49458,"journal":{"name":"Surveys in Geophysics","volume":"32 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149049654","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 Novel Algorithm and Software for Global Apparent Density Mapping using Spherical Harmonic Analysis and Synthesis","authors":"Wenjin Chen, Xiaoyu Tang, Robert Tenzer","doi":"10.1007/s10712-026-09961-8","DOIUrl":"https://doi.org/10.1007/s10712-026-09961-8","url":null,"abstract":"","PeriodicalId":49458,"journal":{"name":"Surveys in Geophysics","volume":"36 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148842934","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":"Stochastic Representation of Finite Distributions for Gravity Field Modelling and Interpretation","authors":"Dimitrios Tsoulis, Georgia Gavriilidou","doi":"10.1007/s10712-026-09958-3","DOIUrl":"https://doi.org/10.1007/s10712-026-09958-3","url":null,"abstract":"","PeriodicalId":49458,"journal":{"name":"Surveys in Geophysics","volume":"488 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148768921","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 Review on Recent High-Resolution Edge Filters for Interpreting Potential Field Data","authors":"Luan Thanh Pham, Saulo P. Oliveira, Erdinc Oksum","doi":"10.1007/s10712-026-09960-9","DOIUrl":"https://doi.org/10.1007/s10712-026-09960-9","url":null,"abstract":"","PeriodicalId":49458,"journal":{"name":"Surveys in Geophysics","volume":"21 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148728720","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}
A. Cazenave, R. Almar, P. Almeida, N. K. Ayoub, J. H. Bettencourt, F. Birol, W. Han, M. Herrmann, S. Jevrejeva, L. Leclercq, F. Niño, J. Oelsmann, F. Papa, S. Ponce de León, A. Tarpanelli, V. D. Vinh
{"title":"Present-Day Sea Level Variations in Coastal Areas from Daily to Multidecadal Time Scales: Observations and Causes","authors":"A. Cazenave, R. Almar, P. Almeida, N. K. Ayoub, J. H. Bettencourt, F. Birol, W. Han, M. Herrmann, S. Jevrejeva, L. Leclercq, F. Niño, J. Oelsmann, F. Papa, S. Ponce de León, A. Tarpanelli, V. D. Vinh","doi":"10.1007/s10712-026-09956-5","DOIUrl":"https://doi.org/10.1007/s10712-026-09956-5","url":null,"abstract":"","PeriodicalId":49458,"journal":{"name":"Surveys in Geophysics","volume":"13 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148728786","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}