{"id":28217136,"url":"https://github.com/compgeolab/euler-inversion","last_synced_at":"2025-10-13T13:38:51.944Z","repository":{"id":268949813,"uuid":"58158846","full_name":"compgeolab/euler-inversion","owner":"compgeolab","description":"Paper: A new method for location sources of gravity and magnetic data using Euler's homogeneity equation","archived":false,"fork":false,"pushed_at":"2025-04-01T16:56:54.000Z","size":282193,"stargazers_count":8,"open_issues_count":0,"forks_count":4,"subscribers_count":2,"default_branch":"main","last_synced_at":"2025-06-12T12:47:37.060Z","etag":null,"topics":["earth-science","geophysics","geoscience","gravity","inverse-problems","magnetic","potential-fields"],"latest_commit_sha":null,"homepage":"https://doi.org/10.1093/gji/ggaf114","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"cc-by-4.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/compgeolab.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE-CC-BY.txt","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2016-05-05T20:33:07.000Z","updated_at":"2025-05-19T19:09:44.000Z","dependencies_parsed_at":"2025-03-24T17:42:18.522Z","dependency_job_id":null,"html_url":"https://github.com/compgeolab/euler-inversion","commit_stats":null,"previous_names":["compgeolab/euler-inversion"],"tags_count":4,"template":false,"template_full_name":null,"purl":"pkg:github/compgeolab/euler-inversion","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/compgeolab%2Feuler-inversion","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/compgeolab%2Feuler-inversion/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/compgeolab%2Feuler-inversion/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/compgeolab%2Feuler-inversion/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/compgeolab","download_url":"https://codeload.github.com/compgeolab/euler-inversion/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/compgeolab%2Feuler-inversion/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":279015351,"owners_count":26085684,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","status":"online","status_checked_at":"2025-10-13T02:00:06.723Z","response_time":61,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["earth-science","geophysics","geoscience","gravity","inverse-problems","magnetic","potential-fields"],"created_at":"2025-05-18T00:11:24.600Z","updated_at":"2025-10-13T13:38:51.935Z","avatar_url":"https://github.com/compgeolab.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Euler inversion: Locating sources of potential-field data through inversion of Euler’s homogeneity equation\n\nby\n[Leonardo Uieda](https://leouieda.com),\n[Gelson Ferreira Souza-Junior](https://github.com/souza-junior),\n[India Uppal](https://github.com/indiauppal),\n[Vanderlei Coelho Oliveira Jr.](https://www.pinga-lab.org/people/oliveira-jr.html)\n\nThis repository contains the data and source code used to produce the results\npresented in:\n\n\u003e Uieda, L., Souza-Junior, G. F., Uppal, I., Oliveira Jr., V. C. (2025). Euler\n\u003e inversion: Locating sources of potential-field data through inversion of\n\u003e Euler’s homogeneity equation. *Geophysical Journal International*.\n\u003e doi:[10.1093/gji/ggaf114](https://doi.org/10.1093/gji/ggaf114).\n\n|                                    | **Information** |\n|-----------------------------------:|:----------------|\n| Version of record                  | https://doi.org/10.1093/gji/ggaf114 |\n| Open-access preprint on EarthArXiv | https://doi.org/10.31223/X5T41M |\n| Archive of this repository         | https://doi.org/10.6084/m9.figshare.26384140 |\n| Software Heritage ID               | [`swh:1:snp:b0d1f8fdbf57f87e0ce56d5dda0f360c4a314d9d`](https://archive.softwareheritage.org/swh:1:snp:b0d1f8fdbf57f87e0ce56d5dda0f360c4a314d9d;origin=https://github.com/compgeolab/euler-inversion) |\n| Reproducing our results            | [`REPRODUCING.md`](REPRODUCING.md) |\n\n## About\n\nThe main idea for this paper came about during an potential-field methods class\nwhich Leo took in 2012 with his then PhD supervisor\n[Prof. Valéria C. F. Barbosa](https://www.pinga-lab.org/people/barbosa.html).\nWhile learning about the Euler deconvolution method, which is a speciality of\nValéria, Leo connected it with the geodetic network adjustment theory he had\nbeen taught by\n[Prof. Spiros Pagiatakis](https://www.yorku.ca/spiros/spiros.html) during an\nexchange program at York University, Canada, in 2008. An initial prototype was\ndeveloped in 2012 but there were still some rough edges and the project was\nshelved to make way for other more urgent projects at the time. Leo returned to\nthis every few years, making slow progress, and involving Vanderlei in the\nplanning and discussion of the theory. In 2024, co-authors Gelson, India, and\nVanderlei joined Leo for a sprint to finish the method and produce this paper.\n\n## Abstract\n\nEarth scientists can estimate the depth of certain rocks beneath Earth's\nsurface by measuring the small disturbances that they cause in the Earth's\ngravity and magnetic fields. A popular method for this is **Euler deconvolution**,\nwhich is widely available in geoscience software and can be run quickly on\na standard computer. Unfortunately, Euler deconvolution has some shortcomings: 1) \nthe approximate shape of the rocks must be known, for example, a sphere or\na wide flat slab, represented by the **structural index** 2) the depth of the\nrocks is not well estimated when there is noise in our data, which is a common\noccurrence. We propose a new method, **Euler inversion**, which fixes some of\nthe shortcomings of Euler deconvolution by using more adequate (and complex)\nmathematics. Our method is less sensitive to noise in the data and is also able\nto determine the approximate shape of the source (the structural index). Euler\ninversion is also fast to execute on a standard computer, making it a practical\nalternative to Euler deconvolution on an Earth scientists toolbox.\n\n\u003cfigure\u003e\n  \u003cimg src=\"https://github.com/compgeolab/euler-inversion/raw/main/graphical-abstract.jpg\" alt=\"Left panel: Euler inversion is a new method for finding depths from gravity and magnetic data. It's much more robust to noise and interfering sources than Euler deconvolution and can estimate the structural index. Right panel: Map with red-white-blue colored dots representing the magnetic anomaly. There are several dipolar looking anomalies and some linear anomalies in the NE-SW direction. Overlaid are small triangles, circles, and squares which follow the dipolar and linear anomalies.\"\u003e\n  \u003cfigcaption\u003e\n  \u003cstrong\u003eFigure:\u003c/strong\u003e Results of applying Euler inversion with a window\n  size of 12 000 m and a window step of 2400 m to the aeromagnetic data from\n  Rio de Janeiro, Brazil. Estimated source locations and structural indices\n  obtained from Euler inversion are shown as triangles (𝜂 = 1), squares (𝜂\n  = 2), and circles (𝜂 = 3). The colour of each symbol represents the estimated\n  depth below the surface of the Earth (topography). Also shown are the\n  total-field anomaly flight-line data, the contours of the post-collisional\n  magmatism and alkaline intrusions (solid black lines) and dykes (dashed\n  lines). The purple squares highlight the A, B, C, and D anomalies that are\n  discussed in the text.\n  \u003c/figcaption\u003e\n\u003c/figure\u003e\n\n## Citing\n\nPlease cite this work as:\n\n\u003e Uieda, L., Souza-Junior, G. F., Uppal, I., Oliveira Jr., V. C. (2025). Euler\n\u003e inversion: Locating sources of potential-field data through inversion of\n\u003e Euler’s homogeneity equation. *Geophysical Journal International*.\n\u003e doi:[10.1093/gji/ggaf114](https://doi.org/10.1093/gji/ggaf114).\n\nYou can also reference the supplementary files (data and software) as:\n\n\u003e Uieda, L., Souza-Junior, G. F., Uppal, I., Oliveira Jr., V. C. (2024).\n\u003e Supplementary material for \"Euler inversion: Locating sources of\n\u003e potential-field data through inversion of Euler's homogeneity equation\".\n\u003e *figshare*. doi:[10.6084/m9.figshare.26384140](https://doi.org/10.6084/m9.figshare.26384140).\n\n## License\n\nAll Python source code (including `.py` and `.ipynb` files) is made available\nunder the MIT license. You can freely use and modify the code, without\nwarranty, so long as you provide attribution to the authors. See\n`LICENSE-MIT.txt` for the full license text.\n\nThe manuscript text (including all LaTeX files), figures, and data/models\nproduced as part of this research are available under the\n[Creative Commons Attribution 4.0 License (CC-BY)][cc-by]. See\n`LICENSE-CC-BY.txt` for the full license text.\n\n[cc-by]: https://creativecommons.org/licenses/by/4.0/\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fcompgeolab%2Feuler-inversion","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fcompgeolab%2Feuler-inversion","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fcompgeolab%2Feuler-inversion/lists"}