Add a news item about the Euler inversion preprint

news/euler-inversion-preprint.md

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+---
+title: 'A better method for locating sources of gravity and magnetic anomalies'
+date: 2024-12-20
+author: Leonardo Uieda
+---
+
+We have a new [preprint out on EarthArXiv](https://doi.org/10.31223/X5T41M)
+which introduces **Euler inversion**, a new method for finding the location and
+approximate geometry of sources of gravity and magnetic anomalies.
+
+We're very excited about Euler inversion because it's a significant departure
+from existing methods based on Euler's homogeneity equation (mainly Euler
+deconvolution and its many many variants). It's a brand new mathematical
+formulation which solves many of the existing issues Euler-based methods,
+mainly: high sensitivity to noise and interfering sources and the dependence on
+knowledge of the structural index of the sources.
+This opens a new research field for us as we continue to improve it further and
+to explore the capabilities of Euler inversion in difference scenarios!
+
+<div class="callout">
+
+**Open science:**
+As always, all of the source code and data needed to reproduce our results are
+in the GitHub repository
+[compgeolab/euler-inversion](https://github.com/compgeolab/euler-inversion)
+and archived on figshare at
+doi:[10.6084/m9.figshare.26384140](https://doi.org/10.6084/m9.figshare.26384140).
+We'll soon have a version of Euler inversion implemented in the Python library
+[Harmonica](https://www.fatiando.org/harmonica/latest/) as well.
+
+</div>
+
+Here's a sneak peek at our main result from applying Euler inversion to an
+aeromagnetic dataset from Rio de Janeiro, Brazil:
+
+<figure>
+  <img src="../images/news/euler-inversion-preprint.jpg" alt="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.">
+  <figcaption>Results of applying Euler inversion with a window size of 12 000 m and a window step of 2400 m to the aeromagnetic data from Rio de Janeiro, Brazil. Estimated source locations and structural indices obtained from Euler inversion are shown as triangles (𝜂 = 1), squares (𝜂 = 2), and circles (𝜂 = 3). The colour of each symbol represents the estimated depth below the surface of the Earth (topography). Also shown are the total-field anomaly flight-line data, the contours of the post-collisional magmatism and alkaline intrusions (solid black lines) and dykes (dashed lines). The purple squares highlight the A, B, C, and D anomalies that are discussed in the text.</figcaption>
+</figure>
+
+The main idea for this paper came about during an potential-field methods class
+which I took in 2012 with my then PhD supervisor [Valéria C. F.
+Barbosa](https://www.pinga-lab.org/people/barbosa.html).
+While learning about the Euler deconvolution method, which is a speciality of
+Valéria, I connected it with the geodetic network adjustment theory that I had
+been taught by [Spiros Pagiatakis](https://www.yorku.ca/spiros/spiros.html)
+during an exchange program at York University, Canada, in 2008. An initial
+prototype was developed in 2012 but there were still some rough edges and the
+project was shelved to make way for other more urgent projects at the time.
+I returned to this every few years, making slow progress, and involving
+[Vanderlei C. Oliveira Jr.](https://www.pinga-lab.org/people/oliveira-jr.html)
+in the planning and discussion of the theory.
+In 2024, lab members [Gelson](../team/#Souza-junior) and
+[India](../team/#indiauppal) joined me and Vanderlei for a sprint to finish the
+method and produce this paper.
+
+Here's the full reference for the preprint:
+
+> Uieda, L., Souza-Junior, G. F., Uppal, I., Oliveira Jr., V. C. (2024). Euler
+> inversion: Locating sources of potential-field data through inversion of
+> Euler’s homogeneity equation. EarthArXiv.
+> doi:[10.31223/X5T41M](https://doi.org/10.31223/X5T41M).
+
+We have submitted this to the Geophysical Journal International and are waiting
+for their reviews. Hopefully everything will work out and we'll get a nice
+surprise in the new year when a decision comes back from the editor!
+
+**If you have any feedback or would like to use the method**, please let us
+know!
+
+## Abstract
+
+Earth scientists can estimate the depth of certain rocks beneath Earth's
+surface by measuring the small disturbances that they cause in the Earth's
+gravity and magnetic fields. A popular method for this is **Euler
+deconvolution**, which is widely available in geoscience software and can be
+run quickly on a standard computer. Unfortunately, Euler deconvolution has some
+shortcomings: 1) the approximate shape of the rocks must be known, for example,
+a sphere or a wide flat slab, represented by the **structural index** 2) the
+depth of the rocks is not well estimated when there is noise in our data, which
+is a common occurrence. We propose a new method, **Euler inversion**, which
+fixes some of the shortcomings of Euler deconvolution by using more adequate
+(and complex) mathematics. Our method is less sensitive to noise in the data
+and is also able to determine the approximate shape of the source (the
+structural index). Euler inversion is also fast to execute on a standard
+computer, making it a practical alternative to Euler deconvolution on an Earth
+scientists toolbox.