diff --git a/images/news/euler-inversion-preprint.jpg b/images/news/euler-inversion-preprint.jpg new file mode 100644 index 0000000..b5e2daf Binary files /dev/null and b/images/news/euler-inversion-preprint.jpg differ diff --git a/news/euler-inversion-preprint.md b/news/euler-inversion-preprint.md new file mode 100644 index 0000000..5402c25 --- /dev/null +++ b/news/euler-inversion-preprint.md @@ -0,0 +1,87 @@ +--- +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! + +
+ +**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. + +
+ +Here's a sneak peek at our main result from applying Euler inversion to an +aeromagnetic dataset from Rio de Janeiro, Brazil: + +
+ 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. +
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.
+
+ +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.