3D magnetic inversion by planting anomalous densities

Code, text, notebooks, slides, etc for the AGU 2013 Meeting of the Americas.

All results in the presentation were generated by the IPython notebooks in the notebooks folder:

• Results for the abstract
• Inversion of the ME and A2 anomalies
• Synthetic test with 2 bodies
• Run an inversion step-by-step
• Extract seeds from a previous solution

The slides for this presentation are available on figshare in PDF format.

Abstract

We present a new 3D magnetic inversion algorithm based on the computationally efficient method of planting anomalous densities. The algorithm consists of an iterative growth of the anomalous bodies around prismatic elements called "seeds". These seeds are user-specified and have known magnetizations. Thus, the seeds provide a way for the interpreter to specify the desired skeleton of the anomalous bodies. The inversion algorithm is computationally efficient due to various optimizations made possible by the iterative nature of the growth process. The control provided by the use of seeds allows one to test different hypothesis about the geometry and magnetization of targeted anomalous bodies. To demonstrate this capability, we applied our inversion method to the Morro do Engenho (ME) and A2 magnetic anomalies, central Brazil (Figure 1a). ME is an outcropping alkaline intrusion formed by dunites, peridotites and pyroxenites with known magnetization. A2 is a magnetic anomaly to the Northeast of ME and is thought to be a similar intrusion that is not outcropping. Therefore, a plausible hypothesis is that A2 has the same magnetization as ME. We tested this hypothesis by performing an inversion using a single seed for each body. Both seeds had the same magnetization. Figure 1b shows that the inversion produced residuals up to 2000 nT over A2 (i.e., a poor fit) and less than 400 nT over ME (i.e., an acceptable fit). Figure 1c shows that ME is a compact outcropping body with bottom at approximately 5 km, which is in agreement with previous interpretations. However, the estimate produced by the inversion for A2 is outcropping and is not compact. In summary, the estimate for A2 provides a poor fit to the observations and is not in accordance with the geologic information. This leads to the conclusion that A2 does not have the same magnetization as ME. These results indicate the usefulness and capabilities of the inversion method here proposed.

Figures

Figure 1: a) total field magnetic anomaly map with the ME and A2 anomalies. b) map of the inversion residuals (observed minus predicted data). c) the two bodies estimated by the inversion.

References

Dutra, A. C., and Y. R. Marangoni (2009), Gravity and magnetic 3D inversion of Morro do Engenho complex, Central Brazil, Journal of South American Earth Sciences, 28(2), 193-203, doi:10.1016/j.jsames.2009.02.006.

Uieda, L., and V. C. F. Barbosa (2012a), Robust 3D gravity gradient inversion by planting anomalous densities, Geophysics, 77(4), G55-G66, doi:10.1190/geo2011-0388.1. [pdf]

Uieda, L., and V. C. F. Barbosa (2012b), Use of the "shape-of-anomaly" data misfit in 3D inversion by planting anomalous densities, SEG Technical Program Expanded Abstracts, 1-6, doi:10.1190/segam2012-0383.1. [pdf]