# The 2008–2010 Subsidence of Dallol Volcano on the Spreading Erta Ale Ridge: InSAR Observations and Source Models

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{6}km

^{3}/year. The most likely explanation for the subsidence of Dallol volcano is a combination of outgassing (depressurization), cooling and contraction of the roof of a shallow crustal magma chamber or of the hydrothermal system.

## 1. Introduction

**Figure 1.**The main figure shows the area of Dallol. The red oval is the Dallol explosive crater and hydrothermal area (https://volcano.si.edu/volcano.cfm?vn=221041, accessed on 17 May 2021), and the white filled circles are earthquakes from [20]. (

**a**) Panchromatic satellite image of the Dallol area. (

**b**) Afar rift—the red line marks the rift axis and black lines are the rift-bounding faults. RS-Red Sea rift, GA-Gulf of Aden rift and MER-Main Ethiopian rift. The black box marks the location of the main figure.

## 2. InSAR Processing and Time-Series

## 3. InSAR Modelling

#### 3.1. Models of Reservoir Contraction

^{6}m

^{3}/year (Table 1). The fit between model and data for a spherical source is shown in Figure 5, Figure 6 and Figure 7, for illustrative purposes. Overall, the RMSE of the sphere, spheroid and penny-shaped crack are similar (Table 2), likely because of the limited number of pixels covering the central part of Dallol, which makes it difficult to discriminate between the three different geometries.

#### 3.2. Thermomechanical Models

**Table 3.**Estimate of poro-elastic pressure and thermoelastic temperature changes for a penny-shaped crack, sub-surface structure. Errors are one standard deviation. Parameters for the hydrothermal system are from Hellisheidi volcano, a possible natural analog [37].

## 4. Discussion

^{6}m

^{3}/year. Our best-fit depth for the Dallol magma chamber is consistent with a previous InSAR study of the 2004 dyke-induced subsidence which placed the Dallol chamber between 1.5–3.3 km of depth [15]. Although the difference in magma chamber depths between the two InSAR studies is not significant, our model places the deformation source at the roof of the source inferred by [15].

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Lu, Z.; Dzurisin, D.; Biggs, J.; Wicks, C., Jr.; McNutt, S. Ground surface deformation patterns, magma supply, and magma storage at Okmok volcano, Alaska, from InSAR analysis: 1. Interruption deformation, 1997–2008. J. Geophys. Res.
**2010**, 115. [Google Scholar] [CrossRef][Green Version] - Segall, P. Earthquake and Volcano Deformation; Princeton University Press: Princeton, NJ, USA, 2010. [Google Scholar]
- Girona, T.; Costa, F.; Schubert, G. Degassing during quiescence as a trigger of magma ascent and volcanic eruptions. Sci. Rep.
**2015**, 5, 18212. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hamlyn, J.; Wright, T.; Walters, R.; Pagli, C.; Sansosti, E.; Casu, F.; Pepe, S.; Edmonds, M.; McCormick, B.; Kilbride, G.; et al. What causes subsidence following the 2011 eruption at Nabro (Eritrea)? Prog. Earth Planet Sci.
**2018**, 5, 31. [Google Scholar] [CrossRef][Green Version] - Lundgren, P.; Usai, S.; Sansosti, E.; Lanari, R.; Tesauro, M.; Fornaro, G.; Berardino, P. Modeling surface deformation observed with synthetic aperture radar interferometry at Campi Flegrei caldera. J. Geophys. Res.
**2001**, 106, 19355–19366. [Google Scholar] [CrossRef][Green Version] - Gottsmann, J.; Rymer, H.; Berrino, G. Unrest at the Campi Flegrei caldera (Italy): A critical evaluation of source parameters from geodetic data inversion. J. Volcanol. Geotherm. Res.
**2006**, 150, 132–145. [Google Scholar] [CrossRef] - Fournier, T.J.; Pritchard, M.E.; Riddick, S.N. Duration, magnitude, and frequency of subaerial volcano deformation events: New results from Latin America using InSAR and a global synthesis. Geochem. Geophys. Geosyst.
**2010**, 11. [Google Scholar] [CrossRef] - Biggs, J.; Anthony, E.Y.; Ebinger, C.J. Multiple inflation and deflation events at Kenyan volcanoes. East African Rift. Geology
**2009**, 37, 979–982. [Google Scholar] [CrossRef] - Pagli, C.; Sigmundsson, F.; Árnadóttir, T.; Einarsson, P.; Sturkell, E. Deformation of the Askja volcanic system: Constraints on the deformation source from combined inversion of satellite radar interferograms and GPS measurements. J. Volcanol. Geotherm. Res.
**2006**, 152, 97–108. [Google Scholar] [CrossRef] - de Zeeuw-van Dalfsen, E.; Pedersen, R.; Hooper, A.; Sigmundsson, F. Subsidence of Askja caldera 2000–2009: Modelling of deformation processes at an extensional plate boundary, constrained by time series InSAR analysis. J. Volcanol. Geotherm. Res.
**2021**, 213, 72–82. [Google Scholar] [CrossRef] - Tizzani, P.; Battaglia, M.; Castaldo, R.; Pepe, A.; Zeni, G.; Lanari, R. Magma and fluid migration at Yellowstone Caldera in the last three decades inferred from InSAR, leveling, and gravity measurements. J. Geophys. Res.
**2015**, 120, 2627–2647. [Google Scholar] [CrossRef][Green Version] - Troise, C.; De Natale, G.; Schiavone, R.; Somma, R.; Moretti, R. The Campi Flegrei caldera unrest: Discriminating magma intrusions from hydrothermal effects and implications for possible evolution. Earth-Sci. Rev.
**2019**, 188, 108–122. [Google Scholar] [CrossRef] - Ferguson, D.J.; Barnie, T.D.; Pyle, D.M.; Oppenheimer, C.; Yirgu, G.; Lewi, E.; Hamling, I. Recent rift-related volcanism in Afar, Ethiopia. Earth Planet. Sc. Lett.
**2010**, 292, 409–418. [Google Scholar] [CrossRef] - Bastow, I.D.; Booth, A.D.; Corti, G.; Keir, D.; Magee, C.; Jackson, C.A.-L. The development of late-stage continental breakup: Seismic reflection and borehole evidence from the Danakil Depression, Ethiopia. Tectonics
**2018**, 37, 2848–2862. [Google Scholar] [CrossRef][Green Version] - Nobile, A.; Pagli, C.; Keir, D.; Wright, T.; Ayele, A.; Ruch, J.; Acocella, V. Dike-fault interaction during the 2004 Dallol intrusion at the northern edge of the Erta Ale Ridge (Afar, Ethiopia). Geophys. Res. Lett.
**2012**, 39, L19305. [Google Scholar] [CrossRef][Green Version] - Pagli, C.; Wang, H.; Wright, T.J.; Calais, E.; Lewi, E. Current plate boundary deformation of the Afar rift from a 3-D velocity field inversion of InSAR and GPS. J. Geophys. Res.
**2014**, 119, 8562–8575. [Google Scholar] [CrossRef] - Wang, H.; Wright, T.J. Satellite geodetic imaging reveals internal deformation of western Tibet. Geophys. Res. Lett.
**2012**, 39, L07303. [Google Scholar] [CrossRef][Green Version] - Biggs, J.; Wright, T.; Lu, Z.; Parsons, B. Multi-interferogram method for measuring interseismic deformation: Denali fault, Alaska. Geophys. J. Int.
**2007**, 170, 1165–1179. [Google Scholar] [CrossRef][Green Version] - Ferretti, A.; Prati, C.; Rocca, F. Permanent scatterers in SAR interferometry. IEEE Trans. Geosci. Remote
**2001**, 39, 8–20. [Google Scholar] [CrossRef] - llsley-Kemp, F.; Keir, D.; Bull, J.M.; Gernon, T.M.; Ebinger, C.; Ayele, A. Seismicity during continental breakup in the Red Sea rift of Northern Afar. J. Geophys. Res.
**2018**, 123, 2345–2362. [Google Scholar] [CrossRef] - Rosen, P.A.; Hensley, S.; Peltzer, G.; Simons, M. Updated repeat orbit interferometry package released. Eos Trans. AGU
**2004**, 85, 47. [Google Scholar] [CrossRef] - Elliott, J.R.; Biggs, J.; Parsons, B.; Wright, T.J. InSAR slip rate determination on the Altyn Tagh Fault, northern Tibet, in the presence of topographically correlated atmospheric delays. Geophys. Res. Lett.
**2008**, 35, L12309. [Google Scholar] [CrossRef][Green Version] - . Ng, A.H.-M.; Wang, H.; Dai, Y.; Pagli, C.; Chen, W.; Ge, L.; Du, Z.; Zhang, K. InSAR Reveals Land Deformation at Guangzhou and Foshan, China between 2011 and 2017 with COSMO-SkyMed Data. Remote Sens.
**2018**, 10, 813. [Google Scholar] [CrossRef][Green Version] - Aly, Z.; Bonn, F.J.; Magagi, R. Analysis of the Backscattering Coefficient of Salt-Affected Soils Using Modeling and RADARSAT-1 SAR Data. IEEE Trans. Geosci. Remote
**2007**, 45, 332–341. [Google Scholar] [CrossRef] - Battaglia, M.; Cervelli, P.; Murray, J. dMODELS: A MATLAB software package for modeling crustal deformation near active faults and volcanic centers. J. Volcanol. Geotherm. Res.
**2013**, 254, 1–4. [Google Scholar] [CrossRef] - McTigue, D.F. Elastic stress and deformation near a finite spherical magma body: Resolution of the point source paradox. J. Geophys. Res.
**1987**, 92, 12931–12940. [Google Scholar] [CrossRef] - Williams, C.A.; Wadge, G. The effects of topography on magma chamber deformation models: Application to Mt. Etna and radar interferometry. Geophys. Res. Lett.
**1998**, 25, 1549–1552. [Google Scholar] [CrossRef] - Yang, X.-M.; Davis, P.M.; Dieterich, J.H. Deformation from inflation of a dipping finite prolate spheroid in an elastic half-space as a model for volcanic stressing. J. Geophys. Res.
**1988**, 93, 4249–4257. [Google Scholar] [CrossRef] - Fialko, Y.; Khazan, Y.; Simons, M. Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy. Geophys. J. Int.
**2001**, 146, 181–190. [Google Scholar] [CrossRef][Green Version] - Okada, Y. Surface deformation due to shear and tensile faults in a half-space. Bull. Seismol. Soc. Am.
**1985**, 75, 1135–1154. [Google Scholar] - Bergstra, J.; Bengio, Y. Random search for hyper-parameter optimization. J. Mach. Learn. Res.
**2012**, 13, 281–305. [Google Scholar] - Mathworks. Optimization Toolbox™ User’s Guide (R2020b). 2020. Available online: www.mathworks.com (accessed on 17 May 2021).
- Deutsch, V.C. Geostatics. In Encyclopedia of Physical Science and Technology, 3rd ed.; Meyers, R.A., Ed.; Academic Press: Cambridge, MA, USA, 2003; pp. 697–707. [Google Scholar] [CrossRef]
- Gordon, R.G.; Stein, S.; DeMets, C.; Argus, D.F. Statistical tests for closure of plate motion circuits. Geophys. Res. Lett.
**1987**, 14, 587–590. [Google Scholar] [CrossRef] - Carniel, R.; Jolis, E.M.; Jones, J. A geophysical multi-parametric analysis of hydrothermal activity at Dallol, Ethiopia. J. Afr. Earth Sci.
**2010**, 58, 812–819. [Google Scholar] [CrossRef] - Cavalazzi, B.; Barbieri, R.; Gómez, F.; Capaccioni, B.; Olsson-Francis, K.; Pondrelli, M.; Rossi, A.P.; Hickman-Lewis, K.; Agangi, A.; Gasparotto, G.; et al. The Dallol Geothermal Area, Northern Afar (Ethiopia)—An Exceptional Planetary Field Analog on Earth. Astrobiology
**2019**, 19, 553–578. [Google Scholar] [CrossRef] [PubMed] - Juncu, D.; Árnadóttir, T.; Geirsson, H.; Gunnarsson, G. The effect of fluid compressibility and elastic rock properties on deformation of geothermal reservoirs. Geophys. J. Int.
**2019**, 217, 122–134. [Google Scholar] [CrossRef][Green Version] - Masterlark, T.; Lu, Z. Transient volcano deformation sources imaged with interferometric synthetic aperture radar: Application to Seguam Island, Alaska. J. Geophys. Res.
**2004**, 109, B01401. [Google Scholar] [CrossRef][Green Version] - Hutnak, M.; Hurwitz, S.; Ingebritsen, S.E.; Hsieh, P.A. Numerical models of caldera deformation: Effects of multiphase and multicomponent hydrothermal fluid flow. J. Geophys. Res.
**2009**, 114, B04411. [Google Scholar] [CrossRef][Green Version] - Meuti, S.; Pagli, C.; Pepe, S.; Battaglia, M.; Casu, F.; De Luca, C.; Pepe, A. Subsidence at Dallol proto-volcano, Afar (Ethiopia): Cooling of the magma chamber or deep interconnection? Geophys. Res. Abs
**2017**, 19, EGU2017. [Google Scholar] - Albino, F.; Biggs, J. Magmatic Processes in the East African Rift System: Insights From a 2015–2020 Sentinel-1 InSAR Survey. Geochem. Geophys. Geosyst.
**2020**, 22, e2020GC009488. [Google Scholar] [CrossRef] - Johnson, D.J. Dynamics of magma storage in the summit reservoir of Kilauea Volcano, Hawaii. J. Geophys. Res.
**1992**, 97, 1807–1820. [Google Scholar] [CrossRef] - Johnson, D.; Sigmundsson, F.; Delaney, P. Comment on “Volume of magma accumulation or withdrawal estimated from surface uplift or subsidence, with application to the 1960 collapse of Kīlauea volcano” by P. T. Delaney and D. F. McTigue. Bull. Volcanol.
**2000**, 61, 491–493. [Google Scholar] [CrossRef] - Rivalta, E.; Segall, P. Magma compressibility and the missing source for some dike intrusions. Geophys. Res. Lett.
**2008**, 35, L04306. [Google Scholar] [CrossRef][Green Version] - Iddon, F.; Edmonds, M. Volatile-rich magmas distributed through the upper crust in the Main Ethiopian Rift. Geochem. Geophys. Geosyst.
**2020**, 21, e2019GC008904. [Google Scholar] [CrossRef] - Dzurisin, D.; Poland, M.P.; Bürgmann, R. Steady subsidence of Medicine Lake Volcano, Northern California, revealed by repeated leveling surveys. J. Geophys. Res.
**2002**, 107, 2372. [Google Scholar] [CrossRef] - Wicks, C.W.; Dzurisin, D.; Lowenstern, J.B.; Svarc, J. Magma intrusion and volatile ascent beneath Norris Geyser Basin, Yellowstone National Park. J. Geophys. Res.
**2020**, 125, e2019JB018208. [Google Scholar] [CrossRef]

**Figure 2.**InSAR line-of-sight (LOS) average velocity maps of deformation at Dallol crater and surrounding areas from ENVISAT data. In this map, a LOS increase implies a subsidence. T300: ascending orbit; T321: descending orbit; T028: ascending orbit. (

**a**–

**c**) InSAR average LOS velocity maps from 2008 to 2010, showing subsidence (increase in the LOS length) in the topographic depression of Dallol; the box marks the area shown in (

**d**–

**f**). (

**d**–

**f**) The black line marks the approximate boundary of the topographic depression marking the Dallol crater and hydrothermal area. The volcano formed by the intrusion of basaltic magma into the salt plains of Dallol (Figure 1), a vast area of uplifted thick salt deposits affected by intense fumarolic activity (https://volcano.si.edu/volcano.cfm?vn=221041 accessed on 09 April 2021). (

**g**,

**h**) LOS cumulative displacements at the numbered pixels in (

**d**,

**e**). No significant deformation is measured before October 2008 and after January 2010.

**Figure 3.**Stairs plot of the grid searches for the joint inversion of the InSAR data from orbits T300 and T321 (dataset DALLOL 2, sill source; Table 1). The inversion code implements a weighted least-squares algorithm combined with a random search grid to infer the minimum of the penalty function [31]. The red line points out the best fit solution. (

**a**) penalty function ${\chi}_{\nu}^{2}$; (

**b**) source location, X

_{0}; (

**c**) source location, Y

_{0}; (

**d**) source depth, Z

_{0}; (

**e**) dimensionless pressure change, $\Delta P/\mu $; (

**f**) source radius.

**Figure 4.**Example of semi-variograms of the deformation data (Figure 2) and models (Table 1) for the inversion of InSAR data from orbits T321 and T300 (dataset DALLOL 2). If the misfit (difference between data and model) is completely random (white noise), its variogram is a flat line (slope ~0). Full results are in Table 2.

SOURCE | Sphere | Spheroid | Penny-Shaped Crack | Dike |
---|---|---|---|---|

nRMSE | 0.12 | 0.10 | 0.13 | 0.20 |

slope of misfit | 0.018 | 0.018 | 0.016 | 0.004 |

**Figure 5.**Spherical source solution: comparison between InSAR line-of-sight deformation, model (see Table 1, DALLOL 2), and misfit for the three orbits. The image coordinates are in UTM [m]. The scale of the data and model is in m/year. The scale of the misfit is based on measurement errors (5 means the misfit is five times the measurement error); all the pixels where the misfit is smaller than 2 error bars are in white. Dallol volcano is at the center of the images (white/black contour line). The red star with yellow fill is the location of the source. The red line in the data plot identifies the deformation profiles shown in Figure 6.

**Figure 7.**Spherical solution (Table 1, DALLOL 2). (

**Left**) Source location (red circle, yellow fill); Dallol mountain is at the center of the image (white contour line); DEM from 1 Arc-Second Global SRTM (https://earthexplorer.usgs.gov/ accessed on 09 April 2021). (

**Right**) Source location and depth (red star, yellow fill); the green line is the topography along the profile identified by the white diagonal line on the left panel.

**Table 1.**Summary of modeling results. Number of random searches 256. Selection radius for data set: 10 km from center of Dallol crater. Regular sub-sampling.

Data Set | Description | Orbits | # of Pixels | Source | # of PARAMETERS | Orbits | Χ_{v}^{2} | RMSE (1) Semi Variogram | ΔX0 (2)m | ΔY0 (2)m | Depthm b.s.l. | Radiusm | ΔV 10 ^{6}m ^{3}/Year |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

DALLOL 1 | Original data set | T321 &T300 | 78,467 | Sphere | 5 | T321 & T300 | 14.1 | 0.31 | 1647 | 841 | 24,437 | 172 | 5.29 |

T321 & T028 | 18.2 | 0.28 | 1604 | 726 | 13,827 | 69 | 0.001 | ||||||

Spheroid | 8 | T321 & T300 | 13.0 | 0.32 | −205 | 215 | 14,814 | 1228 | 45.3 | ||||

T321 & T028 | 15.4 | 0.30 | 1630 | 821 | 17,443 | 1049 | 46.2 | ||||||

T321 &T028 | 77,008 | Penny-shaped crack | 5 | T321 & T300 | 14.0 | 0.87 | 1720 | 912 | 805 | 128 | 0.009 | ||

T321 & T028 | 18.0 | 0.27 | 1720 | 912 | 5849 | 169 | 0.45 | ||||||

Dike (3) | 8 | T321 & T300 | 10.4 | 0.22 | 1502 | 139 | 2684 | - | −0.93 | ||||

T321 & T028 | 11.6 | 0.20 | 461 | 912 | 5416 | - | −3.10 | ||||||

DALLOL 2 | Reference point defined such that average deformation far away from crater is zero | T321 &T300 | 79,188 | Sphere | 5 | T321 & T300 | 10.4 | 0.12 | −96 | −92 | 1234 | 556 | −0.56 |

T321 & T028 | 13.6 | 0.15 | −143 | −124 | 1277 | 60 | −0.59 | ||||||

Spheroid | 8 | T321 & T300 | 10.3 | 0.10 | −112 | −127 | 1274 | 287 | −0.63 | ||||

T321 & T028 (4) | 13.4 | 0.63 | −53 | 561 | 21,083 | 1103 | −117 | ||||||

T321 &T028 | 75,864 | Penny-shaped crack | 5 | T321 & T300 | 10.3 | 0.13 | −168 | −108 | 1470 | 1560 | −0.62 | ||

T321 & T028 | 13.9 | 0.17 | −183 | −168 | 1241 | 1628 | −0.53 | ||||||

Dike (3) | 8 | T321 & T300 | 11.8 | 0.20 | 63 | −278 | 551 | - | −0.48 | ||||

T321 & T028 (4) | 11.0 | 0.26 | 1526 | 815 | 7023 | - | −2.68 | ||||||

DALLOL 3 | Masked (only data that show subsidence) | T321 &T300 | 6127 | Sphere | 5 | T321 & T300 | 5.1 | 0.09 | −32 | −71 | 915 | 449 | −0.30 |

T321 & T028 | 4.2 | 0.07 | −79 | −135 | 1046 | 463 | −0.32 | ||||||

Spheroid | 8 | T321 & T300 | 5.0 | 0.10 | −83 | −77 | 798 | 582 | −0.31 | ||||

T321 & T028 | 4.2 | 0.08 | −82 | −142 | 1037 | 159 | −0.39 | ||||||

T321 &T028 | 17,075 | Penny-shaped crack | 5 | T321 & T300 | 4.8 | 0.12 | −166 | −196 | 566 | 1430 | −0.26 | ||

T321 & T028 | 3.8 | 0.12 | −216 | −223 | 516 | 1557 | −0.26 | ||||||

Dike (3) | 8 | T321 & T300 | 3.9 | 0.06 | 605 | 305 | 707 | - | −0.29 | ||||

T321 & T028 | 3.6 | 0.09 | 764 | 196 | 724 | - | −0.28 |

**Table 2.**Average source parameters. Parameters are estimated from the solutions for DALLOL2 and DALLOL3 (Table 1) using a weighted average; uncertainties are the standard deviation of the weighted average. Uncertainties σ are one standard deviation.

Source | X2v (1) | RMSE (1) | ΔX0 (2) | ±σ | ΔY0 (2) | ±σ | Depth | ±σ | Radius | ±σ | ΔV | ±σ | A | ±σ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Variogram | m | m | m b.s.l. | m | 10^{6} m^{3}/Year | |||||||||

Sphere | 9.0 | 0.11 | −110 | 24 | −106 | 17 | 1232 | 63 | 380 | 230 | −0.55 | 0.07 | ||

Spheroid | 9.0 | 0.10 | −110 | 8 | −128 | 5 | 1255 | 69 | 280 | 39 | −0.61 | 0.06 | 0.34 | 0.15 |

Penny-shaped crack | 8.9 | 0.13 | −175 | 10 | −132 | 33 | 1357 | 199 | 1582 | 34 | −0.58 | 0.08 | ||

Dike (3) | 10.0 | 0.17 | 215 | 281 | −164 | 210 | 589 | 71 | - | - | −0.44 | 0.08 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Battaglia, M.; Pagli, C.; Meuti, S.
The 2008–2010 Subsidence of Dallol Volcano on the Spreading Erta Ale Ridge: InSAR Observations and Source Models. *Remote Sens.* **2021**, *13*, 1991.
https://doi.org/10.3390/rs13101991

**AMA Style**

Battaglia M, Pagli C, Meuti S.
The 2008–2010 Subsidence of Dallol Volcano on the Spreading Erta Ale Ridge: InSAR Observations and Source Models. *Remote Sensing*. 2021; 13(10):1991.
https://doi.org/10.3390/rs13101991

**Chicago/Turabian Style**

Battaglia, Maurizio, Carolina Pagli, and Stefano Meuti.
2021. "The 2008–2010 Subsidence of Dallol Volcano on the Spreading Erta Ale Ridge: InSAR Observations and Source Models" *Remote Sensing* 13, no. 10: 1991.
https://doi.org/10.3390/rs13101991