# 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

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**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 |

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**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