# Magma Pathways and Their Interactions Inferred from InSAR and Stress Modeling at Nyamulagira Volcano, D.R. Congo

^{1}

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^{8}

^{*}

## Abstract

**:**

_{v}) is 9.3, consistent with pressure recovery by gas exsolution in the small, shallow modeled magma reservoir. We derive a modified analytical expression for r

_{v}, accounting for changes in reservoir volume induced by gas exsolution, as well as eruptive volume. By using the precise magma composition, we estimate a magma compressibility of 1.9–3.2 × 10

^{9}Pa

^{−1}and r

_{v}of 6.5–10.1. From a normal-stress change analysis, we infer that intrusions in 2010 could have encouraged the ascent of magma from a deeper reservoir along an ~N45E orientation, corresponding to the strike of the rift transfer zone structures and possibly resulting in the 2011–2012 intrusion. The intrusion of magma to greater distances from the summit may be enhanced along the N45E orientation, as it is more favorable to the regional rift extension (compared to the local volcanic rift zone, trending N155E). Repeated dike intrusions beneath Nyamulagira’s SSE flank may encourage intrusions beneath the nearby Nyiragongo volcano.

## 1. Introduction

**Figure 1.**Geological setting of the Virunga Volcanic Province (VVP), western branch of the East African Rift System (EARS), north of Lake Kivu. The rift extension direction in this area is ~N110E, with an estimated extension rate of 2-2.8 mm/year [11,12]. The Goma–Gisenyi urban area is outlined in white on the northern shores of Lake Kivu. Eruptive fissures and lava flows (see the legend) were mapped from radar and optical images [7]. Nyamulagira’s caldera rim is outlined with a white dashed line. Faults are from [13], and rose diagrams of VVP’s faults (yellow) and eruptive fissures (red) are from [9]. The white rectangle gives the extent of Figure 2.

**Figure 2.**Data, 1st column: most coherent wrapped interferograms covering the entire 2010 Nyamulagira eruption (heights of ambiguity, i.e., the topographic altitude difference, which generates one residual topographic fringe in a differential interferogram [14]; for interferograms, (

**a**)–(

**d**) are 45, 430, 704 and 3000 m, respectively). Pixels with coherence lower than 0.2 have been masked out (the unmasked wrapped interferograms are shown in Figure S1, and the four selected unwrapped interferograms are shown in Figure S2). Nyamulagira’s summit caldera is outlined with a dashed white line. Note that the ALOS interferogram has been rewrapped to the ENVISAT’s wavelength of 5.6 cm. Model, 2nd column, and residuals, 3rd column, for the preferred best-fit model (Figure 3), including two dike intrusions associated with the 2010 eruptive fissures (bold green lines) and a deflating reservoir, for the four interferograms (

**a**)–(

**d**).

## 2. Background

#### 2.1. Geologic Setting

**Figure 3.**Geometry of the preferred best-fit model including two dikes and a deflating reservoir: (

**a**) Map view. The 2010 eruptive fissures are shown as bold green lines. (

**b**) North-vertical cross-section. (

**c**) East-vertical cross-section. Volume changes of the dike associated with the caldera’s fissure, the southern flank’s fissure and the spherical reservoir are 0.74, 4.2 and −5.1 × 10

^{6}m

^{3}, respectively.

#### 2.2. Characteristics of Recent Eruptions

^{6}m

^{3}of lava [9]. The magma that feeds such upper flank eruptions likely intrudes as subvertical dikes from a storage area located at a depth of up to 5 km below the ground surface [19,20]. In contrast, the 1989, 1991–1993, 2001 and 2011–2012 eruptions correspond to less frequent (roughly decennial) long-lived eruptions, which last from several months to years, produce larger volumes of lava (i.e., >80 × 10

^{6}m

^{3}) and occur in the summit area (as in 2001) or >9 km from the summit [9]. The location of the ~N70E 2011–2012 eruptive fissures (Figure 4) corresponds to the eastern extension of an unusual ~4 km-deep long-period (LP) earthquake swarm oriented ~N45E, which was recorded the month preceding the 2010 eruption (Figure 5). Dikes feeding these larger volume eruptions might initiate from a deeper (~20-km depth) magma reservoir located between Nyamulagira and Nyiragongo [9]. An alternative hypothesis is that eruptions fed by dikes parallel to local EARS structures (i.e., oriented ~N45E, Figure 1) have a longer duration and larger volumes because they are more favorably oriented with respect to the remote stress associated with the rift extension [8].

**Figure 4.**Close-up of the distribution of recent eruptive fissures at Nyamulagira. The potential dike surface orientations investigated in the normal stress analysis (Section 5.4) and shown in Figure 6 and Figure S3 are represented with brown dashed lines. SC stands for south of the caldera.

**Figure 5.**Sequence of seismic, volcanic and deformation events related to the 2010 Nyamulagira eruption. a–d correspond to the time spanned by the corresponding interferograms shown in Figure 2. See [10] for a detailed review of the four eruptive stages. SP and LP stand for short and long period, respectively.

#### 2.3. The January 2010 Eruption

## 3. Methods

#### 3.1. InSAR Processing

#### 3.2. Boundary Elements Modeling and Non-Linear Inversions

## 4. Numerical 3D Modeling Results

**Table 1.**Comparison of the best-fit model obtained for each combination of sources inverted. Note that several inversions were run for each possible source combination; only the best-fit result obtained for each combination is shown. * denotes the preferred model among all of the best-fit models. Percentage of explained deformation and RMS error are defined in the Supplementary Materials.

Model | Explained Deformation (%) | RMS Error (cm) | AIC |
---|---|---|---|

1 dike | 68 | 2.5 | 702 |

2 dikes | 71 | 2.5 | 746 |

2 dikes + quadrangular connection | 60 | 2.5 | 1216 |

1 dike + circular sill | 83 | 1.9 | 295 |

1 dike + rectangular sill | 82 | 2 | 374 |

1 dike + spherical reservoir | 86 | 1.7 | 295 |

2 dikes + circular sill | 87 | 1.6 | 65 |

2 dikes + rectangular sill | 87 | 1.6 | 96 |

2 dikes + spherical reservoir* | 90 | 1.5 | 29 |

2 dikes + laccolith | 86 | 1.7 | 164 |

^{6}m

^{3}. The second dike, connected to the southern eruptive fissure on the SE flank (the “southern dike”), extends to a greater depth, reaching ~3.5 km beneath the surface. It has an ~6 km-long bottom side dipping at ~40 degrees northward (Figure 3 and Table 2). It experiences a larger volume increase of ~4.2 × 10

^{6}m

^{3}. The spherical magma reservoir, located beneath the SW depression in Nyamulagira caldera (Figure 3) and centered at a depth of ~4 km beneath the summit, experiences a volume decrease of ~5.1 × 10

^{6}m

^{3}.

Parameter | Dike Connected to the Caldera Fissure | Dike Connected to Southern Flank Fissure | Reservoir |
---|---|---|---|

Static pressure change (MPa) | 1.4 ^{[1, 1.6]} | 1.4 ^{[1, 1.6]} | −26 ^{[−26, −17]} |

Elevation of the base (middle point) for dikes or center of the reservoir (m a.s.l.) | 1400 ^{[1236, 2314]} | −150 ^{[−620, 486]} | −890 ^{[−1462, −181]} |

Dip angle (°) | 90 * | 106 ^{[88, 120]} | - |

Angle between the line connecting the top and base middle points and the dipping direction (°) | 0 * | 42 ^{[0.5, 43]} | - |

Length of the base scaled to that of the top | 1.4 ^{[1.3, 1.7]} | 13 ^{[10, 13]} | - |

Vertical angle of the base (°) | 0 * | −14 ^{[−33, −6]} | - |

Horizontal position of the reservoir (km) | - | - | 744.2 ^{[744.1, 744.5]};9843.2 ^{[98430, 9843]} |

Radius of the reservoir (m) | - | - | 500 ** |

## 5. Discussion

#### 5.1. Sources of Deformation

#### 5.2. Magma Reservoir Size

_{l}, and the tensile strength, T

_{0}[39,56], as:

^{3}[57], ${T}_{0}$ = 0.5–5 MPa [58] and use a value of $H$ = 3.5 km from our inversions, the overpressure $\Delta {P}_{r}$ = 179–183 MPa. If we consider that the pre-eruption excess volume $\Delta {V}_{r}$, which induced the failure, corresponds to the pre-eruptive inflation detected by InSAR, ${u}_{z}=$ 5 cm [21], we can estimate the radius of this reservoir. Assuming the reservoir volume change corresponds to that of a spherical reservoir in an infinite medium (the reservoir depth/radius ratio is >5), we can compute this radius from [59]:

#### 5.3. Magma Budget

^{6}m

^{3}. The intruded magma volume in the two dikes is ~4.9 × 10

^{6}m

^{3}, similar to the reservoir volume decrease. The estimated extruded lava flow and tephra volume is 45.5 ± 7.6 × 10

^{6}m

^{3}[10] and 10 × 10

^{6}m

^{3}[8], respectively, leading to an average dense rock equivalent volume of ~42.3 × 10

^{6}m

^{3}(assuming a lava, tephra and dense rock density of 2200, 1000 and 2600 kg/m

^{3}[8], respectively). The total emitted volume is thus ~47.2 × 10

^{6}m

^{3}(= the sum of dike volumes + dense rock equivalent erupted volume), leading to a ratio (r

_{v}) between the total emitted volume and the reservoir volume decrease of ~9.3. This ratio is an intermediate value between commonly-reported values in the EARS, for instance of ~20–40 [45] for the Dabbahu intrusion and of ~3 for the Dallol intrusion [60]. Refill of the shallow reservoir from a deep reservoir is not necessarily required to explain this discrepancy, as the pressure in the reservoir could have been restored by gas exsolution in the magma chamber [50].

_{v}. We assume that mass is conserved between magma emitted from the reservoir and magma transmitted to the edifice and that magma is compressible. However, we additionally account for the lava erupted at the surface (see Appendix A) and assume that pressure in the magma chamber before the eruption, ${P}_{r}$, corresponds to the maximum sustainable overpressure defined above, ${P}_{r}={P}_{l}+\Delta {P}_{r}=3{P}_{l}+{T}_{o}$, and that, after the eruption, pressure in the magma chamber returns to a lithostatic state. Thus, we obtain the following:

_{2}and H

_{2}O, and the magma compositions are estimated from recent studies of the volcano [10,65] (Table 3). Using the online code for thermodynamics computation of Papale et al. [64], we find that for a 1200 °C magma at a 3.5-km depth, almost all CO

_{2}is gaseous and all H

_{2}O is liquid, so that ${\chi}_{C{O}_{2}}\left(P\right)=0.1\text{wt\%}$ and ${\chi}_{{H}_{2}O}\left(P\right)=0\text{wt\%}$. At the pressure corresponding to rupture of the reservoir, ${P}_{r}$, we find ${\chi}_{C{O}_{2}}\left({P}_{r}\right)=0.05\text{wt\%}$. Successively using Equations (5) and (6), we get a magma compressibility of ${\beta}_{m}$ = 1.9-3.2 × 10

^{9}Pa

^{−1}. If we consider a reservoir compressibility for a source in an infinite medium [50] and take ${\rho}_{e}=$ 2600 kg/m

^{3}for the dense rock equivalent density and ${V}_{e}$ = 47.2 × 10

^{6}m

^{3}, using Equation (4), we obtain r

_{v}= 6.5–10.1, a value consistent with that determined from modeled volume changes. The contribution of the emitted lava flow to r

_{v}is 0.5, thus it accounts for approximately only 5% of r

_{v}. This value of ${r}_{v}$ indicates that the magma emitted can be entirely issued from the 3.5-km depth shallow magma chamber and that discrepancy between the emitted and the reservoir volume change are compensated by CO

_{2}exsolution.

**Table 3.**Thermodynamics parameters and major and minor element composition considered for the 2010 lavas of Nyamulagira used to compute the weight percent of the exsolved gases.

T (°C) | P (MPa) | SiO_{2} | TiO_{2} | Al_{2}O_{3} | Fe_{2}O_{3} | FeO | MnO | MgO | CaO | Na_{2}O | K_{2}O | H_{2}O (wt%) | CO_{2} (wt%) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1200 | 87.5 | 45 | 3.5 | 15 | 13.1 | 12 | 0.2 | 4.5 | 11,5 | 3 | 2.2 | 1.25 | 0.1 |

#### 5.4. Stress Analysis

^{2}, respectively) to greater depths. Stress changes from the 2010 intrusions and reservoir beneath the SSE flank could have thus encouraged the vertical ascent of magma from a deeper crustal reservoir along the ~N45E SC surface below the volcanic edifice. This interpretation is consistent with the hypothesis of a deep (~20–30-km depth) magma reservoir feeding the less common distal lower flanks’ eruptions [19].

**Figure 6.**Perspective plots from two orthogonal viewing angles showing the changes in the normal stress on the potential dike surfaces (Figure 4) caused by the preferred model of the 2010 best-fitting deformation sources (black mesh). The color scale corresponds to normal stress change in MPa, with positive values (clamping) clipped to dark red and negative values (unclamping) from blue to red. SC stands for south of the caldera. Both the N155 and N45E SC dike surfaces are unclamped over large and deep areas beneath the volcano by the 2010 eruption sources, while only a small area of the N45E (caldera intersecting) surface is unclamped.

#### 5.5. Influence of the Crustal Extension

_{m}) whatever the intrusion orientation, which might be the case around a reservoir, as each intrusion changes the state of stress in the host medium. We find that the overpressure along the N45E surface $\Delta {P}^{N45E}={P}_{m}-{P}_{l}+0.9{\sigma}_{t}$ is larger than the overpressure along the N155E surface $\Delta {P}^{N155E}={P}_{m}-{P}_{l}+0.7{\sigma}_{t}$. If we consider that the length of the intrusion is a linear function of the overpressure, because the length is limited either by magma cooling [69] or by the resistance to fracture at the dike tip [70], dike intrusions are expected to be longer along the N45E direction than along the N155E direction.

#### 5.6. Magma Storage and Transport

_{v}. The magma overpressure keeps the dike open. Just after the eruption onset, the dike may grow laterally due to the decreased buoyancy corresponding to the increased density of the underlying, gas-poor magma, mainly in the direction of the slope, into a weak and fractured area beneath the SSE flank, as observed, for instance, at Piton de La Fournaise [39] and Etna [71]. As the overpressure in the reservoir is relaxed, the magma flow rate decreases; magma can no longer reach the summit caldera and erupts only at the lower flank vent. A few days after the eruption onset, the eruption is restricted to a small portion at the base of the fracture. Finally, after a few more days or weeks, the activity stops.

**Figure 7.**Schematic shallow magma plumbing system for the period 2006–2012. Arrows represent possible magma migration paths. Red and blue sources experience inflation and deflation, respectively. Orange stars denote the locations of eruptive fissures and vents. SC stands for south of the caldera. The two dikes and magma reservoir inferred from the modeling of the 2010 eruption data are represented with black meshes.

## 6. Conclusions

## Supplementary Files

Supplementary File 1## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A: Ratio of Emitted over Reservoir Volume Change, Taking Lava Erupted at the Surface into Account

_{v}, the ratio of magma intruded in the dikes, ${V}_{d}$, and erupted at the surface, ${V}_{e}$, over the reservoir volume change,

_{v}. After neglecting second order terms, we finally obtain:

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**MDPI and ACS Style**

Wauthier, C.; Cayol, V.; Smets, B.; D’Oreye, N.; Kervyn, F. Magma Pathways and Their Interactions Inferred from InSAR and Stress Modeling at Nyamulagira Volcano, D.R. Congo. *Remote Sens.* **2015**, *7*, 15179-15202.
https://doi.org/10.3390/rs71115179

**AMA Style**

Wauthier C, Cayol V, Smets B, D’Oreye N, Kervyn F. Magma Pathways and Their Interactions Inferred from InSAR and Stress Modeling at Nyamulagira Volcano, D.R. Congo. *Remote Sensing*. 2015; 7(11):15179-15202.
https://doi.org/10.3390/rs71115179

**Chicago/Turabian Style**

Wauthier, Christelle, Valérie Cayol, Benoît Smets, Nicolas D’Oreye, and François Kervyn. 2015. "Magma Pathways and Their Interactions Inferred from InSAR and Stress Modeling at Nyamulagira Volcano, D.R. Congo" *Remote Sensing* 7, no. 11: 15179-15202.
https://doi.org/10.3390/rs71115179