# Post-Eruptive Inflation of Okmok Volcano, Alaska, from InSAR, 2008–2014

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## Abstract

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## 1. Introduction

**Figure 1.**Shaded relief image of Okmok volcano, with some of the intra-caldera cones labelled. Cone A was the vent for historical eruptions prior to 2008, while Ahmanilix is the new cone formed during the 2008 eruption. OKSO, OKFG, OKNC, and OKCE are continuous GPS stations. The dashed blue frame shows the area of the DEM created from 21 January 2010 with Worldview imagery [8], while the remaining area topography is from the 1-arc-second (~30 m) SRTM DEM. Inset shows the location of Okmok in the central Aleutian volcanic arc.

## 2. InSAR Processing and Analysis

#### 2.1. Multi-Temporal InSAR Algorithm

#### 2.1.1. PSInSAR Processing

_{x}, which is a representation of variations in the residual phase at the PS candidate pixel [22,33,38] is proposed as the iteration stopping criterion:

^{th}interferogram, $\Delta {\widehat{\psi}}_{\theta ,x,i}^{u}$ is the estimated spatially-uncorrelated look angle error term and ${\tilde{\psi}}_{x,i}$ is the estimate of the spatially-correlated term. The root-mean-square change in γ

_{x}(Equation (1)) is calculated within each iteration. When the value is no longer decreasing, the solution has converged and the iteration stops. More details about StaMPS can be found in Hooper et al. [22,38] and Hooper [33].

#### 2.1.2. SBAS Processing

#### 2.1.3. MTI Processing

#### 2.2. Datasets and Processing

**Figure 2.**Temporal-spatial baseline distributions of interferograms for the four datasets: (

**a**,

**b**) interferograms with perpendicular baselines less than 300 m for ENVISAT C-band data, and (

**c**,

**d**) interferograms with perpendicular baselines less than 200 m for TerraSAR-X X-band data.

Sensor | Envisat ASAR | TerraSAR-X | ||
---|---|---|---|---|

Band | C | X | ||

Polarization | VV | HH | ||

Wavelength (cm) | 5.7 | 3.1 | ||

Track | 222 | 115 | 93 | 116 |

Heading (˚) | −16.4 | −163.5 | 350 | 192.1 |

Incidence angle (˚) | 22.5 | 22.8396 | 41.9804 | 24.625 |

Number of used scenes | 5 | 7 | 11 | 9 |

Number of pairs | 7 | 11 | 23 | 18 |

Date range (yyyymmdd) | 20081029–20100825 | 20090623–20100921 | 20080914–20140912 | 20110727–20141005 |

**Figure 3.**Selected interferograms showing surface deformation of Okmok volcano from 2008 to 2014 ordered by start date: (

**a**) 20081029–20090701 (Envisat 222), (

**b**) 20081029–20090805 (Envisat 222), (

**c**) 20080925–20090810 (TerraSAR-X 93), (

**d**) 20090701–20100825 (Envisat 222), (

**e**) 20090805–20100825 (Envisat 222), (

**f**) 20090623–20100921 (Envisat 115), (

**g**) 20090728–20100713 (Envisat 115), (

**h**) 20080914–20110806 (TerraSAR-X 93), (

**i**) 20090810–20110806 (TerraSAR-X 93), (

**j**) 20090821–20110908 (TerraSAR-X 93), (

**k**) 20110727–20120917 (TerraSAR-X 116), (

**l**) 20121009–20130904 (TerraSAR-X 116), (

**m**) 20130711–20141005 (TerraSAR-X 116), (

**n**) 20130711–20140822 (TerraSAR-X 116), (

**o**) 20130904–20140822 (TerraSAR-X 116), (

**p**) 20110806–20140912 (TerraSAR-X 93). Satellite ID (E is Envisat and T is TerraSAR-X), satellite flight direction, and radar look direction are labelled. The total amounts of LOS displacements vary among InSAR images due to the time-varying deformation nature and different time-spans of interferograms, so different color scales are used to highlight the deformation in subfigures.

#### 2.3. InSAR Results

## 3. Model-Assisted Phase Unwrapping

#### 3.1. Deformation Modelling and Analysis

**Figure 4.**Observed (

**Left**), modeled (

**Middle**), and residual (

**Right**) average LOS deformation maps for the four independent tracks of InSAR data during September 2008 to October 2014 (Table 1). Satellite flight direction and radar look direction are labelled. The cold colors (blue to yellow) represent subsidence, i.e., incremental displacement away from the satellite, to low-rate uplift, i.e., displacement towards the satellite, and the hot-colored points show high-rate uplift. The color scale is the same for all images.

#### 3.2. Phase Unwrapping Error Deduction

**Figure 5.**(

**a**) Original unwrapped phase of interferogram 20110806–20140912 from TerraSAR track 93, with inset enlarging area marked by black rectangle. (

**b**) Modeled phase from TerraSAR track 116 during the period 2011–2014. (

**c**) Modeled phase for TerraSAR track 93 during 2011–2014 as derived from track 116 model parameters. (

**d**) Unwrapped residual phase for TerraSAR-X track 93 found by subtracting the modelled (c) from the observed (a) phase. (

**e**) New unwrapped phase for interferogram 20110806–20140912 based on addition of residual (d) and modeled (c) phase. (

**f**) LOS deformation along profile A-A’ (e) from unwrapped phase produced using standard (black; part a) and model-assisted (red; part e) techniques.

## 4. Post-2008 Deformation

#### 4.1. Time Series Deformation Since 2008

**Figure 6.**Cumulative deformation maps for each InSAR dataset: (

**a**) Envisat track 222, (

**b**) Envisat track 115, (

**c**) TerraSAR-X track 93, (

**d**) TerraSAR-X track 116, all referenced temporally to the earliest scene for each (20090623 for E222, 20081029 for E222, 20080914 for T93, and 20110727 for T116). The cold colors (blue to yellow) represent LOS subsidence (i.e., incremental displacement away from the satellite) to small LOS uplift (i.e., displacement towards the satellite), and the hot-colored points show large LOS uplift.

#### 4.2. Accuracy Assessment of InSAR Results

**Figure 7.**Comparison of InSAR-derived LOS deformation with that from GPS: (

**a**) deformation from Envisat track 115 and GPS at station OKSO, (

**b**) deformation from Envisat track 222 and GPS at station OKSO, (

**c**) deformation from TerraSAR-X track 93 and GPS at station OKNC, (

**d**) deformation from TerraSAR-X track 93 and GPS at station OKSO, (

**e**) deformation from TerraSAR-X track 116 and GPS at station OKSO, (

**f**) deformation from TerraSAR-X track 116 and GPS at station OKCE. GPS station locations are shown in Figure 1, and all the GPS measurements are reference to OKFG.

#### 4.3. Mogi Modeling of Time-Series Deformation

**Figure 8.**(

**a**) Best-fit Mogi source horizontal locations (X is easting and Y is northing) for time-series deformation results from 2008 to 2014, superimposed on a shaded relief DEM image of Okmok volcano. Black cross represents the average position of the Mogi sources, green cross shows the average position of the deformation sources acquired from 1997 to 2008, and blue cross is the average position of the deformation sources from the 2008 eruption interferograms. (

**b**) X position of the best-fit Mogi source as a function of time from 2008 to 2014, plotted relative to an arbitrary reference point R that is shown in Figure 8a. (

**c**) Y position of the best-fit Mogi source as a function of time, plotted relative to an arbitrary reference point R that is shown in Figure 8a. East and north are taken as positive in both plots; (

**d**) Depth of the best-fit Mogi source as a function of time from 2008 to 2014.The average source depth is about 3.9 km below sea level.

^{3}/y, with the rate during 2008–2010 being slightly higher than that of 2010–2013. The rate of magma accumulation increased sharply in 2013, with a volume change of about 0.01 km

^{3}during 2013–2014 (one-year period).

**Figure 9.**Modeled cumulative volume change beneath Okmok as a function of time from 2008 to 5 October 2014 for all four InSAR datasets. The volume of the first scene (20080914) is assumed to be zero.

## 5. Discussion

^{3}[16] and that associated with the 2008 eruption was 0.14 ± 0.01 km

^{3}[18]. The modeled volume of magma accumulated in the reservoir during 2008–2014 is ~0.035 km

^{3}, which is ~75% of the 1997 eruption volume or ~25% of the 2008 eruption volume. We estimate that the post-2008 refilling rate was about 30% more rapid than the post-1997 refilling rate, which required about nine years to recover a similar volume. It should be noted that the time-varying post-eruption inflations could also be due to magma crystallization and degassing and other factors [45].

## 6. Conclusions

^{3}, which is approximately 75% of the 1997 eruption volume and 25% of the 2008 eruption volume.

## Acknowledgements

## Author Contributions

## Conflicts of Interest

## References

- Lu, Z.; Dzurisin, D. InSAR Imaging of Aleutian Volcanoes: Monitoring a Volcanic Arc from Space; Springer Science & Business Media: Chichester, UK, 2014; p. 390. [Google Scholar]
- Larsen, J.F.; Neal, C.; Schaefer, J.; Begét, J.; Nye, C. Late Pleistocene and Holocene caldera-forming eruptions of Okmok caldera, Aleutian Islands, Alaska. In Volcanism and Subduction: The Kamchatka Region; Eichelberger, J., Gordeev, E., Izbekov, P., Kasahara, M., Lees, J., Eds.; Wiley: Washington, DC, USA, 2007; pp. 343–364. [Google Scholar]
- Byers, F.M. Geology of Umnak and Bogoslof Islands, Aleutian Islands, Alaska; U.S. Geological Survey Bulletin B; U.S. Government Printing Office: Washington, DC, USA, 1959; pp. 267–369. [Google Scholar]
- Miller, T.P.; Smith, R.L. Two caldera-forming eruptions on Umnak Island, eastern Aleutian Islands. U.S. Geol. Surv. Circular
**1975**, C0733, 1–45. [Google Scholar] - Miller, T.P.; Smith, R.L. Late Quaternary caldera-forming eruptions in the eastern Aleutian arc, Alaska. Geology
**1987**, 15, 434–438. [Google Scholar] [CrossRef] - Miller, T.P.; McGimsey, R.G.; Richter, D.H.; Riehle, J.R.; Nye, C.J.; Yount, M.E.; Dumoulin, J.A. Catalog of the Historically Active Volcanoes of Alaska; U.S. Geological Survey Open-File Report; U.S. Government Printing Office: Washington, DC, USA, 1998; p. 104. [Google Scholar]
- Larsen, J.F.; Neal, C.A.; Schaefer, J.R.; Kaufman, A.M.; Lu, Z. The 2008 Phreatomagmatic Eruption of Okmok Volcano, Aleutian Islands, Alaska: Chronology, Deposits, and Landform Changes; State of Alaska Department of Natural Resources Division of Geological & Geophysical surveys Report of Investigations 2015-2; Alaska Division of Geological & Geophysical Surveys: Fairbanks, AK, USA, 2015; p. 53. [Google Scholar]
- Schaefer, J.R.; Larsen, J.F.; Unema, J.A. Digital Elevation Model (DEM) And Shaded Relief Image of Okmok Caldera, 2010. Available online: http://dggs.alaska.gov/pubs/id/23223 (accessed on 23 September 2015).
- Lu, Z.; Mann, D.; Freymueller, J. Satellite radar interferometry measures deformation at Okmok Volcano. Eos Trans. AGU
**1998**, 79, 461–468. [Google Scholar] [CrossRef] - Lu, Z.; Dzurisin, D. Ground surface deformation patterns, magma supply, and magma storage at Okmok volcano, Alaska, from InSAR analysis: 2. Coeruptive deflation, July–August 2008. J. Geophys. Res.
**2010**. [Google Scholar] [CrossRef] - Freymueller, J.T.; Kaufman, A.M. Changes in the magma system during the 2008 eruption of Okmok volcano, Alaska, based on GPS measurements. J. Geophys. Res.
**2010**. [Google Scholar] [CrossRef] - Patrick, M.R.; Dehn, J.; Papp, K.R.; Lu, Z.; Dean, K.G.; Moxey, L.; Lzbekov, P.; Guritz, R. The 1997 eruption of Okmok Volcano, Alaska: A synthesis of remotely sensed imagery. J. Volcanol. Geotherm. Res.
**2003**, 127, 87–105. [Google Scholar] [CrossRef] - Lu, Z.; Mann, D.; Freymueller, J.; Meyer, D. Synthetic aperture radar interferometry of Okmok volcano, Alaska-radar observations. J. Geophys. Res.
**2000**, 105, 10791–10806. [Google Scholar] [CrossRef] - Lu, Z.; Fielding, E.; Patrick, M.; Trautwein, C. Estimating lava volume by precision combination of multiple baseline spaceborne and airborne interferometric synthetic aperture radar: The 1997 eruption of Okmok volcano, Alaska. IEEE Trans. Geosci. Remote Sens.
**2003**, 41, 1428–1436. [Google Scholar] - Mann, D.; Freymueller, J.; Lu, Z. Deformation associated with the 1997 eruption of Okmok volcano, Alaska. J. Geophys. Res.
**2002**, 107, 7–13. [Google Scholar] [CrossRef] - Lu, Z.; Masterlark, T.; Dzurisin, D. Interferometric synthetic aperture radar study of Okmok volcano, Alaska, 1992–2003: Magma supply dynamics and post-emplacement lava flow deformation. J. Geophys. Res.
**2005**. [Google Scholar] [CrossRef] - Mogi, K. Relations between the Eruptions of Various Volcanoes and the Deformations of the Ground Surface around Them; Bulletin of the Earthquake Research Institute; University of Tokyo: Tokyo, Japan, 1958; pp. 99–134. [Google Scholar]
- Lu, Z.; Dzurisin, D.; Biggs, J.; Wicks, C.; McNutt, S. Ground surface deformation patterns, magma supply, and magma storage at Okmok volcano, Alaska, inferred from InSAR analysis: 1. Intereruption deformation between 1997 and 2008. J. Geophys. Res.
**2010**. [Google Scholar] [CrossRef] - Lu, Z.; Qu, F.; Dzurisin, D.; Kim, J. Post-2008 inflation of Okmok Volcano, Alaska, from InSAR. In Proceedings of 2014 AGU Fall Meeting, San Francisco, CA, USA, 15–19 December 2014.
- Fournier, T.; Freymueller, J.; Cervelli, P. Tracking magma volume recovery at Okmok volcano using GPS and an unscented Kalman filter. J. Geophys. Res.
**2009**. [Google Scholar] [CrossRef] - Sparks, R.S.J.; Biggs, J.; Neuberg, J.W. Monitoring volcanoes. Science
**2012**, 335, 1310–1311. [Google Scholar] [CrossRef] [PubMed] - Hooper, A.; Zebker, H.; Segall, P.; Kampes, B. A new method for measuring deformation on volcanoes and other natural terrains using InSAR persistent scatterers. Geophys. Res. Lett.
**2004**, 31, 611–615. [Google Scholar] [CrossRef] - Ferretti, A.; Prati, C.; Rocca, F. Permanent scatterers in SAR interferometry. IEEE Trans. Geosci. Remote Sens.
**2001**, 39, 8–20. [Google Scholar] [CrossRef] - Ferretti, A.; Fumagalli, A.; Novali, F.; Prati, C.; Rocca, F.; Rucci, A. A new algorithm for processing interferometric data-stacks: SqueeSAR. IEEE Trans. Geosci. Remote Sens.
**2011**, 49, 3460–3470. [Google Scholar] [CrossRef] - Berardino, P.; Fornaro, G.; Lanari, R.; Sansosti, E. A new algorithm for surface deformation monitoring based on small baseline differential interferograms. IEEE Trans. Geosci. Remote Sens.
**2002**, 40, 2375–2383. [Google Scholar] [CrossRef] - Werner, C.; Wegmuller, U.; Strozzi, T.; Wiesmann, A. Interferometric point target analysis for deformation mapping. In Proceedings of 2003 IEEE International Symposium on Geoscience and Remote Sensing, Toulouse, France, 21–25 July 2003.
- Lu, Z.; Zhang, L. Frontiers of radar remote sensing. Photogramm. Eng. Remote Sens.
**2014**, 80, 5–13. [Google Scholar] - Biggs, J.; Lu, Z.; Fourneir, T.; Freymueller, J. Magma flux at Okmok Volcano, Alaska from a joint inversion of continuous GPS, campaign GPS and InSAR. J. Geophys. Res.
**2010**. [Google Scholar] [CrossRef] - Moxey, L.; Dehn, J.; Papp, K.R.; Patrick, M.R.; Guritz, R. The 1997 eruption of Okmok volcano, Alaska, a synthesis of remotely sensed data. Eos Trans. AGU
**2001**, 82, 1375. [Google Scholar] - Miyagi, Y.; Freymueller, J.T.; Kimata, F.; Sato, T.; Mann, D. Surface deformation caused by shallow magmatic activity at Okmok volcano, Alaska, detected by GPS campaigns. 2000–2002. Earth Planet. Space
**2004**, 56, 29–32. [Google Scholar] [CrossRef] - Freymueller, J.T.; Fournier, T.; Kaufman, A.M. Deformation of Okmok volcano associated with its 2008 eruption. In Proceedings of 2008 AGU Fall Meeting, San Francisco, CA, USA, 15–19 December 2008.
- Zebker, H.A.; Villaseno, J. Decorrelation in interferometric radar echoes. IEEE Trans. Geosci. Remote Sens.
**1992**, 30, 950–959. [Google Scholar] [CrossRef] - Hooper, A. A multi-temporal InSAR method incorporating both persistent scatterer and small baseline approaches. Geophys. Res. Lett.
**2008**. [Google Scholar] [CrossRef] - Hooper, A.; Pedersen, R.; Sigmundsson, F. Constraints on Magma Intrusion at Eyjafjallajökull and Katla Volcanoes in Iceland, from Time Series SAR Interferometry; The VOLUME Project-Volcanoes: Understanding Subsurface Mass Movement; University College: Dublin, Ireland, 2009; pp. 13–24. [Google Scholar]
- Pinel, V.; Hooper, A.; De la Cruz-Reyna, S.; Reyes-Davila, G.; Doin, M.P.; Bascou, P. The challenging retrieval of the displacement field from InSAR data for andesitic strato volcanoes: Case study of Popocatepetl and Colima Volcano, Mexico. J. Volc. Geotherm. Res.
**2011**, 200, 49–61. [Google Scholar] [CrossRef] - Riddick, S.N.; Schmidt, D.A. Time-dependent changes in volcanic inflation rate near Three Sisters, Oregon, revealed by InSAR. Geochem. Geophys. Geosyst.
**2011**. [Google Scholar] [CrossRef] - Parker, A.L.; Biggs, J.; Lu, Z. Investigating long-term subsidence at Medicine Lake Volcano, CA, using multi-temporal InSAR. Geophys. J. Int.
**2014**, 199, 844–859. [Google Scholar] [CrossRef] - Hooper, H.; Segall, P.; Zebker, H. Persistent scatterer interferometric synthetic aperture radar for crustal deformation analysis, with application to Volcán Alcedo, Galápagos. J. Geophys. Res.
**2007**, 112. [Google Scholar] [CrossRef] - Hooper, A.; Zebker, H. Phase unwrapping in three dimensions with application to InSAR time series. JOSA A
**2007**, 24, 2737–2747. [Google Scholar] [CrossRef] [PubMed] - Summer, A.M. Post Eruptive Source Modeling for Okmok Volcano, Alaska using GPS and InSAR. Master’s Thesis, University of Alaska Fairbanks, Fairbanks, AK, USA, 2014. [Google Scholar]
- Zhao, C.; Qu, F.; Zhang, Q.; Zhu, W. A combined multi-interferogram algorithm for high resolution DEM reconstruction over deformed regions with TerraSAR-X data. J. Geodyn.
**2012**, 61, 148–153. [Google Scholar] [CrossRef] - Masterlark, T.; Feigl, K.L.; Haney, M.; Stone, J.; Thurber, C.; Ronchin, E. Nonlinear estimation of geometric parameters in FEMs of volcano deformation: Integrating tomography models and geodetic data for Okmok volcano, Alaska. J. Geophys. Res.
**2012**. [Google Scholar] [CrossRef] - Williams, C.A.; Wadge, G. The effects of topography on magma reservoir deformation models: Application to Mt, Etna and radar interferometry. Geophys. Res. Lett.
**1998**, 25, 1549–1552. [Google Scholar] [CrossRef] - Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P. Numerical Recipes in C: The Art of Scientific Computing, 3rd ed.; Cambridge University Press: Cambridge, UK, 2007; p. 994. [Google Scholar]
- Caricchi, L.; Biggs, J.; Annen, C.; Ebmeier, S. The influence of cooling, crystallization and re-melting on the interpretation of geodetic signals in volcanic systems. Earth Planet. Sci. Lett.
**2014**, 388, 166–174. [Google Scholar] [CrossRef]

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**MDPI and ACS Style**

Qu, F.; Lu, Z.; Poland, M.; Freymueller, J.; Zhang, Q.; Jung, H.-S.
Post-Eruptive Inflation of Okmok Volcano, Alaska, from InSAR, 2008–2014. *Remote Sens.* **2015**, *7*, 16778-16794.
https://doi.org/10.3390/rs71215839

**AMA Style**

Qu F, Lu Z, Poland M, Freymueller J, Zhang Q, Jung H-S.
Post-Eruptive Inflation of Okmok Volcano, Alaska, from InSAR, 2008–2014. *Remote Sensing*. 2015; 7(12):16778-16794.
https://doi.org/10.3390/rs71215839

**Chicago/Turabian Style**

Qu, Feifei, Zhong Lu, Michael Poland, Jeffrey Freymueller, Qin Zhang, and Hyung-Sup Jung.
2015. "Post-Eruptive Inflation of Okmok Volcano, Alaska, from InSAR, 2008–2014" *Remote Sensing* 7, no. 12: 16778-16794.
https://doi.org/10.3390/rs71215839