Using a Refined SBAS Algorithm to Determine Surface Deformation in the Long Valley Caldera and Its Surroundings from 2003-2010

Abstract

The Long Valley area and its surroundings are part of a major volcano system where inflation occurred in the resurgent dome in the 1990s. We used ENVISAT data to monitor surface deformation of the Long Valley area and its surroundings after the inflation, from 2003-2010. To retrieve the time series of the deformation, we applied the refined Small BAseline Subset (SBAS) algorithm which is improved using an iterative approach to minimize unwrapping error. Moreover, ascending and descending data were used to decompose the horizontal and vertical deformation in detail. To confirm refined SBAS results, we used GPS dataset. The InSAR errors are estimated as ${\pm}1.0mm/yr$ and ${\pm}0.8mm/yr$ from ascending and descending tracks, respectively. Compare to the previous study of 1990s over the Long Valley and its surroundings, Paoha Island and CASA geothermal area still subside. The deformation pattern in the Long Valley area during the study period (2003-2010) went through both subsidence (2003-2007) and slow uplift(2007-2010) episodes. Our research also shows no deformation signal near McGee Creek. Our study provided a better understanding of the surface changes of the indicators in the 1990s and 2000s.

1. Introduction

The Long Valley area and Mono Basin region in eastern California consist of four major volcano systems: the Mono Lake Volcanic Field, Mono-Inyo Chain, Long Valley Caldera, and Mammoth Mountain (Fig. 1). The Long Valley caldera has been active recently, with earthquake swarms and deformations occurring since the 1970s. Moreover, there was evidence for dike intrusion beneath Mammoth Mountain, which is also still active (Langbein, 2003; Hill and Prejean, 2005).

Fig. 1. Shaded relief map for Long Valley Caldera and surroundings. Volcano systems and fault area are labeled.

Apart from this volcanic activity, the most likely site for a future eruption in this area (based on the geologic record alone) is the Mono-Inyo volcano chain. It has produced some 20 eruptions at intervals ranging from 200 to 700 years, with the most recent eruption from Paoha Island in Mono Lake occurring 200-300 BP (Hill, 2006).

To investigate recent surface deformations at these four volcano systems, which are spread across huge area of more than 5,000 km², an efficient method is necessary. Therefore, we use Interferometric Synthetic Aperture Radar (InSAR) as the method to measure the surface deformations, due to its high spatial resolution and ability to acquire data remotely on a regular basis

Thatcher and Massonnet (1997) were first to study the Long valley area using an InSAR technique. The interferograms generated y the Eurpean Remote-Sensing Satellite (ERS)-1 and ERS-2 described surface deformations in the caldera using ground-based survey results. Langbein (2003) observed deformations using Electronic Distance Measurement(EDM) and leveling data over Long valley area. By comparing the InSAR and EDM results, InSAR can produce the same results as field geodetic surveys, at much better spatial resolutions. In addition, some studies using InSAR methods modeled various deformation sources to explain observed deformation patterns(e.g. Fialko and Simons, 2000)

Some researchers applied InSAR time-series algorithms, such as Persistent Scatterers Interferometry (Hooper et al., 2004) and Multiscale InSAR Time Series(Hetland et al., 2012), over the Long Valley area. However, these studies focused on the resurgent dome, which means it is difficult to analyze the entire deformation pattern in the Long Valley and Mono Basin region. Tizzani et al. (2007) investigated the surface deformations of the Long Valley caldera and the Mono Basin, using Small Baseline Subset (SBAS) approach to generate mean deformation velocity maps and displacement time series using ERS-1/2 data from 1992-2000. Our investigation method is similar to their work in this way; however, they made little mention of the Casa Diablo geothermal area within the Long Valley caldera because of a study previously conducted there (Howle et al., 2003). Our study is different because we used ENVISAT data from 2003-2010 to explain suface deforation in the Long Valley area, and examined ascending and descending data for a more detailed consideration of the horizontal and vertical deformation.

The aim of this study is to provide an overview of the surface deformations that occurred in the Long Valley and the surrounding regions in 2003-2010. We applied Differential InSAR (DInSAR) technique followed by the SBAS method to determine a time series for the deformations. This paper is structured as follows: first, the refined SBAS algorithm is described based on key improvements in our study compared to the traditional SBAS technique. Second, we evaluate the SBAS result based on GPS data. Third, we analyze the data separated into two parts: one for the Long Valley area and another for its surroundings. Finally, the last section presents comparison of the surface deformations, focusing on the period before and after 2000.

2. Introduction to the refined Small Baseline Subset (SBAS) approach and Data processing

We applied the Small Baseline Subset (SBAS) approach to examine how deformation near the Long Valley and surroundings has been changed over time. The advantages of this method include the use of multilook images over large spatial scales.

1) A short description of SBAS

The SBAS algorithm has previously been used to obtain time-series deformation (Berardino et al., 2002). The most important step in the use of this algorithm, conceptually, is to select data with smal baselines, in ordr to mitigate spatial and temporal decorrelation. The algorithm then uses singular value decomposition (SVD) from temporally disconnected differential interferograms to link adjacent interferograms. It also adopts spatially low-pass and temporally high-pass filters to mitigate atmospheric effects.

Although the SBAS algorithm is effective method to determine the time series of the deformations, this method relies on the use of unwrapped differential interferograms. However, some unwrapping errors lead to mistakes in the estimation of the actual time-series of the deformations. In addition, atmospheric artifacts and orbital errors at the reference points have not been properly considered (Lee et al., 2010).

With this as a background, we applied refined the SBAS algorithm (Jung et al., 2008)to the Long Valley and its surroundings. To sum up the modified processing method of the original SBAS InSAR algorithm in the following:

1. All InSAR interferograms were divided into High Quality (HQ), which are those with no unwrapping errors, and Low Quality (LQ), which were those had low coherence as well as obvious unwrapping errors, such as phase jumps. This is more precise estimation of the mean deformation rate through the use of the HQ interferograms. Thus, we are able to more precisely estimate topographic errors and atmospheric artifacts reduce errors in the residual phase.

2. An iterative approach was applied. The SBAS algorithm frst estimated the atmospheic artifacts and topographic errors using the initial mean deformation rate, and then it calculated the time-series deformation. The algorithm then estimated atmospheric artifacts and topographic errors using time-series deformation data from the first iteration instead of the initial mean deformation rate. This approach thus efficiently separates the atmospheric artifact and the topographic errors from the final data and improves the time-series deformation.

3. The finite-difference smoothing approach (Schmidt and Bürgmann, 2003) was applied to suppress the time-varying noise component of the surface deformation.

4. The reference phase correction was refined using several iterative steps. The initial reference phase correction was applied to the unwrapped residual interferograms, and was performed by removing the mean of the unwrapped residual interferograms and the bias caused by atmospheric artifacts. The initial phase corrections have small biases, but these can be corrected through the iterative process by which the atmospheric artifacts and topographic errors are refined.

5. GPS corrections were made to resolve phase jumps that occur in the time series deformation, for periods that do not include SAR acquisition times because of insufficiencies in unwrapped differential interferogram pairs that the SBAS algorithm uses.

2) Data Processing

To study the ground surface deformation that occurred from 203-2010, we obtained 26 and 28 SAR mages from the ascending and descending tracks, respectively, of the European Environmental Satellite (Envisat). We selected pairs with perpendicular baselines of less than 350 m and distributed these between two small-baseline subsets (Fig. 2). All the interferograms were obtained using a complex multi look operation with 2 range and 10 azimuth looks, resulting in a pixel dimension of about 40 m by 40 m. We applied the DInSAR technique to a 1 arc second digital elevation model (DEM) from the National Elevation Dataset (NED). We separated differential interferograms into HQ and LQ images(Table 1, Table 2), and applied the SBAS processing algorithm to 33 and 38 interferograms from satellite tracks 485 and 120, respectively. Moreover, as the Mammoth mountain area commonly has a low coherence because of snow, we stacked images corresponding to good coherence.

Table1. ENVISAT SAR interferograms (trackno.485, Descending)

^*High-Quality (HQ) Pair.

¹⁾Bperp: Perpendicular Baseline.

²⁾Btemp: Temporal Baseline.

Table 2. ENVISAT SAR interferograms (track no.120, Ascending)

^*High-Quality (HQ) Pair.

¹⁾Bperp: Perpendicular Baseline.

²⁾Btemp: Temporal Baseline

Fig. 2. Perpendiculr baselines used for small baseline subset (SBAS) InSAR processing. Two different small baseline subsets from (a descending and (b) ascending tracks.

3. Results from Interferometric Synthetic Aperture Radar (InSAR) analysis

First, we quantitatively assessed the SBAS result to examine the deformations in the Long Valley and its surroundings and then present the geocoded ascending/descending InSAR mean deformation velocity map with a shaded relief of the DEM in the study area. This format allowed us to discriminate the vertical and horizontal components of displacement. To provide detailed consideration of local deformations, we discuss two parts of Long Valley and surroundings separately.

1) Comparing InSAR results with GPS measurements

We compared the mean deformation rate of the refined SBAS and GPS data to confirm and validate our InSAR result. There are about 30 GPS stations within the study area, where InSAR data are not available because of decorrelation. We therefore carried out a comparison using 17 and 20 stations for pixels from the descending and ascending tracks, respectively (Fig. 3).

Fig. 3. InSAR mean LOS deformation rate map (a) descending and (b) ascending tracks, respectively with shaded relief of the DEM. The pixel identified by the grey rectangular represented fully overlapping time interval between GPS and InSAR. However, the pixel identified by the black triangle represented 2-4 year verlapping time interval.

First, we projected the 3D GPS displacement vectors into the deformations in the InSAR line-of-sight(LOS) direction and estimated the mean InSAR deformation rate corresponding to a nearby GPS station. Fig. 4 compares the line-of-sight deformation rate between the GPS and SBAS approaches. The InSAR errors are estimated as ±1.0 mm/yr and ±0.8 mm/yr from ascending and descending tracks, respectively. Moreover, the standard deviation values of the SAR and GPS deformation time series differences correspond to 3.0 mm and 2.6 mm from ascending and descending tracks, respectively. These values are smaller than the standard deviation of about 5 mm computed by comparing an InSAR deformation times series with GPS measurements (Casu et al., 2006).

Fig. 4. Comparison of mean deformation from InSAR and GPS at 37 GPS station on Long Valley Caldera and surroundings. Moreover, dashed line represents one to-one correspondence. Vertical and horizontal bars denote uncertainties of SBAS deformation rate and GPS deformation rate, respectively. Bias between ascending and descending data means plate movement to the east direction.

Accordingly, it is evident from these results that the SBAS algorithm can provide a deformation time series with a less than sub-centimetric accuracy. The comparison result presented in Fig. 5 shows a good agreement between the InSAR and GPS measurements (the red triangles and blue brs, respectively).

Fig. 5. Comparison between the time series of InSAR deformation in LOS direction (red triangle) and the corresponding GPS measurement projected on the LOS direction (blue) labeled as “Watc” in descending (Fig. 5a) and ascending (Fig. 5b), “Hotk” in descending (Fig. 5c) and ascending (Fig. 5d), “Krac” in descending (Fig. 5e) and ascending (Fig. 5f), “Rdom” in descending (Fig. 5g) and ascending (Fig. 5h).

2) Creation of a deformation rate map of the study area

Ascending and descending InSAR and GPS deformation rates have opposing values because of plate movement (Fig. 3, Fig. 4). To focus on local deformations and remove plate movement, we computed the ascending and descending rates of deformation rate with respect to a reference pixel (represented by a black star) with a stable deformation rate (only plate movement), and created a deformation rate map by fully overlapping this time with InSAR data (Fig. 6a, 6b). After that, ascending and descending deformation rates allowed us to retrieve the horizontal and vertical displacement components (Wright et al., 2004).

Fig. 6. Mean deformation map with shaded relief of the DEM of investigated zone. (a) InSAR mean LOS deformation velocity map for ascending track. (b) InSAR mean LOS deformation velocity map for descending track. (c) InSAR mean horizontal deformation velocity map (d) InSAR mean vertical deformaton velocity map. Note that all pixels calculated with respect to WATC GPS station which was labeled in (a) and (b).

Thus, we were able to observe significant horizontal and vertical displacements on the coherent areas located in the Huntoon fault area (Fig. 6c), Paoha Island and CASA Geothermal area in the Long Valley (Fig. 6d), respectively. There is a slight subsidence of the resurgent dome in the Long Valley caldera.

3) Deformation in the Long Valley area

The maximum uplift of the resurgent dome in the Long Valley area, which measured more than 40 cm, was recorded by two-color EDM surveys and leveling data from mid-1983 to mid-1998. The rates sometimes exceeded 1 cm/yr, and most models of the deformation had a 5-8 km source beneath the resurgent dome (Dzurisin, 2006). Our study paid great attention to this inflation, and provides information on the deformation in the Long Valley area a decade afterthe inflation was surveyed.

(1) The Long Valley resurgent dome

We created a time series deformation using the SBAS method and we could solve for the source volume change. A Mogi model (Mogi, 1958) was applied to each set of time series data in the resurgent dome. Therefore, we produced 19 and 14 Mogi model results from descending and ascending tracks, respectively.

Because of the trade-off between depth and volume change, we fixed the depth at 8.2 km (Feng and Newman, 2009). Then we excluded CASA geothermal area becaus it interrupted the modeling results. The results clearly show that subsidence is the general trend. We also estimated volume change per year using the least squares method because all the interferograms are from SAR images acquired from summer to fall. We weighted the solutions using the standard deviation for each modeled interferogram, producing a time series of cumulative volume change from 2003-2010 (Fig. 7). Overall, the volume changes inferred were -0.0168 km³ of deflation and 0.0020 km³ of inflation for 2003-2007 and 2007-2010, respectively.

Fig. 7. Estimated cumulative volume changes of resurgent dome in the Long valley caldera.

(2) CASA geothermal plant area

There is a clear subsidence trend in CASA geothermal area on the vertical velocity map (Fig. 6d). The result shows continuous subsidence, and the LOS deformation rates are estimated at -12.9 mm/yr and - 12.6 mm/yr from ascending and descending tracks, respectively (Fig. 8a). Subsidence mechanisms have varied over time with changes in the geothermal fluid production, injection depth, and corresponding transient reservoir response (Howle et al., 2003). One simple kinematic description of this subsidence is to consider the geothermal field as a collapsing sill corresponding to the vertical collapse due to thermal contraction and similar collapses due to pressure drops in horizontal cavities (Langbein, 2003). To estimate source depth considering the gothermal field as a collapsing sill, therefore, we fixed the dip angle as zero for Sill modeling. The source depth was obtained from joint modeling proceures using the ascending and descending deformation rates. First, we used forward models to identify initial parameters; then, we applied an iterative simulation until no further improvement was made. The estimated source depth is about 1 km, which coincides with the production and injection depth of the CASA geothermal plant (150-700m).

Fig. 8. (a) InSAR LOS time series deformation for the pixels marked by the white triangles labeled in Fig 6d lower at CASA geothermal plant area (b) InSAR LOS time series deformation for the pixels marked by the white triangles labeled in Fig 6d upper at Paoha Island.

4) Deformation in the surroundings of the Long Valley area

(1) Paoha Island

Paoha Island is volcanic island in Mono Lake north of the Mono-Inyo Chain. Its northern side includes significantly vertical subsided lava domes (Fig. 6d). The continuous subsidence and LOS deformation rates are estimated about-10 mm/yrfrom both the ascending and descending tracks (Fig. 8b). The phenomenon has already been reported the previousstudy (Tizzani et al., 2007). The main reason for the subsidence is the accumulation of different lithologies sediments (lavas and landslides sediments).

(2) Huntoon Valley fault area

The Huntoon Valley is a fault bounded basin within the Excelior Mountains. The valley trends northeast for ~16 km and is bounded by the Adobe Hills to the southeast(Wesnousky, 2005).There is little geophysical instrumentation in the vicinity of this area. However, earthquake information could be retrieved using SAR datasets. Fig. 6c shows horizontal movement associated with a magnitude 5.5 earthquake on September 18, 2004 near the Huntoon Valley fault. This information was already reported in detail in a previous study (Lee et al., 2017). To summarize: the surface deformation was about 1.5 and 1.0 cm in horizontal direction and vertical direction, respectively. There were also differing opinions on the origin of the Huntoon earthquake. Although the crack shows tectonic patterns, the deformation of this region sometimes is associated with volcanic unrest (Tizzani et al., 2007).

(3) Mammoth Mountain

Mammoth Mountain is located on the southwestern rim of the Long Valley caldera (Fig. 6c). Episodic volcanic unrest has been detected beneath the mountain since late 1979, and volcanic system is still active and capable of producing future eruptions(Hill and Prejean, 2005). Mammoth Mountain has heavy winter snowfall and this, in combination with the varied terrain of the mountain (including its position and summit of over 3,000 m), supports one of the largest ski areas in the United States (Hill and Prejean, 2005). For these reasons, it seems reasonable to assume that the data is not very coherent in this area. Furthermore,the duration of an interferogram is limited by temporal decorrelation, making it difficult to find an interferogram covering a sufficiently long time period. Unfortunately, we could not estimate deformation using the SBAS approach in the Mammoth Mountain area. Therefore, we stacked 10 and 12 pairs from the descending and ascending tracks, respectively (Table 1, Table 2), which had good coherence. Moreover, by stacking the interferograms according to the percentage of coherent pixels and adding them successively to the stack, we acquired enough spatial coverage for Mammoth Mountain area (Biggs et al., 2007).

Fig. 9 shows the mean deformation rate of the Mammoth Mountain area. Significantly, it is first time that 2D deformation has been observed. The north side of this area has a subsidence deformation of about - 5mm to about -6 mm/yr in stacking data (Fig. 9a, 9b). Furthermore, GPS results show that the Mammoth Mountain area has subsidence of about-3 mm to about -4 mm/yr in the LOS project (Fig. 9c, 9d). The difference between the InSAR and GPS data is based on GPS discontinuation. This subsidence signal has been associated with the Mammoth Mountain Fumarole (MMF), considering its location (Fig. 9a). A Mogi model is applied to InSAR velocity map to estimate deformation source depth. As a result, the depth of the deformation source was estimated to be about 3 km. From this shallow depth, it seems reasonable to assume that subsidence is related to the MMF.

Fig. 9. InSAR mean deformation rate with shaded relief of the DEM from (a) descending and (b) ascending tracks, respectively. GPS mean deformation rate from (c) descending ad (d) ascending parameters, respectively. GPS position is marked as white rectangle and labeled as LINC. (e) Number of earthquake in the time period of between 2003 and 2010 in the rectangular area.

To verify the seismic activity of the Mammoth Mountain area, we compiled the location and moment magnitude of earthquakes that occurred from 2003- 2010 based on data from the Double-Difference EarthquakeCatalog for Northern California (Waldhauser and Schaff, 2008), which has a completeness of above 0.8 (Wiemer and Wyss, 2000) in the rectangular area shown in Fig. 9a. It is highly probable that an earthquake swarm occurred at less than 6 km depth in the second half of 2006 and the first half of 2007 (Fig. 9e). The Earthquake swarm had magnitudes less than 2 above the completeness threshold of 0.8.

4. Comparing the deformations detected using InSAR: before and after 2000

Our analysis indicates that the Long Valley and its surroundings have been undergoing variety of surface deformations. We focus our attention on comparisons of our results with the surface deformations reported from 1992-2000.

1) Continuous surface deformation before and after 2000

Compared to the surface deformation of the 1990s, there is a resemblance in the deformation patterns in Pahoa Iland and the CASA geothermal area over the two decades of monitoring. Tizzani et al. (2007), who conducted the first investigation of the subsidence on Paoha Island, found that there is a significant continuous subsidence of the lava domes in the northern side zone, of about -1.0 cm/yr along the LOS, and our research shows an equivalent rate of subsidence. The CASA geothermal area has been experiencing continuous subsidence deformation, except for a period in 1998-1999, of about -1.0 cm/yr from 1992-2000 and about-1.2 cm/yr from 2002-2010, respectively, according to InSAR data.

2) Contrast between the period before and after 2000

There have been several studies on the resurgent dome in the Long Valley Caldera, based on surface deformation determined using geodetic data; however, we mainly compare and contrast data on the surface deformation using the analysis of Tizzani et al. (2007) and our own work. First of all, the deformation of resurgent dome pattern was clearly characterized by a sequence of three different events: a 1992-1997 uplift, unrest in 1997-1998, and a subsidence phase from 1998-2000. However,the deformation pattern determined in our study shows a subsidence from 2003-2007 and a slow uplift from 2007-2010. This deformation pattern coincides with GPS analysis (Fig. 5g, 5h).

Second, as Tizzani et al. (2007) observe from previously unreported local deformation, the McGee Creek within the Sierra Nevada Mountains was characterized by subsdence deformation from 1998-2000. Our research, however, shows no signal near the McGee Creek; this is likely because this subsidence was related to slope instability as a temporary phenomenon.

5.Conclusion

This paper has attempted to sketch out the surface deformation in the wide (5,000 km2) Long Valley area and its surroundings. We conducted time-series deformation analysis based on SBAS algorithm using ascending and descending ENVISAT data from 2003-2010.

To achieve research objectives, first, we presented a comparison between the InSAR measurements made using the SBAS technique and GPS data and confirmed the validity of our results. Second, we comparing the deformations detected using InSAR before and after2000. Continuous surface deformation has been observed in CASA geothermal and Paoha Island area. On the contrary, in the resurgent dome and McGee Creek area, different patterns were observed before and after 2000. Also, the unreported 2D surface deformation pattern was observed over Mammoth Mountain area.

Through this study, we observed and compared two decades surface changes in the Long Valley and surroundings. Due to the volcanic activities in the area, various surface deformations are continuously occurring. Therefore, continuous observations will be needed and remote sensing is one of the efficient methods for monitoring wide area.