Routine Processing and Automatic Detection of Volcanic Ground Deformation Using Sentinel-1 InSAR Data: Insights from African Volcanoes

Abstract

Since the launch of Sentinel-1 mission, automated processing systems have been developed for near real-time monitoring of ground deformation signals. Here, we perform a regional analysis of 5 years over 64 volcanic centres located along the East African Rift System (EARS). We show that the correction of atmospheric signals for the arid and low-elevation EARS volcanoes is less important than for other volcanic environments. We find that the amplitude of the cumulative displacements exceeds three times the temporal noise of the time series (3$\sigma$) for 16 of the 64 volcanoes, which includes previously reported deformation signals, and two new ones at Paka and Silali volcanoes. From a 5-year times series, uncertainties in rates of deformation are ∼0.1 cm/yr, whereas uncertainties associated with the choice of reference pixel are typically 0.3–0.6 cm/yr. We fit the time series using simple functional forms and classify seven of the volcano time series as ‘linear’, six as ‘sigmoidal’ and three as ‘hybrid’, enabling us to discriminate between steady deformation and short-term pulses of deformation. This study provides a framework for routine volcano monitoring using InSAR on a continental scale. Here, we focus on Sentinel-1 data from the EARS, but the framework could be expanded to include other satellite systems or global coverage.

1. Introduction

Interferometric Synthetic Aperture Radar (InSAR) can routinely produce ground displacement maps over large areas. Current satellite missions, especially Sentinel-1, are well-suited for carrying out deformation surveys on the scale of entire plate boundaries, which would not be feasible with ground-based stations. Previous large-scale surveys have mostly been retrospective analyses of strain accumulation in tectonically active regions such as Tibet [1] and Anatolia [2,3], and surveys of volcanic unrest [4,5,6,7,8,9].

The availability of SAR datasets has increased dramatically over the past decade. In particular, the open-access policy of the Sentinel-1 mission opened new perspectives for the near real-time monitoring of ground deformation at global and regional scales [3,9,10,11]. This has been supported by the development of automated processing platforms that now produce large databases of InSAR products: ARIA (NASA Jet Propulsion Laboratory), SARVIEWS (University of Alaska Fairbanks), Geohazards Exploitation Platform (European Space Agency), and LïCSAR (COMET) [12,13,14,15].

Satellite observations are particularly critical for sub-saharan Africa, where the resources to deploy and maintain a dense network of ground-based stations are limited. The East African Rift System (EARS) contains 78 volcanoes considered active during Holocene [16]. Population exposure is high, particularly in Ethiopia and Kenya, where over 70 million people live within a 100 km radius of a Holocene volcano [17]. InSAR regional surveys using the ERS (1997–2000) and ENVISAT (2003–2010), satellites improved our knowledge of the dynamics of the EARS magmatic systems [7,8]. However, these early missions were not designed for continuous monitoring, and the dataset had low temporal resolution (3–4 images per year) and many gaps. More recently, [9] analysed Sentinel-1 data over 64 Holocene active volcanoes along the EARS between October 2014 and January 2020 and detected ground deformation signals at 14 volcanic centres.

Here, we discuss the best practices for using Sentinel-1 SAR data for the automatic production of time series and the characterisation of volcanic ground deformation signals, using the EARS as a case study (Figure 1). First, we describe the methodological developments that support the routine production of Sentinel-1 InSAR time series. We then analyse the 64 EARS volcanoes to assess the benefit of atmospheric corrections for rift volcanoes and estimate the uncertainties on the mean line-of-sight (LOS) velocities. We apply a threshold based on the noise level at each volcano to detect deformation and classify the resulting time-series using simple functional forms. Finally, we discuss the implications for this regional study for global volcano monitoring, in terms of the limits of detection and classification.

2. Materials and Methods

In this section, we describe the methods used for the automated processing and classification of Sentinel-1 data over the 64 volcanoes of the EARS (Figure 1). We start by describing the processing of the Sentinel-1 data, and our approach to atmospheric corrections and reference frame selection. We then describe the methods used to analyse the set of time-series, including the automatic detection and classification of deformation signals.

2.1. Pre-Processing of Sentinel-1 Data

Sentinel-1 is a C-band imaging radar mission operated by the European Satellite Agency (ESA) through the Copernicus programme. The constellation consists of two satellites: Sentinel-1A (launched 3 April 2014) and Sentinel-1B (launched 25 April 2016). However, an anomaly occurred on Sentinel-1B satellite on 23 December 2021 and the end of the Sentinel-1B mission was announced by ESA and the European Commission on August 2022. In Africa, revisit time of Sentinel-1 acquisitions is 12 days during the 2017–2021 period and 24 days otherwise. Differential Interferometric Synthetic Aperture Radar (DInSAR) consists of computing the phase difference between two SAR images of the same geographical location acquired at different times [18]. The processing of SAR images produces (i) wrapped interferograms which contain ambiguous phase values between $-\pi$ and $\pi$, (ii) unwrapped interferograms which contain continuous phase values relative to a reference pixel and (iii) coherence maps, which indicate the degree of decorrelation of ground targets.

We generate Sentinel-1 interferograms and coherence maps using the LïCSAR processing system [15], which is built on the GAMMA software package [19] (Figure 1a). Our dataset spans a 5-year period (2015–2020) and consists of a total of 3570 interferograms covering 64 Holocene active volcanoes from the Eastern Branch of the African Rift system, including Ethiopia, Kenya and Tanzania (Table S1). All InSAR products are freely available at https://comet.nerc.ac.uk/comet-lics-portal/ (accessed on 25 October 2022). The LïCSAR system automatically generates the 3–4 shortest temporal baseline interferograms at a spatial resolution of 0.001° (∼111 m at the equator) [15]. To reduce the computing time for the time series analysis, we first crop all the LïCSAR products to a geographical region 0.5° × 0.5° centred on the location of each volcano derived from the Smithsonian catalogue [16] (Figure 1a).

A small proportion of the automatically-generated interferograms have poor quality due to processing issues (e.g., missing data, co-registration errors) or limitations of the InSAR method (e.g., temporal decorrelation). We apply a quality test based on two criteria calculated on the cropped area: (1) the mean coherence and (2) the fraction of pixels unwrapped (Figure 1a). We select images with average coherence exceeding 0.05 and the fraction of pixels unwrapped exceeding 0.2. The aim is to remove images that contain no information due to issues in the processing. For example, among the 294 total interferograms processed at Fentale volcano, only six did not pass the quality test (Figure S1 in Supplementary Materials). For the total dataset, the proportion of rejected interferograms is <8% (Figure S2 in Supplementary Materials).

2.2. Atmospheric Noise

Changes in the atmospheric conditions (mostly pressure and water vapour) between two SAR acquisitions cause phase delays in an interferogram that can potentially mask real ground deformation signals. The impact of these atmospheric signals is expected to be most significant for InSAR measurements in regions with high-relief, as large elevation gradients may cause strong stratified signals, and for regions located in tropical climates where large spatio-temporal variations of water vapour content may induce turbulent signals. Topographically-correlated atmospheric signals have been identified at many high-elevation stratovolcanoes, including arc volcanoes located in tropical regions such as Central America and Indonesia [20,21,22] and continental volcanoes such as Etna (Italy) and Hasan Dagi (Turkey) [23,24]. These topography-dependent signals can be reduced using (1) empirical methods based on the correlation between phase and elevation [23,25,26] and (2) weather-based models [22,27,28,29,30], which have the ability to correct both topographically-correlated and long-wavelength turbulent components.

Although much of the EARS is located in the tropics, most of the volcanoes are low relief and lie in desert and semi-arid climates [31]. More than 80% of the EARS volcanoes have relief <1000 m, with height average value of ∼690 m in Afar, ∼340 m in the Main Ethiopian Rift (MER) and ∼650 m in the Tanzania-Kenya rift (Figure S3 in Supplementary Materials). Previous InSAR studies have reported no obvious atmospheric errors in the MER and Kenya-Tanzania rift [8,32] whereas significant atmospheric noise has been reported in the Afar region [33,34].

We calculate the coefficient of determination, $R^2$, between the interferometric phase and the elevation for each of the >4000 unwrapped interferograms processed (Figure 1b). For each volcano, we then calculate the cumulative distribution function (CDF) of the $R^2$ values for each region (Figure 2a–c). CDF curves located close to the top-left corner of the plot correspond to volcanoes that typically present a low phase-elevation correlation while CDF curves that plot close to the diagonal correspond to volcanoes with a uniform distribution of $R^2$ values.

2.3. Reference Frame

Differential interferometry measures relative displacement, meaning the choice of reference frame has an influence on the time-series and velocity estimates. Possible choices for the reference value include: (i) a single pixel or an average of a region [27,35] located far from the deformation area and coherent in time, (ii) the average value of each unwrapped interferogram [36], (iii) the average of an annulus centred on the volcano summit [20], (iv) the evaluation of all pixels outside the volcanic area as a potential reference [21].

The first approach is based on an arbitrary choice. The second one is based on the assumption of zero mean deformation, which is not appropriated for volcanic areas with potential long-lived surface deformation. The third approach was designed for volcanoes in order to reduce the effect of small-scale atmospheric variations on the time series. However, the method only works for symmetrical edifices with a clearly-identified summit (e.g., stratovolcanoes, cones) and is not suitable for many of the volcanic centres located in the East African Rift.

For these reasons, we chose the method developed by [21] as it provides several advantages for our study: it is well-suited for automation, it minimises the effects of local atmospheric artefacts and it provides an estimate of the associated uncertainty (Figure 1c). We consider all pixels located more than 20 km from the volcano summit as a potential reference pixel to ensure that those are not affected by any ground deformation. Then, we derive the distribution of the corresponding LOS velocity estimates at the centre of the volcano. We select a pixel associated with the peak of the distribution as the reference point. The standard deviation of this distribution, ${\sigma }_{ref}$, is a measure of the uncertainty in the LOS velocity estimate, and we will henceforth refer to it as the ’reference uncertainty’.

2.4. Time Series Characterisation

We produce time series of ground displacements using the classic least-squares approach [35,37] with no temporal filtering applied (Figure 1d). For each volcano, time series are automatically generated at two specific points: (i) the point A, chosen outside the volcanic area and (ii) the point B corresponding to the location where cumulative displacements are maximum in the volcanic area (Figure S4 in Supplementary Materials). For each volcano, we calculate (1) the temporal standard deviation of the time series at the point A, ${\sigma }_A$, which characterises the noise level and (2) the modulus of the cumulative LOS displacement at the point B, $|A_B|$, which characterises the amplitude of the signal (Figure 1d).

2.4.1. Time Series Functions

For those volcanoes showing deformation signals, we fit the time series, $U\left(t\right)$ in the point B by using two simple models: a linear function to represent steady-state deformation and a sigmoid function to represent transient deformation. These are not intended to reflect the underlying geophysical processes but are a simple way to parametrize and compare a range of signals (Figure 1d). The functions are chosen to have a small number of unknown parameters (2–3) and the ability to approximate a range of behaviours.

The linear function, $U\left(t\right)=vt+U\left(0\right)$, has two parameters with v corresponding to the mean velocity. The sigmoid function

$$U\left(t\right)=\frac{U_{max}}{1+e^{-\left(\frac{t-t_c}{\tau }\right)}}$$

(1)

has three parameters: $U_{max}$, the maximum displacement at $t=\infty$, $\tau$ is the characteristic time and $t_c$ is the time at the centre of the sigmoid. We consider the time period between $t=t_c-2\tau$ and $t=t_c+2\tau$, which contains 76% of the total displacements $U_{max}$, as a proxy of the period of unrest.

For each time series, we calculate the $R^2$ for the linear and sigmoid functions. For those time series where both linear and sigmoid models provide an acceptable fit ($R^2>0.5$), we then use Akaike’s Information Criterion ($AIC$) [38] to compare the goodness of fit while accounting for the different number of model parameters. Since $AIC$ is a relative measure, we quote the value $\Delta AIC=AI{C}_{sigmoid}-AI{C}_{linear}$ and assume that the errors have independent identical normal distributions, such that

$$\Delta AIC=(nln\frac{RS{S}_s}{n}+2k_s)-(nln\frac{RS{S}_l}{n}+2k_l)$$

(2)

where n is the number of data in the time series, $RSS$ is the residual sum of squares, and k is the number of model parameters. The subscripts l and s correspond to the linear and sigmoidal models, respectively. Here, $k_l=2$ and $k_s=3$, the expression can be simplified as:

$$\Delta AIC=n(ln\frac{RS{S}_s}{RS{S}_l})+2$$

(3)

If $\Delta AIC<<0$, the best model is the sigmoid and, if $\Delta AIC>>0$, the best model is linear. For $-10<\Delta AIC<10$, the two models are roughly equivalent, and we select the linear model for simplicity.

2.4.2. Velocity Uncertainties

We then evaluate the LOS velocity uncertainties in the Sentinel-1 time series for our EARS dataset by looking at the time series for the volcanoes that show a continuous linear trend. The standard deviation of the LOS velocity is derived using the percentile bootstrap method [39]. The method consists of computing the distribution of the velocity using a random selection of N resampled datasets with data replacement (here, we chose N = 100). The standard deviation of the velocity is then calculated for different duration from 1 to 5 years.

Regional and global analysis of geodetic time series have showed that velocity uncertainties ${\sigma }_v$ decrease with the duration of the time series $\Delta t$, following a power-law function ${\sigma }_v=\Delta t^{-b}$ [40,41,42]. The parameter b corresponds to the decay rate, and it usually ranges between 1 for flicker noise (correlated) and $\frac{3}{2}$ for pure white noise (uncorrelated). For two previous studies using Sentinel-1 InSAR dataset, such power-law relationships have been modelled with a decay rate corresponding to white noise ($b=\frac{3}{2}$) [3,43].

3. Results

3.1. Atmospheric and Reference Frame Uncertainties

The EARS volcano dataset shows a low correlation between elevation and the phase of the interferograms. We found that (i) the coefficient of determination, $R^2$, has an average value of 0.2 and (ii) only 15% of the interferograms processed show a $R^2>0.5$. As an illustration, Figure 3a shows one interferogram containing a strong stratified signal from Silali volcano. An empirical model based on the linear correlation between phase and elevation ($R^2$ = 0.8) largely removes the atmospheric signal (Figure 3b,d) and the residuals after correction have a standard deviation of <2 cm (Figure 3c). Figure 3e shows one interferogram containing low atmospheric signal from Suswa volcano. Here, the empirical model based on the phase-elevation correlation ($R^2$ = 0.04) does not improve the quality of the data (Figure 3f,h) and the corrected interferogram is very similar to the original interferogram (Figure 3g).

To avoid over-correcting any real deformation signals, we only apply the empirical phase-elevation corrections at volcanoes for which many interferograms show high correlation. We chose to apply phase-elevation corrections at volcanoes for which more than 20% of interferograms have a correlation coefficient larger than 0.5 [CDF(R${}^2$ = 0.5) < 0.8] (Figure 2a,c—red lines). This corresponds to only 15 of the 64 volcanoes processed (23%) (Figure 2d,e): seven volcanoes in Afar (Alid, Ma-Alalta, Dabbayra, Manda-Gargori, Asavyo, Nabro and Dubbi), three in the Main Ethiopian Rift (Bishoftu, Butajiri-Silti field and Tullu Moye) and five in the Kenyan-Tanzania Rift (Emuruangogolak, Silali, Paka, Korosi and Ol Doinyo Lengai). For Afar and the MER, we notice that the volcanoes that require corrections are mostly located at the margin of the rift (Figure 2d), where the relief of the border faults rather than the topography of the volcanic edifice generates the topographically-correlated signal. Our statistic analysis confirms that atmospheric noise is generally low for the EARS volcanoes and consequently atmospheric corrections are not a critical step for the detection of volcanic ground deformation signals.

Reference frame uncertainties vary widely among the EARS volcanoes with values ranging between 0.18 cm/yr (Groppo) and 1.65 cm/yr (Gufa) with an average of ∼0.5 cm/yr (Figure 4d, Tables S1–S3 in Supplementary Materials). Figure 4a–c shows example histograms from Dallol (0.4 cm/yr), Nabro (0.8 cm/yr) and South Island (1.6 cm/yr). Two thirds of the 64 EARS volcanoes studied have reference uncertainties between 0.3 $<{\sigma }_{ref}<$ 0.6 cm/yr. The four end-members (Alid, Gufa, South island and The Barrier) with reference uncertainties greater than 1 cm/yr (Figure 4e) are volcanoes that have the smallest number of interferograms processed (Figure S2 in Supplementary Materials).

3.2. Analysis of Deformation Signals

3.2.1. Signal-To-Noise Ratio

We plot the amplitude of the signal ($|A_B|$) as a function of the temporal noise (${\sigma }_A$) for each of the 64 volcanoes processed (Figure 5). The noise level ${\sigma }_A$ is similar between the three EARS regions, with mean values of 1.4 ± 0.5 cm, 1.2 ± 0.4 cm, and $1.4\pm 0.5$ cm (1$\sigma$) for Afar, MER and Kenya-Tanzania, respectively (

Table 1. Statistical values (mean, median, standard deviation, minimum and maximum values) associated with the temporal noise ${\sigma }_A$ for each of the three EARS regions (Afar, MER, Kenya-Tanzania). Units are in centimetres.

Region	Nb of Volc.	Mean	Median	Std	Min/Max
Afar	31	1.4	1.3	0.5	0.7/2.8
MER	16	1.2	1.1	0.4	0.2/2.2
Kenya-Tanzania	17	1.4	1.4	0.5	0.4/2.2

).

For volcanoes which did not deform, the amplitude of the signal is the same order of magnitude as the noise level (e.g., Gedamsa: $|A_B|$ = 0.9 cm and ${\sigma }_A$ = 1 cm) (Figure S4a–c in Supplementary Materials). For volcanoes that did deform, the amplitude of the signal is much higher than the temporal noise (e.g., Tullu Moje: $|A_B|$ = 14.7 cm and ${\sigma }_A$ = 1 cm) (Figure S4d–f in Supplementary Materials).

We evaluate two threshold’s values for the detection of volcanic unrest: $|A_B|$ = 2${\sigma }_A$ and $|A_B|$ = 3${\sigma }_A$. The amplitude $|A_B|$ exceeds 3${\sigma }_A$ for 19 volcanoes, which is ∼30% of the total number (

Table 2. Values of the signal-to-noise ratio and the best-fit model for InSAR time series of all volcanoes where $|A_B|>3{\sigma }_A$.

Volcano		Detection		Model	Sigmoid	${\mathit{R}}^2>0.75$
	$|{\mathit{A}}_{\mathit{B}}|$ (cm)	${\mathit{\sigma }}_{\mathit{A}}$ (cm)	$|{\mathit{A}}_{\mathit{B}}|/{\mathit{\sigma }}_{\mathit{A}}$	$\mathsf{\Delta }\mathit{A}\mathit{I}\mathit{C}$	${\mathit{t}}_{\mathit{c}}$ (Days)	$\mathit{\tau }$ (Days)	${\mathit{U}}_{\mathit{m}\mathit{a}\mathit{x}}$ (cm)
Fentale	5.8	1.0	5.8	−133	20150422	43	8.3
Erta Ale	18.0	1.9	9.5	−86	20170626	146	−19.0
Tullu Moje	14.7	1.0	14.7	−61	20161130	212	13.4
Suswa	5.5	1.0	5.5	−49	20181025	64	6.2
Kone	6.1	1.2	5.1	−31	20190329	426	−8.2
Olkaria	7.9	1.4	5.6	−10	20170429	261	−10.7
				Model	Linear	${\mathit{R}}^{\mathbf{2}}>\mathbf{0.75}$
				$\mathsf{\Delta }\mathit{A}\mathit{I}\mathit{C}$	${\mathit{v}}_{\mathit{B}}$ (cm/yr)	${\mathit{\sigma }}_{\mathit{B}}$ (cm/yr)	$\mathit{b}$
Corbetti	26.1	1.6	16.3	−4	4.6	0.1	1.47
Alu−Dallafilla	6.10	1.5	4.1	−3	−1.3	0.1	1.53
Silali	3.4	0.4	8.5	−2	−0.7	0.05	1.35
Dallol	14.6	1.2	12.2	10	−3.2	0.1	1.45
Paka	4.4	0.5	8.8	11	−0.7	0.06	1.61
Gada Ale	9.9	1.4	7.1	21	−1.9	0.1	1.45
Dabbahu	22.0	2.7	8.1	23	3.9	0.2	1.65
				Model	Linear	+ Seasonal
					${\mathit{v}}_{\mathit{B}}$ (cm/yr)	${\mathit{A}}_{\mathit{s}}$ (cm)
Nabro	5.5	1.2	4.6		1.7	2.9
Alutu	3.8	0.2	19		−0.8	2.1
Haledebi	5.8	1.3	4.5		0.4	2.1

; coloured circles in Figure 5). This includes eight volcanoes in Afar (Nabro, Alu-Dalafilla, Gada Ale, Dallol, Alu Bagu, Hayli Gubbi, Erta Ale and Dabbahu-Hararo), seven in the MER (Alutu, Fentale, Kone, Haledebi, Bora-Bericcio, Tullu Moje and Corbetti) and four in Kenya-Tanzania (Suswa, Olkaria, Paka and Silali). Three of these are actually duplicates, where two or more closely spaced volcanoes appear in the same 0.5° × 0.5° tile: the signal from Erta Ale also appears in the tiles for Alu Bagu and Hayli Gubbi and the signal from Tullu Moje also appears in the tile for Bora Bericcio. These duplicates are removed from the subsequent analysis, leaving 16 unique signals. With the exception of Silali and Paka, all these signals were reported as ground deformation signals in Albino and Biggs [9].

As we decrease the threshold to 2${\sigma }_A$ (dashed line in Figure 5), five volcanoes will be flagged in addition to the 16 previously detected, with three in Afar (Ma Alalta, Adwa, Ayelu), one in the MER (O’a caldera) and one in Kenya-Tanzania (Longonot). The choice of the appropriate threshold is a compromise between the number of false alarms (if the threshold is too low) and the numbers of missed detections (if the threshold is too high). In our case, we suggest to automatically flag as deformation each signal with amplitude exceeding 3$\sigma$, and to manually inspect signals with amplitude between 2$\sigma$ and 3$\sigma$ (see Section 4).

3.2.2. Deformation Characteristics

Four of the volcanoes are best fit by a linear model: Dallol, Paka, Gada Ale and Dabbahu (Table 2 and Figure 6a,b). Although the sigmoidal model was preferred at Corbetti, Alu-Dallafilla and Silali, $|\Delta AIC|$ was small (<10) and $\tau$ was large (461, 557 and 281 days, respectively), and we classify these as linear too (Figure 6c). For the seven steady deformation signals detected, velocities range from −3.2 to 4.6 cm/yr with most of the cases showing slow subsidence (Table 2). Steady uplift over the 5-year time period was only reported at two volcanoes, Corbetti and Dabbahu, where sustained uplift has been attributed to a combination of magma movement and a viscoelastic rheology [44,45].

The sigmoidal model is preferred for six volcanoes: Fentale, Suswa, Erta Ale, Tullu Moje, Olkaria and Kone, but there is significant variation in the time-scale of the deformation episodes (Figure 6d,i). For Fentale, Suswa and Erta Ale, the characteristic time $\tau$ is smaller than 0.5 year with values of one month and half, two months and five months, respectively (Table 2). For Fentale, the time series shows a ramp increase with $U_{max}$ = 8.3 cm in March 2015. For Suswa, the time series show a ramp increase with $U_{max}$ = 6.2 cm with the onset of deformation starting around June 2018. For Tullu Moje, Olkaria and Kone, the characteristic time $\tau$ is larger than 0.5 year with values of 0.6 year, 0.7 year and 1.2 years, respectively (Table 2). Both Tullu Moje and Olkaria show an exponential decay trend, with LOS cumulative displacements of ∼15 cm and ∼−8 cm, respectively. Based on the sigmoid fit, the ground deformation started in early June 2015 for Olkaria and late September 2015 for Tullu Moje.

Three volcanoes (Nabro, Alutu and Haledebi) do not fit either the linear or sigmoidal models ($R^2<0.5$). All three can be described by a linear model superimposed with a seasonal signal (Figure S5 in Supplementary Materials). The amplitude of the seasonal signal, $A_s$, is ∼3 cm for Nabro and ∼2 cm for Alutu and Haledebi (Table 2).

3.3. Velocity Uncertainties

For the seven volcanoes whose time-series were classified as linear deformation (Corbetti, Alu-Dallafilla, Silali, Dallol, Paka, Gada Ale and Dabbahu), we estimate the LOS velocity uncertainties at the point B. In each case, the standard deviation of the velocity, ${\sigma }_v$, decreases linearly with the duration of time series $\Delta t$ in a log-log plot (Figure 7). This indicates a power-law relationship: ${\sigma }_v=a\Delta t^{-b}$, in which a corresponds to the LOS velocity uncertainties after a 1-year period, and b corresponds to the decay rate. The value $b=1$ is an indication of flicker noise (correlated), whereas $b=\frac{3}{2}$ indicates pure white noise (uncorrelated). After 5 years, LOS velocity uncertainties range from 0.05 cm/yr at Silali to 0.2 cm/yr at Dabbahu with an average value of 0.1 cm/yr and the decay rate b ranges from 1.35–1.65 with an average value of 1.5. These results indicate (1) a typical detection threshold of ∼1 mm/yr for EARS volcanoes based on 5 years of Sentinel-1 data and (2) that the velocity uncertainties in the Sentinel-1 time series are dominated by uncorrelated noise in agreement with previous InSAR studies [3,43].

4. Discussion

4.1. Automated Detection Based on Signal-To-Noise Ratio

Based on our Sentinel-1 survey, the average temporal noise at EARS volcanoes, ${\sigma }_A$, is ∼$1.35\pm 0.5$ cm, with little systematic variation between regions. Using a threshold of $3{\sigma }_A$ (∼4 cm), we detected all the ground deformation signals reported by the manual study of Albino and Biggs [9], and in fact detected two previously unreported signals at Paka and Silali volcanoes (see Section 4.3). However, subtle signals with small amplitudes could still be missed (false negatives).

A threshold of $2\sigma$ (∼3 cm) is able to detect smaller signals, but a number of false positives can occur (Figure 5). In our study, there were five volcanoes with $2\sigma <|A_B|<3\sigma$ after 5-years: Ma Alalta, Adwa and Ayelu in Afar, O’a caldera in the MER and Longonot in Kenya. None of these were reported by the study of Albino and Biggs [9].

• At Adwa and Ayelu, the velocities recorded at point B are 0.1 cm/yr, which is in the same order of magnitude as our estimates of LOS velocity uncertainties. In addition, part of the signal is correlated with topography, which suggests tropospheric residuals signals.
• At O’a caldera, the phase information is very sparse as the volcanic area is covered by three lakes (Shala, Abijata and Langano). Ground displacements has been only retrieved at the caldera rim and LOS velocities do not exceed 0.2 cm/yr. No clear deformation signal has been observed.
• At Longonot, the temporal noise is ∼2 cm, which is larger than the mean value calculated for the EARS. The signal detected has a long wavelength, and it can be observed in the entire scene ($50\times 50$ km), with LOS rates of displacement ranging from 0.5 cm/yr in the NW to −0.5 cm/yr in the SE. This pattern may suggest residual orbital ramps.
• At Ma Alalta, the signal is located on Quaternary rhyolite lava flows [46]. The maximum rate of LOS displacement is about −0.7 cm/yr, which is larger than the four cases previously described. Therefore, it is difficult to determine if this signal is noise or real ground deformation associated with the compaction or remobilization of volcanic products as previously observed in Kone lava flow [9].

In the framework of an automatic detection system, we recommend the use of a lower detection threshold (e.g., 2$\sigma$ for the EARS) and re-evaluating positive results based on an expert analysis to identify potential false positives.

4.2. Previously Unreported Deformation

For two of the volcanoes with a high signal-to-noise ratio, Paka and Silali, no deformation has previously been reported in the Sentinel dataset (2015–2020). However, both experienced deformation during the Envisat era (2006–2010) [7,47,48]. At Paka, five distinct phases of unrest were identified with surface LOS displacement rates between 95 ± 1.3 cm/yr (July–August 2006) and 2.5 ± 0.9 cm/yr (February 2008–July 2010) [47]. Based on the modelling of ground deformation, unrest phases have been interpreted as the inflation and deflation of four simple sources located beneath the northeastern and southern flanks of the volcano at depths between 1 and 5 km. At Silali, a long-term linear subsidence signal with maximum LOS displacement rates of 1.6 ± 0.4 cm/yr was detected between October 2003 and September 2010, and modelled by the deflation of a source located at 4–5 km depth below the caldera [47].

For the period 2015–2020, $|A_B|/{\sigma }_A=8.8$ at Paka and $|A_B|/{\sigma }_A=8.5$ at Silali. Both timeseries were classified as linear, and the maximum LOS displacement rate was $-0.7\pm 0.1$ cm/yr (Figure 8b,e) at both. This rate is much smaller than observed during 2006–2010 but significantly greater than the uncertainty. The signals both show that LOS range increases in the same area as the previously detected signals (Figure 8), which is suggestive of long-term subsidence associated with magmatic or hydrothermal processes [49]. However, the profiles of displacements also show some similarity with the topography of the edifice (Figure 8c,f), which is typical of stratified atmospheric signals. Phase elevation corrections have already been applied at both of these volcanoes (see Section 3.1), but we cannot rule out that the signal may be the result of residual tropospheric signals instead of ground deformation.

4.3. Deformation Classification

We automatically classify the time-series associated with positive detections as ‘linear’ or ‘sigmoidal’ using Akaike’s Information Criterion to chose the most appropriate functional form. Although, there were three signals that did not fit either the linear or sigmoidal models (Alutu, Haledebi and Nabro); these were well fit by a ‘hybrid’ model combining linear and seasonal models (Figure 9). Albino and Biggs [9] noted the seasonal signals at both Alutu and Haledebi and showed that they correlated with rainfall. The linear rate estimated for Nabro of 1.7 cm/yr (Table 2) is comparable to the $1.5\pm 0.5$ cm/yr estimate of Albino and Biggs [9]. Thus, the scheme could be easily improved by including an additional functional form to represent seasonal patterns combined with underlying deformation sources, e.g., [50].

However, the categories provided by the empirical time-series fits do not directly correspond with the process-based categories of Albino and Biggs [9]. The ’sigmoidal’ classification represents a range of processes: the signals at Fentale and Erta Ale have been attributed to dyke intrusions [51,52], while Suswa, Tullu Moje and Olkaria are considered to be restless calderas [7]. For Erta Ale, the sigmoid fit is poorer than for the other cases (Figure 9), as the time series shows a complex trend: (1) a step-like LOS decrease of ∼10 cm on January 2017 associated with co-eruptive processes [51,53] followed by (2) a slow decay in displacement rate related to post-eruptive processes [54].

Similarly, the processes responsible for the five examples of linear subsidence are varied (Figure 9). The subsidence at Alu-Dalafilla and Dallol are thought to be long-term responses to recent activity: Alu-Dalafilla last erupted in 2008 [55] and there was a dike intrusion at Dallol in 2004 [56]. In contrast, Paka and Silali are restless calderas, with no recent activity [7]. The signal at Gada Ale has previously been attributed to poro-elastic fluid effects [9].

Although the spatial pattern of deformation can be used to discriminate between source processes with different geometries, many of the deformation signals are radially symmetrical. Thus, while empirical fitting can be useful for a first order categorisation of the InSAR dataset, it cannot be used to uniquely determine the magmatic processes. Additional information from other monitoring streams, e.g., [57,58] or baseline knowledge of the long-term deformation patterns or eruptive history is needed for monitoring purposes.

4.4. Measurement Uncertainty

The uncertainties on InSAR time series are the combination of several different processes: atmospheric noise, orbit and DEM uncertainties, errors in phase unwrapping and temporal decorrelation [59,60,61,62]. Our InSAR regional survey enables us to discuss various measures of uncertainty at the regional scale and to compare to other geographical environments.

For the EARS, interferograms from the majority of the volcanoes (∼75%) had a low phase-elevation correlation and did not require atmospheric corrections. Given that most EARS volcanoes have low relief (<1000 m), this is consistent with previous studies that have shown atmospheric uncertainty increases with volcano height, e.g., [28]. The only volcanoes at which atmospheric corrections were considered necessary (CDF(R${}^2$ = 0.5) < 0.8) were high and/or large edifices (e.g., Silali and Paka) and volcanic systems located at the margin of the rift (e.g., Alid, Dubi, Butajiri), where the high relief is associated with the rift border faults rather than the volcanic edifice itself.

4.4.1. Regional Detection Threshold

InSAR measurement accuracy can be evaluated by the detection threshold defined as the minimum velocity that can be detected in the time series. This can be evaluated by calculating the noise $\delta$ of N independent interferograms or the noise of interferogram stacking with $v_{limit}=\frac{{\delta }_{ifg}\sqrt{N}}{t}=\frac{{\delta }_{stack}}{t}$, e.g., [4,59]. The detection threshold largely decreases with the duration of the time series and is highly dependent on the content of atmospheric noise. Assuming that the noise is characterised by the value of $2{\sigma }_A$, the detection threshold can be expressed as $v_{limit}=\frac{2{\sigma }_A}{t}$.

Therefore, the average detection threshold in the East African Rift System is 0.5–0.6 cm/yr for a 5-year duration. For volcanoes in Central Andes, Pritchard and Simons [63] found a detection threshold of 0.4 cm/yr for a 5-year ERS-1/2 (C-band) time series, assuming a maximum error of 2 cm per interferogram. Thus, our estimates of the detection threshold in the EARS are in good agreement with previous ones found for Central Andes volcanoes. We may conclude that, for C-band sensors, the limit of detection is 0.4–0.6 cm/yr for volcanoes located in arid or semi-arid environment (high coherence and low atmospheric noise), such as the EARS and Central Andes.

In comparison, [20] estimated the average detection threshold for a set of 20 volcanoes in Central America to be 2.4 cm/yr using a 3-year time-series of ALOS-PALSAR (L-band) data, equivalent to 1.4 cm/yr for a 5-year duration. Such results are three times higher than our estimates. Discrepancies are due to the tropical environment of Central America (low coherence and high atmospheric noise) as well as the difference in radar wavelength. Indeed, long wavelength sensors such as L-band are less sensitive to detecting small displacements.

4.4.2. Velocity Errors for Long-Term Signals

Analysis of the persistent linear trend at seven EARS volcanoes shows that velocity uncertainties are inversely proportional to the duration of the time series. For the 5-year observation period, the typical LOS velocity uncertainty in the EARS was ∼0.1 cm/yr and related to uncorrelated noise, that is consistent with results from two previous Sentinel-1 studies conducted in Japan and Turkey [3,43]. Our results are also in good agreement with theoretical simulations, looking at the effect of tropospheric delays, which demonstrates that a detection level of 0.1 cm/yr can be achieved for Sentinel-1 time series having regularly sampled data for a period longer than 5 years [64].

Small phase biases due to the variation in scattering properties of sub-resolution scatterers caused by moisture changes and vegetation growth can propagate through time series of multi-looked interferograms causing a significant bias in velocity maps [65,66,67]. Although the EARS is mostly arid and sparsely vegetated, this effect could explain some of the uncertainties in our velocity estimates, particularly for volcanoes with multiple land cover types as the impact of the phase errors varies across the scene.

Most InSAR studies do not explicitly consider the choice of reference frame as a source of uncertainty. Here, we demonstrate that this choice is not trivial and can induce variations up to 1 cm/yr on the LOS velocity derived. From our study, we show that the average error is ∼0.5 cm/yr for the EARS, which is five times larger than the errors associated with noise. Therefore, the use of an external dataset (e.g., GNSS data) for referencing Sentinel-1, e.g., [3,45], is crucial to be able to study strain accumulation and partitioning in the EARS, where extension rates range from ∼2 mm/yr in Malawi to ∼6 mm/yr in the Main Ethiopian Rift [68].

5. Conclusions

Here, we provide a framework to produce routinely Sentinel-1 InSAR time series of displacements from LïCSAR products that is adapted to semi-arid volcanic environment. We apply our methodology to the EARS for the period 2015–2020. Among the 64 volcanic centres, sixteen show large signal-to-noise ratio with the amplitude of the cumulative displacements exceeding three times the temporal noise of the time series (Figure 9).

By performing a regional statistical analysis of the time series, we found that the average limit of detection in the EARS region is around 3 cm (2$\sigma$). Therefore, we expect to detect linear trend with rates larger than 0.5 cm/yr with an uncertainty of 0.1 cm/yr after a 5-year period.

We automatically classify the deformation signals as ‘linear’, ‘sigmoidal’ or ‘hybrid’. Although this classification in three classes does not reflect the diversity of magmatic processes, the automatic fitting provides an easy way to discriminate between steady deformation (linear), slowly varying deformation rate (large sigmoid with $\tau$ > 0.5 yr) and short-term pulses of deformation (tight sigmoid with $\tau$ < 0.5 yr). Such information can be used during real-time monitoring to detect anomalies in the time series by comparing the “real” ground displacements with the “predicted” displacements derived from the trend.