The El Forn landslide is a large deep-seated landslide located southeast of the town of Canillo, Andorra, nestled in the Pyrenees (see Fig. ) that is triggered by snowmelt and season rainfall that collect into an aquifer located below the sliding surface. This landslide has a sliding mass of approximately 300 Mm3 that creeps at an average rate of 1.2 cmyr-1 . Within the main sliding mass of the landslide, there is a faster-moving lobe (Cal Ponet–Cal Borronet lobe) that slides at a maximum velocity of 2–4 cmyr-1 . At present, this lobe is equipped with 12 boreholes dispersed between the top and bottom of the landslide collecting continuous in situ data. However, S10 is the only continuously monitored borehole on the landslide, with measurements every 20 min. Other boreholes are monitored via analog non-continuous measurements (irregularly, approximately once per month), which is why we chose to work exclusively with S10. It is important to note that, while there are available analog data over the landslide, only one point is a viable option for comparison with InSAR, given the no-snow period of 2019. In order to not reduce the fidelity of the continuous time series from S10, the authors choose to not include these data in the body of this text. The authors have made these data available upon request.

The sliding surface is located at 29 m depth, and the landslide moves as a rigid block on top of it, creeping into the town of Canillo, as shown in Fig. , with the periods of greatest acceleration during the no-snow periods (May–August) each year. The shear band is comprised of 80 % Silurian shales rich in phyllosilicates (muscovite, paragonite, and chlorite) and 20 % quartz . A more detailed explanation of the geological makeup of the shear band can be found in . The terrain of the landslide can be seen in Fig. .

The primary instrumentation and data considered in this study are housed within the S10 borehole, noted as the yellow marker in Fig. . Data from S10 are sampled continuously every 20 min via instrumentation including an extensometer, three piezometers, and a thermometer within the shear band, which measure horizontal displacement, water pressure, and temperature changes in the material, respectively. The data considered in this study for El Forn are displacement measurements gathered from the extensometer. Detailed information about the location of S10 and the depth profile of the landslide with S10 borehole readings can be found in .

One of the key objectives of this work is to compare InSAR to sub-surface ground measurements. This is achieved through interferograms obtained by Sentinel-1A and Sentinel-1B over a period of 6 months in 2019 with a 6 d acquisition interval. It is important to note that the landslide was arrested at the end of 2019, so 2019 remains the year of focus for the intent and purpose of this work. Additionally, a 6-month InSAR time interval is chosen in order to avoid snow cover seasons on El Forn since backscatter from snow cover makes use of InSAR particularly difficult due to low coherence . Interferograms are then processed to obtain displacement time series over the landslide's surface using two different approaches.

A high-precision (fine-spatial-resolution), low-accuracy (noisy) approach was employed, whereby Sentinel-1 data are retrieved and pre-processed with a low coherence threshold to obtain high-spatial-resolution (40m×40m grid) displacement data so that geospatial analysis can be conducted to determine the minimum number and location of observations required for landslide monitoring and reconstruction with quantified uncertainty. This approach was deployed using the Alaska Satellite Facility (ASF) On Demand InSAR processing tools from the Vertex platform and will be hereinafter referred to as ASF.

Note that the SAR imagery for both the data retrieved via the ASF On Demand InSAR processing tools and the Copernicus EGMS portal was taken from the Sentinel-1A and Sentinel-1B satellites on a descending track with a 270° angle of incidence from the vertical. Using the slope of the ground at S10, the data for the EGMS displacement and ASF–MintPy (Miami INsar Time-Series software in Python) readings were translated into the displacement along the direction of the landslide movement so they could be compared to S10's strain gauge readings.

While displacement data from EGMS are readily available, data retrieval from ASF requires a more hands-on approach, going through a short baseline subset pre-processing step via ASF On Demand InSAR processing tools, followed by an interferogram time series inversion via MintPy that allows us to generate mean deformation velocity maps and deformation time series . Subsequent displacement data from this time series inversion, alongside displacement data pulled from the EGMS platform, are compared with in situ displacement data from S10 to understand the correlation between InSAR and in situ data. The other key objective of this work is to understand how InSAR can be used for a general uncertainty quantification for planning future borehole placement, should the first objective prove InSAR can be correlated with sub-surface measurements. This will be done via iterative ordinary kriging, with the normalized root mean square error (RMSE) being used as the statistical parameter of interest for confidence. The next paragraphs outline the technical details of data retrieval and processing for each of these approaches.

Ordinary kriging was conducted by first creating a grid of x and y coordinates and corresponding velocity values at these points. Distances between the random observations and each individual grid point were calculated such that 1d1=(xg-xobsT)2+(yg-yobsT)2, where xg and yg are the grid coordinates and xobs and yobs are the random observation coordinates. The covariance matrix was determined using the range τ and variance σ2 from the semivariogram such that 2C=σ2(e(-d1/τ)T).

The Euclidean distances between the random observations and each other were calculated, as well as the corresponding covariance matrix Σ, such that 3d2=(xobs-xobsT)2+(yobs-yobsT)2,4Σ=σ2(e(-d2/τ)T).

The covariance matrices were appended into two matrices that would be used Lagrange multipliers, matrices Σ′ and C′, respectively. The weights were calculated by solving the linear equations created by the Σ and C matrices. From there, we calculate predictions Z* by taking the velocity values at the random observations zt, multiplying them by the corresponding weights W such that 5Z*=Σ(W⋅zt).

The mean square error is then solved such that 6MSE=σ2-Σ(W⋅C′)-W.

As a result, fidelity was assessed via the root mean square error (RMSE=MSE) of a kriged landslide surface via random sampling without replacement per iteration.

As previously noted, ASF and EGMS data showcase a key trade-off between precision and accuracy for the purposes of landslide monitoring. Figure a demonstrates that with a lower coherence value, more, albeit noisy, data are available. In a separate vein, the EGMS data (pictured in Fig. b) demonstrate the utility of an increased coherence value in reducing noise and producing high-accuracy data usable for landslide detection.

Upon data retrieval, both ASF and EGMS InSAR displacements were compared along the direction of sliding in situ strain gauge data from the S10 borehole in order to understand the fidelity of InSAR in monitoring sub-surface ground motion. This direct comparison of InSAR readings from ASF and EGMS over the S10 borehole can be seen in Fig. . Retrieval of InSAR displacement data from EGMS required manual comparison of a couple of neighboring points with S10's in situ data in order to find points with a signal strong enough to use for comparison since there was no individual measurement point at the location of S10 after the increased threshold was applied (see Fig. ).

Indeed, the increased sparsity from EGMS resulted in a lack of precision of the individual measurement points in comparison with in situ measurements, as seen in Fig. c, as compared to data retrieved via ASF On Demand tools (as seen in Fig. b). Since data for the exact location of the S10 borehole on the landslide were not immediately available on the EGMS platform, two coordinates neighboring the WGS84 coordinate of S10 were pulled and compared to the S10 data and InSAR data. Heterogeneity within the landslide prevented selecting just one point as close to the S10 point as possible without properly examining other neighbors. Figure  details which point was examined, with “EGMS” being the point in the EGMS database that was ultimately used because of its close alignment with S10's raw displacement data. Figure  directly compares data retrieved with ASF On Demand processing tools (and inverted via MintPy) and EGMS with in situ displacement measurements. We observe that while InSAR displacement measurements pulled from EGMS are helpful in detection, the higher accuracy creates data that lack the precision necessary for in situ comparison.

In order to justify this claim and quantify the performance of the two approaches in time, a measure of linear independence (correlation) was conducted with data with in situ measurements from EGMS and ASF, respectively. The equation used for the calculation of the correlation coefficient ρ(A,B) of datasets A (in this case EGMS or ASF) and B (in this case the in situ data) is 7ρ(A,B)=1N-1∑i=1NAi-μAσABi-μBσB, where μ and σ are the mean and standard deviation of the datasets, respectively. The results of the performance of ASF and EGMS against the in situ data are detailed in Table , where we see that the ASF dataset (ρ(ASF,in situ)=0.6957) performs considerably better against in situ data than EGMS (ρ(EGMS,in situ)=0.0761). This is presumably due to the spatial heterogeneity of the landslide's displacement around the point of measurement, which is not exactly on S10 (see Fig. ), and is not reflective of the overall quality of the EGMS data.

Having shown the correlation between ASF and in situ measurements in the previous section, we move forward with the densely populated ASF mapping to carry out ordinary kriging. In order to best understand how many observations (i.e., boreholes) impact the ability to remotely model ground motion of a deep-seated landslide, 200 iterations of randomly selected samples (with sizes ranging from 5–100 points) along the main landslide surface were selected and had ordinary kriging performed on them to assess the RMSE in predicting ground motion over the surface of the landslide, with summaries of RMSE for each number of iterations visible in the box-and-whisker plot in Fig. . Similarly, single-iteration ordinary kriging was conducted over the sliding mass to assess how various sample sizes (ranging from 10–2000) were involved in re-creating velocities of the sliding mass and where possible areas of interest for further investigation were.

More specifically, 200 iterations were conducted per number of random observations of the average velocity in 2019 (pulled from a uniform distribution, as seen in Fig. b), results of which can be seen in Fig. c. Figure c, the diagram of the normalized root mean square error (RMSE), indicates a marked drop in the interquartile range (IQR) between 20 and 25 observations. Also important to notice is that the range of outliers is significantly lower, starting from n=25 observations and going forward. Note that the dots outside of the whiskers are outliers, meaning they lie outside of the whiskers defined by Q1-1.5⋅IQR and Q3+1.5⋅IQR.

Figure  reflects how n samples re-create the average landslide velocity movement over the no-snow periods in 2019 in the line of sight (LOS) and the fidelity (RMSE) of doing so. For example, n=30 random samples re-create certain parts of the landslide better than others for one iteration. Figure  shows the evolution of how increased random samples that go through the process of ordinary kriging then re-create certain parts of the landslide surface faster or better than others. In the case of n=30, the top and bottom of the landslide are better developed than the middle of the landslide, which indicates where further investigation may be necessary. More specifically, the center of the landslide is the least developed throughout the iterations of ordinary kriging – for modeling purposes then, further investigation would be required on this part of the sliding mass (either further instrumentation or a more narrow scope of InSAR).