How Groundwater Level Fluctuations and Geotechnical Properties Lead to Asymmetric Subsidence: A PSInSAR Analysis of Land Deformation over a Transit Corridor in the Los Angeles Metropolitan Area

Abstract

Los Angeles has experienced ground deformations during the past decades. These ground displacements can be destructive for infrastructure and can reduce the land capacity for groundwater storage. Therefore, this paper seeks to evaluate the existing ground displacement patterns along a new metro tunnel in Los Angeles, known as the Sepulveda Transit Corridor. The goal is to find the most crucial areas suffering from subsidence or uplift and to enhance the previous reports in this metropolitan area. For this purpose, we applied a Persistent Scatterer Interferometric Synthetic Aperture Radar using 29 Sentinel-1A acquisitions from June 2017 to May 2018 to estimate the deformation rate. The assessment procedure demonstrated a high rate of subsidence in the Inglewood field that is near the study area of the Sepulveda Transit Corridor with a maximum deformation rate of 30 mm/yr. Finally, data derived from in situ instruments as groundwater level variations, GPS observations, and soil properties were collected and analyzed to interpret the results. Investigation of geotechnical boreholes indicates layers of fine-grained soils in some parts of the area and this observation confirms the necessity of more detailed geotechnical investigations for future constructions in the region. Results of investigating line-of-sight displacement rates showed asymmetric subsidence along the corridor and hence we proposed a new framework to evaluate the asymmetric subsidence index that can help the designers and decision makers of the project to consider solutions to control the current subsidence.

1. Introduction

Ground subsidence is mainly due to fluid overexploitation and expanding construction [1,2,3,4]. There are several cities and regions suffering from land subsidence, such as Mexico City [5,6], Shanghai, China [7,8,9], Lhokseumawe, Medan, Jakarta, Bandung, Blanakan, Pekalongan, Bungbulang, and Semarang, Indonesia [10,11,12,13], Ravenna, Prato, Bologna, Italy [14,15,16,17,18], Tehran, Rafsanjan, Neyshabour, Mashhad, Iran [19,20,21,22,23,24,25], Los Angeles, United States [26,27,28,29,30,31,32], and many more places around the world. In the present study, we studied land deformation in Los Angeles metropolitan area, Southern California, with a focus on the study area of a new transit corridor, known as Sepulveda Transit Corridor. This investigation is crucial because land displacement will affect the design and depth of a tunnel [33,34,35,36] and should be assessed based on soil properties. Also, all the information about the location, soil and groundwater needs to be carefully managed, analyzed and investigated in planning and design phase of the road construction to ensure the reliability of the subgrade [37,38,39]. Based on the previous researches in Los Angeles [26,27,28,29,30,31,40], the ground displacements in this area are mainly due to the groundwater level variations and oil extraction [26].

Advances in technology and science have made accurate measurement of ground deformation simple. Interferometric Synthetic Aperture Radar (InSAR) technique is a geodetic tool to image ground displacement in centimeter-scale and can be a very helpful technique in understanding the earthquakes, volcanos and glaciers [41]. InSAR can also benefit geomorphologists and hydrologist by providing an accurate measurement of slope motion, sediment erosion and deposition, water level fluctuation and soil moisture content [42,43,44,45,46]. InSAR has been considered as a powerful method to monitor ground surface deformations [47] and is an alternative technique to measure surface displacement. InSAR can measure small surface deformations in different situations and projects such as ground settlement and excavations [48]. Using the high spatial and temporal resolution of radar images, the InSAR technique can provide reliable results in the application of subsidence monitoring of such infrastructures as roads [49], subways, rails, and tunnels. Tunnels are visible because of localized subsidence of the above ground surface along their tunnel path. It means that it is possible to determine the effect of tunnel excavation on the ground surface. Highways, standing over the ground surface, in most cases show reliable stability compared to the surrounding areas [50].

A number of studies have used geodetic and InSAR techniques to evaluate the ground deformation in Los Angeles Basin. For example, the radar data acquired by the European Remote Sensing Satellites (ERS-1 and ERS-2) from 1992 to 1999 were analyzed [51] using InSAR to study the ground deformations along the southern San Andreas fault system. In addition, the interseismic crustal movement was measured [52] near Los Angeles, along the San Andreas Fault (SAF), by a new technique for integrating InSAR analysis on ERS descending and ALOS ascending radar images, and GPS data. The outputs display the vertical velocity of land deformation between −2 to +2 mm/yr, and shows uplift on the SAF in the Los Angeles area. Several researchers investigated the ground displacements related to groundwater level changes and fluid extraction in the Los Angeles Basin. For instance, radar images of ERS-1/2 satellite and GPS data were deployed [29] to infer the seasonal land deformations related to groundwater extraction in the Los Angeles basin. Also, a study on metropolitan Los Angeles [40] evaluated seasonal oscillations of the Santa Ana aquifer (uplift and subsidence), located in Los Angeles Basin, using InSAR technique from 1998 to 1999. The analysis provided estimates of ground displacement in the Line of Sight (LOS) of the European Remote Sensing (ERS) satellite in the time between satellite passes. The InSAR outputs showed uplift and subsidence in metropolitan Los Angeles to in response to extraction of fluid resources.

The subsidence associated with groundwater pumping and faulting in Santa Ana basin, CA was measured using InSAR technique from 1997 to 1999 and GPS data from 1999 to 2000 [53]. The results showed subsidence as high as 12 mm/yr is happening by groundwater withdrawal and re-injection in metropolitan Los Angeles. A time series analysis of ground deformation by InSAR based on small baseline subset (SBAS) algorithm was carried out [28] for Santa Ana basin in Los Angeles metropolitan area. ERS satellite data from 1995 to 2002 were used and it was found that ground deformations time series from InSAR significantly agree with GPS time series from Southern California Integrated GPS Network (SCIGN). A temporarily coherent point InSAR method [30] was applied on the Los Angeles Basin, using 32 ERS-1/2 images acquired during 1995 to 2000 to detect land subsidence. InSAR and GPS measurements were used [26] for detecting ground deformations caused by injection of groundwater and oil in Los Angeles from 2003 to 2007. A dataset of 64 TerraSAR-X images has been processed [27] in Los Angeles in the period 2010–2014 and showed a cumulative displacement of −50 mm in oil extraction fields. In 2018, a research [54] conducted to quantify ground deformation in the Los Angeles Basin due to groundwater withdrawal and showed −20 to +10 mm/yr LOS displacement rate.

A number of studies have been carried out to measure surface deformation along the transit corridors and their near infrastructures such as aqueducts and levees in California [55,56] and Rome (Italy) [57]. For instance, land subsidence rate of Hampton Roads in Virginia, USA, was estimated [58] using GPS observation and InSAR applied to ALOS-1 radar data. The outputs showed decent agreement between GPS data and InSAR-generated subsidence rate map. In a study in Shanghai, China [50], the X-band sensor Cosmo-SkyMed was used to monitor the subway tunnels and highways by Persistent Scatterer Interferometric Synthetic Aperture Radar (PSInSAR) analysis. In order to detect and monitor ground subsidence caused by tunneling, InSAR time series analysis was applied [59] on RADARSAT-1 and RADARSAT-2 radar data in the urban area of Vancouver, Canada. InSAR technique was also used to monitor landslide displacements induced by excavations related to tunneling in the Northern Apennines, Italy [48]. The tunnel was part of a larger project that contains the improvement of a highway that connects Bologna and Florence. The InSAR outputs showed high agreement with inclinometer and GPS as ground-based monitoring data.

Land surface deformation depends on many factors such as the depth of sediments and the amount of fluid extraction. Therefore, each area may behave differently at different places and different periods. In geotechnical engineering, land subsidence is estimated by considering the following parameters: deformable soil thickness, effective stress variation, and modulus relating the two previous parameters. The changes in the stress state are due to variations in the groundwater level. As the piezometric levels were measured frequently during a period, they are used to determine the groundwater table depth and pore water pressure changes are assumed equal to changes of ground water table [24,60]. Drainage of groundwater in soil deposits can induce huge ground subsidence. Thus, it is imperative to investigate the soil properties of deep geotechnical wells to detect thick compressible sediments particularly in the areas suffering from groundwater extraction.

In this research, we focused on the study area of the Sepulveda Transit Corridor which is planned to improve transportation means between the Los Angeles International Airport and the San Fernando Valley. The previous studies considered the displacements of constructed or under-construction infrastructures such as ground deformations caused by tunnel excavations. The main goal of conducting the present study is to obtain the current ground deformation pattern of a new transit corridor, which can affect its designing criteria and help the designers and decision makers of future constructions. In addition, it is necessary to investigate the subsidence rates in recent years to modify and update the past reports. This paper is organized as follows. First, the study area and the Sepulveda Transit Corridor project is introduced. Second, a brief description of the basic concepts of PSInSAR and the dataset is given. In this study, we used Sentinel-1A SAR images, provided by the European Space Agency (ESA) [61], acquired over the study area from June 2017 to May 2018. Third, the subsidence map derived from PSInSAR analysis is presented. Fourth, piezometric data, GPS observations, and geotechnical properties are provided to assess the outputs. Finally, a framework for evaluation of asymmetric subsidence is proposed. The research objectives of this research are:

• To assess and complement the previous studies on subsidence monitoring in Los Angeles using more recent data.
• To evaluate the PSInSAR results considering soil properties, and hydrological data and GPS information in the area.
• To identify deformation patterns over the study area of the corridor to inform and warn the managers, designers and other stakeholders about the future hazardous consequences.
• To show the variation in displacement rates along the alignment of corridor to help the designers and decision makers of the project to detect the places that require considering immediate solutions to control the current displacements.

2. Study Area: Sepulveda Transit Corridor, Los Angeles, California

The main aim of the Sepulveda Transit Corridor is to enhance transportation between the Los Angeles International Airport (LAX) and the San Fernando Valley. In the current situation, the I-405 highway in this area bear more than 400,000 travel every day and known as one of the most traveled urban freeways in the US [62]. As such, the Los Angeles County Metropolitan Transportation Authority (known as Metro), the agency that controls public transportation for the County of Los Angeles, is conducting a study to assess a range of high-capacity rail transit alternatives between the San Fernando Valley and LAX. The study conducted by Metro is expected to take approximately 20 months, from December 2017 (study kickoff) to Summer/Fall 2019 (study completion). It should be noted that due to the importance of the Sepulveda project, it is funded by the Measure M expenditure plan, with around $5.7 billion for construction of new transportation service to connect the San Fernando Valley and the Westside, and around $3.8 billion for extending that transit service between the Westside and LAX [62]. Figure 1 shows the study area of the Sepulveda Transit Corridor covering an area of about 229 km².

3. Methodology

3.1. PSInSAR Time Series Analysis

The PSInSAR technique [63] was used in this research to monitor ground deformation through the study are. This technique is one of the powerful SAR time series applications which can analyze land displacements, particularly in urban areas [64]. PSInSAR looks for Permanent Scatterers [65] with stable scattering properties and also relatively good coherence, over long period intervals in multi-temporal data [66]. For mapping ground deformation, a stack of SAR images of the same area is selected. Afterwards, one single master acquisition is chosen from the stack based on the measured baselines in time and space to achieve an appropriate coherence in interferograms. A reference point is chosen, among the selected Persistent Scatterer Candidates (PSCs), which is relatively unaffected by ground surface displacement. Then, a stack of co-registered Single Look Complex (SLC) images is created using this single master configuration. Phases of each pixel are acquired when the topography and earth curvature influence is removed from the phase. There are a number of factors influenced the acquired phases, such as external DEM inaccuracy, Atmospheric Phase Screen (APS), linear phase ramp, the scatterer movement, and decorrelation and speckle noise. The following equation [67] shows the main factors in the phase calculation.

$${\varphi }^k=\frac{4\pi }{\lambda }(\frac{B_{\perp }^k}{R\sin \theta })h+\frac{4\pi }{\lambda }{T}^{k}v+{\varphi }_{atm}^k+{\varphi }_{orb}^k+{\varphi }_{noise}^k$$

(1)

where the first term is related to the DEM error (h) because of the external DEM inaccuracy, the second term is related to the linear deformation velocity (v) during the acquisition period. In this equation, ${\varphi }_{atm}^k$, ${\varphi }_{orb}^k$ and ${\varphi }_{noise}^k$ denote the atmospheric phase delay, the residual orbital error phase, and the temporal and geometrical decorrelation noise, respectively. In this study, we implemented PSInSAR analysis in SARPROZ [4] and the applied processing steps are as the following:

First, each pixel could be a PS candidate if it satisfies the amplitude stability index for the pixel have a value of at least 0.85. The amplitude stability index can be calculated as follow:

$$D_{stab}=1-\frac{{\sigma }_a}{\overline{a}}$$

(2)

where $D_{stab}$, ${\sigma }_a$ and $\overline{a}$ are the amplitude stability index, the standard deviation and the mean of amplitude values, respectively. This condition resulted in 57,667 points in the present study.

Second, the unknown parameters of DEM error and the velocity are estimated. For this purpose, the spatial graph of connections between points is considered and the initial parameters are estimated along the connections. Then, the absolute values are achieved by numerical integration considering a reference point as a starting point for the integration. Careful selection of the reference point is a key factor in the accuracy of outputs, as careless reference selection will result in biased parameters for all points.

Finally, a wider set of points are selected considering a spatial coherence of 0.80 and temporal coherence of 0.85 conditions. At this stage, a second approximation of the parameters were applied on the new dataset. Then, all PS points above the temporal coherence threshold were selected for the final estimation. The DEM error, the linear deformation rate along the Line of Sight and the subsidence time series are approximately calculated for the selected PS points.

It should be noted that differentiating between the contributions made to the phase by deformation and atmosphere would be difficult, if we only had two SAR images. As we are using a time-series of SAR images, we can take advantage of this fact that often the atmospheric perturbations exhibit typically high spatial correlation but low temporal correlation [66]. Therefore, we can estimate the atmospheric signal by applying a high-pass filtering in time and a low-pass filtering in space [63]. This is how the atmospheric phase signal was computed and removed from the total phase. Furthermore, the displacement measured by InSAR can be decomposed into two main components: a periodical component and a linear component. The periodical signal is a seasonal deformation phenomenon which is occurred due to the thermal expansion and contraction particularly evident on skyscrapers, bridges, etc. which is not the case in our study area. Therefore, in our work, we only considered the linear trend signal and did not take the seasonality signal into account. Here, we used descending images which resulted in LOS displacement. So, in order to compare the PSInSAR and GPS data, we used the following equation to obtain GPS measurements in LOS direction [66]:

$$\begin{array}{l}GP{S}_{LOS}=GP{S}_{up}\times \cos ({\theta }_{inc})\\ -GP{S}_{north}\times \cos ({\theta }_{azi}-3\pi /2)\times \sin ({\theta }_{inc})\\ -GP{S}_{east}\times \sin ({\theta }_{azi}-3\pi /2)\times \sin ({\theta }_{inc})\end{array}$$

(3)

where $GP{S}_{LOS}$ is the converted value of GPS data in LOS direction. $GP{S}_{up}$, $GP{S}_{north}$, and $GP{S}_{east}$ are the values of GPS observation vector in the up, north, and east directions. ${\theta }_{inc}$ represents incidence angle. The radar images were taken from different incidence angles and the average incident angel is about 43.97° in this study. ${\theta }_{azi}$ represents the heading angle of the satellite from the North (azimuth angle) and is about −9.66° in this study.

3.2. Data Collection

Land deformation measurement by PSInSAR needs sufficient number of SAR images. From literature [67,68], the PS analysis requires at least 20 to 25 SAR images to achieve reliable outputs. Considering this important condition on number of images, we collected 29 descending Sentinel-1A SAR images acquired over the study area during June 2017 and May 2018. After collecting the raw data, we defined the study area with an area of 1019 km² to cover the corridor and its neighborhoods. Figure 1 displays the study area. The white line indicates the master area and the black line shows the boundary of the study area of Sepulveda Transit Corridor.

Figure 2 displays the SLC data used in this study and the spatiotemporal baseline configuration of interferometric pairs. To form the interferograms, all images were connected with the master image (5 December 2017). The master image is chosen at the barycenter of the temporal baseline, x-axis, and normal baseline, y-axis, distributions. The dots and lines represent the images and the interferograms, respectively.

4. Results and Discussion

4.1. Ground Deformation

Applying PSInSAR on a dataset of 29 descending Sentinel-1A radar images resulted in mean velocity map of land deformation in the interest area covering a period between June 2017 and May 2018. It should be noted that based on the spatial coherence of the PSs calculated in the area, most of the region is covered by a coherence around 0.85 or higher and it can prove the reliability of the monitoring process (Figure 3).

Figure 4 shows the deformation map along the study area of Sepulveda Transit Corridor and its vicinity. In an overall view, we can categorize the corridor into three zones based on the trend of displacement rates: (a) from 0 to 12 km; (b) from 12 to 24 km; and (c) from 24 to 34 km. The red spots in Figure 4 indicates the southeast of the corridor, located over oil extraction sites. In Particular, Figure 5 shows the deformation map in the Inglewood oil field with the maximum subsidence rate about 30 mm/yr. Therefore, it is essential to investigate such engineering solutions as ground stabilization in this site during the study phase and construction phase of Sepulveda corridor. The deformation pattern, also, displays low amounts of uplift (blue features) in south and east of the region meaning that water or gas probably pumped underground to stabilize the subsidence, or it may be as a result of an increase in groundwater level which will be discussed in Section 4.3 of this paper. For instance, the Los Angeles International Airport (LAX) is located in the regions suffering from low amounts of uplift. Green and yellow features through the corridor demonstrate subsidence rates between −15 and 0 mm/yr. Vegetation areas include less coherent PS points; so, there are some regions without sufficient outputs in the extracted maps. It was one of the main reasons to select a large study area to provide more PS points and obtain the deformation trend.

Figure 6 shows the variations in displacement rates (average) along the corridor from south (0 m) to north (34,000 m). In order to estimate the displacement rates in an arbitrary point through the corridor, we proposed a function as Equation (4) derived from the available deformation rates in the location of PS points. Such categorizations can help the designers and decision makers of the project to detect the places, which require solutions to control the probable asymmetric subsidence along the corridor. The asymmetric subsidence is fully explained in Section 4.5.

$$DR(\frac{\mathrm{mm}}{\mathrm{year}})=\left\{\begin{array}{cc}0.016x+0.51,& \hfill 0<x<12\mathrm{km}\\ -1.028x+11.44,& \hfill 12<x<24\mathrm{km}\\ 0.314x-16.11,& \hfill 24<x<34\mathrm{km}\end{array}\right\}$$

(4)

where DR is the displacement rate in each point through the alignment of Sepulveda Transit Corridor, and x (km) is the distance from the start point (LAX).

4.2. GPS Monitoring

In order to assess the results of PSInSAR analysis, the GPS observations and piezometric data are collected in the present study. Figure 7 shows the location of GPS stations and piezometric wells (P1 to P6). The characteristics and information of the well points are fully explained in Section 4.3.

GPS data has high temporal resolution because of continuous measurements while the PSInSAR method provides high spatial resolution and lower temporal resolution compared to data from GPS stations. Thus, the integration of GPS and PSInSAR measurements can be used to interpret the land displacements. In order to evaluate the PSInSAR results in the previous section, GPS data [69] were collected and introduced in

Table 1. GPS Stations in the Study Area.

GPS Station	Start Date	Location		Current Situation
		Long.	Lat.
DSHS	1999	−118.3485°	34.0239°	Inactive (since 2011)
FXHS	1999	−118.3595°	34.0806°	Inactive (since 2011)
BRAN	1994	−118.2771°	34.1849°	Active
NOPK	1999	−118.3480°	33.9797°	Active
LAPC	1999	−118.5747°	34.1819°	Active
LFRS	1999	−118.4128°	34.0951°	Active
CSN1	1999	−118.5238°	34.2536°	Active
WRHS	1999	−118.4276°	33.9582°	Active

. Eight stations are represented which two of them (DSHS and FXHS) are inactive since 2011. So, we considered six active stations to compare their results with the PSInSAR outputs in their locations and then, two stations (BRAN and NOPK) with more noises and insufficient observations were removed. Figure 8 shows the comparison between PSInSAR-derived time series deformation and the corresponding GPS observations. For this comparison, the RMSE was computed between each PSInSAR output and GPS measurement and demonstrated relatively good agreement between them. Lacking sufficient number of GPS stations is a significant weakness of GPS stations in monitoring the land displacements compared to SAR Interferometry. Also, the fluctuations in GPS results referred to seasonal effects and the instrument inherit errors [69]. These are the main disadvantageous or weaknesses of GPS observations compared to the SAR analysis performed in the present study.

Table 2. The comparison between GPS and PSInSAR outputs.

GPS Station	GPS Observation		PSInSAR Deformation Rate from 2017 to 2018 (mm/yr)	Standard Deviation of GPS Data (mm)	Standard Deviation of PSInSAR Data (mm)	RMSE (mm)
	Long-Term Deformation Rate from 1995 to 2018 (mm/yr)	Deformation Rate from 2017 to 2018 (mm/yr)
WRHS	+0.73	−2.61	−2.23	2.16	1.41	0.54
LAPC	+0.84	+0.49	+0.31	1.94	2.13	0.48
LFRS	−0.19	−0.72	−0.49	2.09	1.37	0.48
CSN1	+0.20	+0.08	+0.06	1.95	1.34	0.77

shows the comparison between GPS and PSInSAR deformation rates in long-term and short period. Overall, from Table 2 it can be found that the Standard Deviation of GPS data is in average (2.04) bigger than the Standard Deviation of PSInSAR data (1.56) which is because there are more noises in GPS measurements.

4.3. Monitoring of Groundwater Level Variations

According to the literature, one of the main reasons for ground displacements in the study area is water withdrawal or increase in groundwater level, except the red spots in the deformation map which suffer from oil extraction in the region. Based on the project’s official report [70], groundwater is highly variable along the extent of the project corridor. Unfortunately, the groundwater depths and elevations are not well-documented throughout the Santa Monica Mountains. The historical groundwater level data of the Inglewood quadrangle [71] shows the groundwater depths for the southern end of the Sepulveda corridor and indicates that groundwater level in the southerly part of the project alignment is about 12 m below grade and deepens to 15 m as the corridor extends northward through Inglewood city. In addition, data from another project in the region, called the Crenshaw/LAX Transit Corridor Project, show the areas along the southern part of the project corridor have measured depths of groundwater ranging between 12 and 27.5 m below grade. As the corridor bends northwest, the groundwater moves closer to the ground surface, with an approximate depth of 3 m or less [70].

Much of the I-405 highway in Sepulveda Canyon along the Santa Monica Mountains is not known to encounter shallow groundwater [72]. Based to groundwater monitoring data of the widening project of I-405 corridor from 2008 to 2009, groundwater was reached at depths greater than 21 m below the corridor surface. However, higher groundwater levels were observed during drilling between 1958 and 2007 for the purpose of as-built data at bridge locations through the existing Sepulveda Pass. This data contains groundwater depths between 0.6 and 24 m below existing grade [70]. The historical groundwater level data of the Van Nuys quadrangles [72] and the San Fernando [73] displays groundwater to be progressively shallower northward from the base of the Santa Monica Mountains where the groundwater depth is 12 m below grade and rises to 0 m below grade where the transit corridor intersects the 101 freeway. From the 101 freeway north along the corridor, the groundwater ascends progressively northward along alignment up to approximately 67 m below grade, where it reaches an abrupt groundwater barrier at the location of the Mission Hills fault. At this area, where the I-405 meets SR-118, the groundwater jumps to 12 m below grade. This site is where the San Fernando fault exists and groundwater data is probably not sufficient enough to show accurate contours due to the extensive faulting and deformation within the area [70].

We monitored the variations in groundwater level in the study area of Sepulveda Transit Corridor. Figure 9 shows temporal evaluation of groundwater level changes for the piezometers (the locations of piezometers are shown in Figure 7).

Table 3. Overall characteristics of the studied piezometric wells.

Piezometric Well	Deformation Rate by PSInSAR (mm/yr)	∆h (m)	∆t (year)	∆h/∆t (mm/yr)	Overall Trend of Ground Water Level Variations
P1	0	5.08	8	0.64	Remained stable.
P2	0	6.5	59	0.11	Remained stable.
P3	+3	−34.9	49	−0.71	Increased during the whole period and slightly decreased after 2009.
P4	−6.7	5	45	0.11	Relatively stable up to 1995 and then decreased slightly up to now.
P5	−11	11.4	43	0.27	Experienced several fluctuations, but decreased after 2008 up to now.
P6	−5	67.9	55	1.23	Decreased about 40 m between 1985 and 1995 and relatively stable up to now.

shows the overall trend of groundwater level changes at the studied piezometric wells and their corresponding PSInSAR deformation rate. The groundwater level in the location of P5 experienced several fluctuations and dramatically decreased since 2008. Surprisingly, this point shows the maximum subsidence rate among the piezometers with 11 mm/yr. On the other hand, the water level remained stable during the period at P1 and P2. Both piezometers have negligible displacements at their locations based on PSInSAR outputs. The rising trend of groundwater in piezometer P3 confirms the PSInSAR analysis which shows uplift of almost 3 mm/yr in P3 location. It should be noted that PSInSAR computes the total displacement rate and there may be some other factors as parts of ground movements. In order to investigate the relation between land deformation rate and water level variation it is imperative to know soil properties that are thoroughly explained in Section 4.4.

4.4. Geological Characteristics of the Sepulveda Project and Hydrogeology of Basins

The Los Angeles area consists of several basins containing groundwater systems. The Sepulveda project extends through numerous geologic characteristics of Los Angeles County within the Santa Monica (SM) and San Fernando (SF) Groundwater Basins.

Table 4. Overall characteristics of San Fernando (SF) and Santa Monica (SM) basins [74,75].

Basin	Confined/Unconfined	Recharge	Groundwater Level Trend
SF	Mainly unconfined with some confinement	Natural streamflow from the surrounding mountains, precipitation falling on impervious areas, reclaimed wastewater, and industrial discharges.	fairly stable over about the past 20 years
SM	Confined	Mainly by percolation of precipitation and surface runoff onto the sub-basin from the SM Mountains.	fairly stable over about the past 20 years

shows the overall properties of SM and SF basins. The recharge of SF is by natural streamflow from the surrounding mountains, precipitation falling on impervious areas, reclaimed wastewater, and industrial discharges [74]. The replenishment of SM is mainly by percolation of precipitation and surface runoff onto the sub-basin from the SM Mountains [75].

The SF Valley Basin is bounded by the Santa Susana Mountains on the north and northwest, the San Gabriel Mountains on the north and northeast, the San Rafael Hills on the east, the Santa Monica Mountains and Chalk Hills on the south, and the Simi Hills on the west. The groundwater in this basin is mainly unconfined with some confinement. Also, several structures disturb the flow of groundwater through this basin such as faults and subsurface dams [74]. The groundwater in the SM Basin is mainly confined and this basin underlies the northwestern part of the Coastal Plain of Los Angeles Basin. SM bounded by impermeable rocks of the SM Mountains on the north and by the Ballona escarpment on the south [75].

The main water-producing units of SM include the relatively coarse-grained sediments of the Recent Alluvium, Lakewood Formation, and San Pedro Formation [76]. The Recent Alluvium reaches a maximum thickness of around 27 m and comprises the clays of the Bellflower aquiclude and the underlying Ballona aquifer, depositing gravels resulting in the present Ballona Gap structure. These gravels are dominant at an approximate depth of 15 m. The Ballona aquifer is generally separated from the underlying San Pedro Formation by the confining layer [77]. The Lakewood Formation seems to be present only in the northern half of the SM Basin. The most significant water-bearing units are the sands and gravels within the San Pedro Formation. The Silverado aquifer of the San Pedro Formation has the greatest lateral extent and saturated thickness, and is considered as the main source of groundwater. The average thickness of San Pedro Formation is about 60 m in the SM Basin. Beneath the Silverado aquifer are relatively low-permeability sediments of the lower San Pedro and upper Pico formations [77].

The Sepulveda project cuts through San Fernando Valley in the north and extends through the Santa Monica Mountains in the south. The corridor is underlain by a layer of horizontal Quaternary sediment and also Tertiary-age sediments and sedimentary rocks which faced deformation into folds and offset by faults. Sedimentary and metamorphic bedrock are exposed with colluvial and alluvial soil at the surface at high elevations such as Santa Monica Mountains. In the north and south of Santa Monica Mountains, there is a thick layer of alluvial sediments. Also, the portion of the corridor located above San Fernando Valley is underlain by up to 600 m of alluvial deposits and a layer of Cretaceous-aged crystalline bedrock which exists below the alluvium [78]. The southern part of the project corridor, located in the Los Angeles Basin, is underlain by unconsolidated Quaternary-aged sandy deposits. These deposits can be subdivided into a loose unconsolidated Holocene-age layer and late-Pleistocene sediments. Also, hard rocks only exist in the mountainous portion of the basin at depth of 1500 m to 9000 m.

Figure 10 shows surface soil map of the study area including various soil types (the map is created based on raw soil data provided by the Los Angeles County Department of Public Works). In order to investigate the subsidence and uplift in the region, it is needed to study the soil properties in depth. Figure 11 displays the location of nine geotechnical boreholes in the region. The raw data of boreholes are collected from geotechnical report of the corridor and a number of geotechnical reports in the area [79,80,81,82,83,84].

Groundwater pumping has the potential to cause subsidence which can induce structural impacts. Induced subsidence is caused by the lowering of groundwater levels causing compaction of the aquifer materials to a point that the ground surface changes elevation. As water is withdrawn and groundwater levels declines, the effective pressure in the drained sediments increases. Compressible layers then compact under the over-pressure burden that is no longer compensated by hydrostatic pressure. The subsequent subsidence, includes both a component of elastic (recoverable) and inelastic (unrecoverable) subsidence, and is most pronounced in poorly compacted sediments. As a historical subsidence example, there is evidence for subsidence near Redondo Beach, in south of SM, that is attributed to oil and gas extraction [85]. From literature, a review of the geotechnical logs for wells completed in the SM Basin does not show considerable evidence of a thick compressible layer. Groundwater levels have also experienced significant drawdown in the past prior to the importation of water into the area. So, inelastic subsidence, which is of most concern, by nature can only occur once; consequently, any potential subsidence would have already occurred. Land subsidence in the study area does not appear to be a significant concern [76]. It should be added that as shown in Figure 12, investigation of the boreholes indicates some layers of fine-grained materials in some parts of the study area, which are susceptible to variations in groundwater level, an indication of the necessity of more detailed geotechnical investigations for the future constructions in the region.

4.5. Asymmetrical Subsidence

In most cases, the subsidence profile during the design phase of construction is considered symmetrical due to the assumptions inherent in the analysis and oversimplifications of the ground behavior. However, the ground behavior is not simple but instead very complex with different types of materials and different stress-strain responses. Such complexities can lead to the ground surface displacement to occur in such a way that it is not symmetrical (asymmetrical). In other words, asymmetrical subsidence means the difference in the amount of ground deformation between two near points which could be devastating especially to the available infrastructure and the infrastructure under construction such as the Sepulveda Transit Corridor. Asymmetry in subsidence can be observed in such industries [86,87,88] as mining, tunneling, groundwater withdrawal, oil and gas extraction, and geothermal fluid withdrawal.

Asymmetrical ground subsidence can be economically devastating to structures at surface. The heterogeneity of the ground layers (soil or rock) contribute to difficult estimation of asymmetrical subsidence [86,89]. As discussed in the Section 4.4, the Sepulveda project extends through numerous geologic characteristics and the region suffers from ground deformations. Accordingly, it is necessary to provide a certain procedure for the evaluation of asymmetric subsidence. Therefore, to detect the areas suffering from asymmetric subsidence, we propose a simplified version of strain rate based on the PSInSAR outputs to calculate Asymmetric Subsidence Index (ASI) as the following steps:

In step 1, consider two close PS points through the corridor length (L_L) and two PS points on/near both sides of the corridor width (L_W).

In step 2, determine the displacement rate (DR) of the selected points in step 1 based on PSInSAR analysis.

In step 3, calculate the ASI along length (ASI_L) by the ratio between the displacement rates (step 2) and length (L_L), Equation (5). Calculate the ASI along width (ASI_W) by the ratio between the displacement rates and length (L_W), Equation (6).

$$AS{I}_L=\frac{d_L}{L_L}=\left|\frac{D{R}_2-D{R}_1}{L_L}\right|$$

(5)

where DR₁ and DR₂ are the displacement rate of the PS points in length. For instance, the value of DR₁ and DR₂ of the Sepulveda Transit Corridor can be estimated by Equation (4).

$$AS{I}_W=\frac{d_W}{L_W}=\left|\frac{D{R}_{Right}-D{R}_{Left}}{L_W}\right|$$

(6)

where DR_Right and DR_Left are the displacement rate of the PS points in width.

In step 4, the final Asymmetric Subsidence Index of the interest area is defined as the maximum of ASI_L and ASI_W, Equation (7).

$$ASI=\max \left\{AS{I}_L,AS{I}_W\right\}$$

(7)

It should be noted that for practical purposes, it is more accurate and better to use vertical displacements, to provide much more meaningful result, instead of line-of-sight deformations in engineering problems. The higher the value of ASI, the higher the asymmetry of the deformation and the value of allowable ASI depends on the sensitivity of each especial structure. Therefore, we suggest computing ASI for new constructions for considering possible evaluations and solutions. For practical calculation, we suggest considering the average of ASI values for a several points. Clearly, the amount of d_L and d_W must be less than allowable displacement which depends on the sensitivity of each particular project. Figure 13 displays a simple example in the study area to show how to calculate the ASI. The required calculations for this example are shown in

Table 5. The ASI calculation for the example.

Point	Temporal Coherence	DR (mm/yr)	Length (m)	ASI	Max ASI
A	0.99	−14.6	LAB = 53.4	$AS{I}_L=\left|\frac{-14.6-(-14.1)}{53.4\times 1000}\right|=-9\times {10}^{-6}$	$3\times {10}^{-5}$
B	0.99	−14.1
C	0.99	−13.1	LCD = 31.2	$AS{I}_W=\left|\frac{-13.1-(-14.1)}{31.2\times 1000}\right|=3\times {10}^{-5}$
D	0.99	−14.1

and the computed ASI in this example is negligible; so, it can be assumed symmetrical. The proposed framework can be easily used in engineering applications compared to the more common strain rate analysis.

5. Conclusions

The main aim of this research was to obtain the land displacements along a new metro tunnel under preliminary study in Los Angeles, CA called Sepulveda Transit Corridor; to detect the most crucial areas suffering from subsidence or uplift; and to complement the previous reports in Los Angeles. For this purpose, we applied Persistent Scatterer Interferometric Synthetic Aperture Radar using 29 Sentinel-1A radar images from 2017 to 2018. The outputs demonstrated a high-rate of subsidence in the Inglewood field that is near the south portion of the Sepulveda Transit Corridor. Finally, we used the PSInSAR outputs to calculate Asymmetric Subsidence Index (ASI). The main conclusions of the present study can be drawn as the following:

• The results of this paper showed that the ground subsidence in northern portion of the Sepulveda Transit Corridor is continuous with subsidence rates between 1 and 14 mm/yr and a high-rate of subsidence (30 mm/yr) occurs in the Inglewood field near the south portion of the corridor, which may cause irreversible consequences in the future.
• Based on the variation in displacement rates along the corridor, we categorized the corridor into three zones to help the designers and decision makers of the project to detect the places which require considering solutions to control the probable asymmetric subsidence along the corridor.
• The ground water extraction rate and geotechnical properties in the area both strongly influence the rate and the distribution of subsidence.
• Collecting deep geotechnical boreholes indicated fine-grained layers in the region. This observation confirmed the necessity of more detailed geotechnical investigations in the interest area.
• There are not a sufficient number of piezometers to detect the groundwater level and accurate in-situ instruments such as GPS stations and extensometers to monitor the land displacements in this area. Therefore, for future researches, we recommend adding more piezometers and instruments particularly in the places suffering from continuous subsidence or uplift.
• Asymmetrical subsidence can be devastating to structures. Because of the heterogeneity of the ground layers, it is difficult to estimate asymmetrical subsidence. So, a simplified framework was proposed based on PSInSAR outputs to evaluate asymmetric subsidence.