1 Introduction

In Mexico, land subsidence due to groundwater extraction, a phenomenon resulting from the combination of its local characteristics and anthropogenic activities, has increased in rates and extension after the 1980s, exposing people and constructions and producing economic losses and risk. In Mexico City, since the late XIX century, vertical land subsidence has been measured (Gayol 1925; Figueroa-Vega 1976) and has demonstrated a pre-disposition for developing ground subsidence rates faster than − 10 cm/year because of compaction of the upper aquitard, which corresponds to a wide Pac-Man shape area located to the eastern and southeastern of the urban metropolitan area, where an ancient lake system was located (e.g. Cabral-Cano et al. 2008; Osmanoğlu et al. 2011; Cigna and Tapete 2021a). Among the geotechnical properties that favor the current subsidence rates of the silty clay upper aquitard are very high values of void ratio (6–11), water content (420%), compression index (3–6), porosity (70–90%), and plasticity index (300%) (Marsal and Mazari 1959; Díaz-Rodríguez 2003). Several researchers have also found that the higher the thickness of the upper aquitard, the higher the subsidence rate, finding that for each additional meter of compressible deposits, the rate of subsidence increases by 3 mm/year (Cabral-Cano et al. 2008; Solano-Rojas et al. 2015; Chaussard et al. 2021). The geotechnical and geological characteristics of Mexico City combined with groundwater extraction rates have induced considerable aquifer stress, reduced the pore pressure, and increased the effective stress, producing land subsidence as fast as -50 cm/year.

In this framework, several methodologies have been successfully applied to measure the land subsidence velocity field and spatial distribution characterization, that range from optical leveling, borehole extensometers, to LiDAR, GPS, and InSAR (Cabral-Cano et al. 2008; Calderhead et al. 2011; Osmanoğlu et al. 2011; Auvinet-Guichard et al. 2017a; Hu et al. 2022). InSAR, is a remote sensing technique that can obtain terrain information using SAR microwave radar sensors (e.g., Massonnet et al. 1993; Ferretti et al. 2001; Berardino et al. 2002). Satellite SAR sensors have recorded land surface information for the last 30 years, allowing us to evaluate land subsidence evolution. The InSAR technique measures land deformation in line-of-sight (LOS) direction using the phase difference between at least two SAR scenes acquired in almost the same place at two different times (e.g., Bürgmann et al. 2000). Phase measurement precision is obtained by using the coherences, which depends on the temporal acquisition frequency, orbital separation, atmospheric conditions, radar wavelength, and land cover (Hanssen 2001; Lanari et al. 2004).

Several multitemporal algorithms have been developed to improve the phase displacement measurements and study land deformation for long periods, such as Small BAseline Subset (SBAS; Berardino et al. 2002). SBAS algorithm estimates the land deformation using interferogram networks of differential interferograms with small spatial and temporal baselines, reducing the decorrelation and improving the spatial convergence, obtaining sub-centimetric precision (Manunta et al. 2019). Among the products that have been developed using InSAR to evaluate land subsidence and identify possible associated damages are the characterization of vertical velocity, angular distortion, and differential subsidence (e.g. Fernández-Torres et al. 2020; Cigna and Tapete 2021a).

The vertical land subsidence velocity can be obtained by combining LOS velocities and geometric information of SAR scenes acquired in different path directions (i.e., descending and ascending paths; Cigna et al. 2021a). The methodology to obtain the vertical velocity field allows to separate of the vertical rates from horizontal East-West deformation (Cigna and Tapete 2021a). The InSAR vertical velocity field can also be used to obtain angular distortion by computing the differential velocity in a neighborhood (e.g.Fernández-Torres et al. 2020; Cigna and Tapete 2021a). Angular distortion, which is the ratio of differential subsidence in a distance between two reference points, is a building damageability criterion that has been widely applied in geotechnical engineering (Skempton and Macdonald 1956; Bjerrum 1963; Burland and Wroth 1975). Angular distortion and differential subsidence high values promote the development of surface land subsidence-associated faults. The high rate of differential subsidence and subsidence-associated faulting has been a recurrent problem in Central Mexico because of its lithological and tectonic settings (Ferrari 2000; Garcı́a-Palomo et al. 2000; Arce et al. 2019). The Central Mexico geological settings contribute to the existence of stable volcanic structures adjacent to lacustrine and alluvial compressible deposits (e.g., the area between the stable volcanic rock of the Santa Catarina Range and the surrounding compressible material in southeast Mexico City). Therefore, constructions within these areas with high differential subsidence rates can suffer damages that lead to economic losses (Julio-Miranda et al. 2012; Auvinet-Guichard et al. 2013; Hernández-Madrigal et al. 2015; Solano-Rojas et al. 2020b).

In other Mexican cities undergoing ground subsidence, economic losses due to subsidence-associated faulting have been evaluated under two approaches. The first is a modified version of the Blong (2003) methodology to evaluate economic damage due to subsidence-associated faults. In this approach, the damage severity is evaluated in the field, and estimated the total economic loss in San Luis Potosi households based on the price of an average house (Julio-Miranda et al. 2012). The second approach evaluates the damages due to subsidence-associated faults based on a depreciation factor, which uses a proximity criterion between the ground subsidence associated faults and the constructions. This second approach has been applied considering average construction and land values in Morelia and using both land and cadastral values in Toluca (Hernández-Madrigal et al. 2014, 2015; Camacho-Sanabria et al. 2020). However, these two approaches to evaluate economic losses due to differential land subsidence did not consider any risk, which can be a valuable tool for selecting and prioritizing where mitigation measurements are necessary.

On the other hand, in Mexico City, risk assessment due to differential subsidence has previously used the properties density exposure and socioeconomic vulnerability based on population and households census data (Cigna and Tapete 2021a, b, 2022; Novelo-Casanova et al. 2022; Fernández-Torres et al. 2022) but there is no analysis on economic risk due to differential land subsidence yet.

This research evaluates the economic risk due to differential land subsidence in Mexico City, one of the cities with large population and very fast subsidence rates, to estimate the total economic cost of construction based on risk categories and the economic cost of building that overpass the Limit States to differential subsidence. We used an InSAR vertical velocity field (2014–2022), the cadastral land and construction values, and the Limit States of the current Mexico City building code to compute the differential subsidence economic risk evaluation.

2 Study area

Mexico City is the capital of Mexico, located in Central Mexico in North America (Fig. 1). This city has been built over an endorheic basin surrounded by volcanic ranges (i.e., Sierra de Guadalupe, Sierra de Chichinautzin, Sierra de las Cruces, and Sierra Nevada Fig. 1). This basin was filled with an interdigitation of lacustrine, alluvial and volcanic sediments (Arce et al. 2019), which provide unique mechanical properties (e.g. Marsal and Mazari 1959; Díaz-Rodríguez 2003). Mexico City Metropolitan Area encompasses municipalities of both Ciudad de Mexico (CDMX) as well as other states (i.e., Hidalgo and the State of Mexico), with a total population of 22 million people; making this Metropolitan Area the fifth biggest metropolitan population in the world (United Nations 2018). Mexico City has depended on groundwater extraction for more than 120 years to supply a large portion of its domestic, industrial, and agricultural water necessities (Gayol 1925; Carrillo 1948; Marsal et al. 2016). As a result, Mexico City has suffered land subsidence for more than a century, exhibiting strong subscience gradients and high rates of angular distortion and differential subsidence, resulting in considerable damages to housing and critical infrastructure (e.g.Cabral-Cano et al. 2008; Marsal et al. 2016; Fernández-Torres et al. 2020; Cigna and Tapete 2021a).

Fig. 1
figure 1

Study area. a Location of Mexico City (red polygon) with Google Earth imagery as the base map. b Mexico City’s municipalities (black polygons) and its neighboring states (blue polygons). The shaded elevation used in this research is from Continuo de Elevaciones Mexicano data (INEGI 2013). QGIS 3.28 software was to compose the maps

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3 Methodology

We applied a three-stage methodology to evaluate the economic risk of civil structures to differential subsidence. In the first stage, we used Mexico City’s cadastral information, the 2020 Households and Population Census data (INEGI 2020), the 2022 Fiscal Code (Congreso de la Ciudad de Mexico 2021), the Directorio Estadístico Nacional de Unidades Económicas (DENUE; INEGI 2022), and building height (Esch et al. 2022) to obtain the cadastral value per city block (Figs. 2 and 3). In the second stage, the Mexico City’s Sentinel-1 A/B (ascending/descending) 2014–2022 Single Look Complex (SLC) scenes were used to generate vertical velocity, angular distortion, and differential subsidence maps (Fig. 2). In this stage, we also calibrated the results by comparing the InSAR time series with GPS time series from 4 stations (Fig. 2). In the last stage, the products of stage I (i.e., cadastral value per city block) and stage II (i.e., differential subsidence map) are combined to obtain the differential subsidence per city block (Fig. 2). Then, we used the Limit States of differential subsidence using the Mexico City’s building code to obtain the city blocks exceeding allowable differential subsidence. Finally, we calculated the risk based on a risk matrix where the vertical axis is building volume from Esch et al. (2022), and the horizontal axis represents the number of times the Limit States values are exceeded.

Fig. 2
figure 2

Workflow to calculate the economic risk due to differential subsidence in Mexico City

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3.1 Stage I, cadastral values

The Secretary of Administration and Finance of Mexico City’s Government developed the methodology for calculating the cadastral values and calculation of property taxation. However, in the case of Mexico City, not all the data for calculating properties cadastral values is open-access. Therefore, we combined the partially-open Mexico City’s cadastral information with data from other sources such as the economic census of 2022 (INEGI 2022), the 2020 population and household census (INEGI 2020), Secretaría de Administración y Finanzas (2023), and (Esch et al. 2022), to estimate each cadastral value. These additional considerations, which are necessary to estimate the cadastral values, were developed as part of this research.

For the building use assignations, we used the cadastral information (Agencia Digital de Innovación Pública), DENUE (INEGI 2022), and the Census data (INEGI 2020); we then merged building uses of these three data sources to match them with the tables of construction values from the Mexico City’s Fiscal code using the official building use definitions from Secretaría de Administración y Finanzas (2023) (Supplementary file 2). When there is no match between building uses for the three data sources, we used the building uses from DENUE, because this data source is the most up-to-date (INEGI 2022). The DENUE registers all economic activities within a property (e.g., a shopping mall with many stores may have several DENUE’s building uses such as commerce, office, and health care, among others). Therefore, we established a hierarchical order to assign one building use per parcel of land. The hierarchical order is consecutively commerce, hotel, sport activities, office, health care, household, industry, warehouse, culture, communication, education, parking and squares, garden, and cemetery. This criterion is based on the average construction values per square meter (Congreso de la Ciudad de Mexico 2021). In cases where parcels of land do not have a specific building use, we assigned a household use because this is the most common use for civil structures in Mexico City (see Fig. 4a).

For each building’s number of floor assignation, we used the cadastral information (Agencia Digital de Innovación Pública). In this case, renaming the building floor data to match the Mexico City Fiscal Code was unnecessary. However, for the proprieties without building floor information, we replaced assigned Range 2 (i.e., buildings with 1 or 2 levels), as these constructions are the most common throughout the city (Fig. 4c).

Building class refers to a set of features of a civil structure, such as special building facilities, services, and quality of construction finishes (Congreso de la Ciudad de Mexico 2021). The class value is a unique value per property, and it can range from 1 to 7, where the higher the class value, the better the structure’s physical conditions, and it is reflected in its assigned construction unit cost value (see Supplementary file 1). Building class values were calculated based on the Characteristic Matrix from the Mexico City building code using the cadastral information and building height (Esch et al. 2022 (Supplementary file 3). For the household and household use adapted to office, hotel, commerce, health care, education, or communication, the construction total area categories from the Characteristic Matrix were used to define classes (Supplementary file 3). The number of floor categories from the Characteristic Matrixes were utilized for office, hotel, commerce, health care, education, or communication use. In cases where the building uses are industrial, warehouse, cultural, or sport, the categories from the Characteristic Matrixes based on height values were employed (Supplementary file 3).

To compute the cadastral value per land parcel, we applied a six-step methodology (Congreso de la Ciudad de Mexico 2021) (Fig. 3). In the first step, we computed the land value (LV) of each property as the multiplication of the unit LV per square meter by its total land area (Fig. 3). Then, property building use, floors, and class and the unit value per m2 tables from Mexico City Fiscal Code (Congreso de la Ciudad de Mexico 2021) were used to determine the unit construction value (CV) per square meter. Then, each unit construction value was multiplied by the construction area to obtain its construction value. In the third step, depreciation (TD) was calculated by multiplying 0.8% by the construction age. Next, we evaluated if the TD was higher than the 40% of the CV; in this case, we assigned the 40% of the construction value as the TD; in other cases, we kept the TD value. In the fifth step, we assessed if the building has special facilities (e.g., electric stairs, air conditioning, heating system) using the cadastral data. In cases where the building has special facilities, the construction value increases by 8%; else, the construction value remains the same. In the last step, the cadastral value per parcel of land was calculated as the sum of the final CV (considering TD and special facilities) and the LV (Fig. 3).

Fig. 3
figure 3

Workflow to calculate the cadastral value per parcel of land

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Fig. 4
figure 4

Input elements to determine the cadastral value per parcel of land. a Building use, b building class, and c building floors. RU: Range unique

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In order to cast the cadastral value information within a spatial resolution that is compatible with the 80 m x 80 m pixel size of the Sentinel-1 SBAS velocity maps, we calculated the average city block area of Mexico City’s eastern sector, where most of the subsidence occurs (i.e., Figs. 6, 7, 8 and 9; Gustavo A. Madero, Venustiano Carranza, Cuauhtémoc, Iztacalco, Iztapalapa, Tláhuac, and Xochimilco municipalites). To calculate the average city block area, we used the shapefile of the city block of Mexico City’s eastern municipalities from the Geostatistical frame (INEGI 2020). This analysis resulted in an average of 85 m x 85 m city blocks. We then calculated the cadastral price in US dollars per city block as the sum of all parcels of land inside each city block, assuming an exchange rate of $20 Mexican pesos/US dollar.

3.2 Stage II, InSAR subsidence velocity maps

3.2.1 InSAR descending and ascending average velocity maps

For generating the deformation maps, we used Sentinel-1 A/B SLC scenes downloaded from ESA’s Copernicus Sentinel-1 archive using the Alaska Satellite Facility (ASF) and the Copernicus Open Access hub. The Sentinel-1 A/B data set consists of 907 SLCs, which were acquired using orbits 143 and 78 in descending (543 SLCs) and ascending (364 SLCs) modes (Table 1), respectively, and covering the time window from October 3, 2014, to June 11, 2022. The Interferometric Synthetic Aperture Radar Scientific Computing Environment (ISCE-2; Rosen et al. 2012) software was used for processing SLCs using the Small BAseline Subsets approach (SBAS; Berardino et al. 2002). For the ISCE-2’s setup parameters, we used the Network-Based Enhanced Spectral Diversity (NESD; Fattahi et al. 2017), interferogram network with three connections, and the Statistical-cost Network-flow Algorithm for PHase Unwrapping (SNAPHU; Hooper 2009) for co-registering the SLCs scenes, generating the interferometric network and unwrapping the phase, respectively. We also applied a 5 by 20 multilook, in azimuth and range direction, to improve the spatial coherence, resulting in a pixel size of ~ 80 × 80 m2 (Table 1). The ISCE-2 final products were 1,137 and 969 unwrapped interferograms in descending and ascending modes, respectively (Table 1).

Table 1 SAR data
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The time series and average velocity maps were generated using the ISCE-2’s unwrapped interferograms and the Miami INsar Time-series Python software (MintPy; Yunjun et al. 2019). In MintPy software, the geographic coordinate of the TNGF cGPS station (19.327°,− 99.176°) was set up as the reference point for both descending and descending velocity maps (Supplementary file 4). The reference point was chosen mainly for three reasons. First, the reference pixel is in a null deformation area (i.e., geotechnical hill zone); spatial coherence larger than 0.85; and it shows comparable velocity fields for both acquisition geometries. We employed the empirical relationship between topography and the troposphere to correct the phase tropospheric delay component (Doin et al. 2009).

3.2.2 Vertical velocity, angular distortion, and differential subsidence

Vertical and horizontal velocity calculation based on ascending and descending InSAR-velocity fields may allow a higher accurate measurement of differential subsidence than using the vertical velocity calculated without subtracting the East-West velocity contribution (i.e., projecting LOS velocity into vertical using the incidence angle). We did not consider the North-South component because the near-polar Sentinel-1 orbits considerably reduce the sensor sensibility to measure land deformation in that direction (Torres et al. 2012).

To calculate each pixel’s average vertical \(\:{V}_{U\left(i\right)}\) and horizontal \(\:{V}_{E\left(i\right)}\), velocities, we used Eqs. 1, 2, 4, and 5 (e.g., Cigna et al. 2021). Where the subindexes \(\:D\left(i\right)\) and \(\:A\left(i\right)\) represent each velocity pixel in the descending or ascending (LOS) satellite acquisition mode. \(\:{V}_{A\left(i\right)/D\left(i\right)}\:\) are the ascending  or  descending (LOS) velocities, \(\:{\alpha\:}_{A\left(i\right)/D\left(i\right)}\), and \(\:{\theta\:}_{A\left(i\right)/D\left(i\right)}\) are the incidence angles and the azimuth angles, respectively.

$$V_{U\left(i\right)}=\frac{{E}_{Di}*{V}_{Ai}-{E}_{Ai}*{V}_{Di}}{{E}_{Di}*{U}_{Ai}-{E}_{Ai}*{U}_{Di}}$$
(1)
$$V_{E\left(i\right)}=\frac{{U}_{Ai}*{V}_{Di}-{U}_{Di}*{V}_{Ai}}{{E}_{Di}*{U}_{Ai}-{E}_{Ai}*{U}_{Di}}$$
(2)
$${U}_{A\left(i\right)/D\left(i\right)}=\text{cos}\left({\alpha\:}_{A\left(i\right)/D\left(i\right)}\right)$$
(3)
$${E}_{A\left(i\right)/D\left(i\right)}=-\text{cos}\left({\theta\:}_{\frac{A\left(i\right)}{D\left(i\right)}}\right)\text{sin}\left({\alpha\:}_{\frac{A\left(i\right)}{D\left(i\right)}}\right)$$
(4)

To evaluate civil infrastructure damage severity due to land subsidence, we can use subsidence-related intensity parameters such as angular distortion and differential subsidence (e.g., Skempton and Macdonald 1956; Burland and Wroth 1975). Angular distortion (\(\:\beta\:)\) is a structural engineering parameter that measures the slope between differential subsidence \(\:(ds\)) and their respective distance (\(\:l)\) (e.g., distance between the columns of a building) (see Eq. 5). To compute \(\:\beta\:\), we used the vertical velocity based on ascending and descending InSAR-velocity fields for the 2014–2022-time window as input raster (Fig. 6a), we then applied the Neighborhood Slope Algorithm (NSA) from Burrough et al. (2015). The NSA algorithm measures the maximum change rate between a central pixel and its closest neighbors in the horizontal \(\:(dz/dx)\) and vertical \(\:(dz/dy)\:\)directions (see Eq. 6). The NSA algorithm was applied in the QGIS spatial analysis software using the Slope tool, which considers a mobile window of 3 by 3 pixels length and has to posse at least seven valid values to calculate a no NAN \(\:\beta\:\) value. The angular distortion values were computed in radians to compare with Limit States values of \(\:\beta\:\) (e.g., Skempton and Macdonald 1956). Finally, the differential subsidence raster map (i.e., \(\:ds)\) was computed by multiplying the (\(\:\beta\:)\) value of each cell by the pixel size of the vertical velocity raster (\(\:l)\) (i.e., 80 m; Eq. 5) (e.g. Cigna and Tapete 2021a). The resulting angular distortion and differential subsidence calculated under this methodology only shows the civil structure differential deformation for the 2014–2022 period.

$$\beta\:=\frac{ds}{l}$$
(5)
$$\beta\:=\:\sqrt{{(dz/dx)}^{2}+{(dz/dy)}^{2}}$$
(6)

3.2.3 InSAR time series calibration

To calibrate the 2014–2022 InSAR velocity maps, we compared the time series from InSAR with four GPS stations (MXAZ, ICMX, MMX1, and UFXN; Supplementary file 4) using the descending and ascending velocity fields in LOS and 3D GPS time series (i.e., Vertical, North-South, East-West components), respectively. To perform the calibration, we first obtained the time series information of four Mexico City’s GPS stations with position information in the 2014–2022 time span (Blewitt et al. 2018; Cabral-Cano et al. 2018). Then, we projected all the GPS time series into LOS, considering the incidence angle of each GPS’s station pixel and using the information from InSAR descending and ascending acquisition geometries. Finally, we calculated the slope of both InSAR and GPS time series as the better linear regression adjustment (see Supplementary file 4).

3.3 Stage III, economic risk

3.3.1 City block exceeding Limit States due to differential subsidence

The economic exposure for each of Mexico City’s civil structure due to differential subsidence was calculated following a four steps methodology, which are:

  1. 1.

    We joined the differential subsidence map (see Stage II, Fig. 2) with the cadastral value per city block (see Stage I, Fig. 2).

  2. 2.

    The mean differential subsidence per city block was computed.

  3. 3.

    We compared the city blocks’ mean differential subsidence with the Limit State values from Mexico’s City Building Code (Table 2).

    Table 2 Limit states for differential subsidence in structures.
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  4. 4.

    Finally, we calculated the cadastral value of the city blocks exceeding the Limit State values under two scenarios, including or excluding the land value.

The Limit States values represent maximum tolerable differential subsidence based on building typologies and Mexico City’s building code; however, the information on typologies for each of Mexico City’s building does not exist. Therefore, to evaluate each city’s street block exceeding the Limit States value due to differential subsidence, we assumed two scenarios. The first assumes Mexico City only has masonry constructions with less than 2 floors high and the second assumes that all constructions of the city are made of steel frames with less than 4 floors. We used masonry and steel frame typology scenarios because they are the end members of the construction deformation spectrum. When masonry material suffers deformation higher than the elastic limit, it tends to have a fragile behavior, producing brittle fractures (e.g., Drysdale et al. 1994; De Angelis and Cancellara 2012); as a result, differential land subsidence produces fractures and structural damages without much resistance. On the other hand, steel frame constructions have a ductile behavior; they can deform plastically under high stress before failure; as a consequence, these structures can undergo larger differential subsidence while still preserving the construction stability by being more resilient and flexible (e.g., Salmon et al. 1990; Ohsaki et al. 2022); therefore, they can tolerate higher differential deformation.

The definition of the State Limits for differential subsidence only considers the structure’s differential deformation without considering the other geological conditions (GCDMX 2017). On the other hand, other building deformation features, such as total subsidence, do consider the geotechnical zone (i.e., Lake, Transition, and Hill) to define the Limit States (GCDMX 2017).

3.3.2 Differential subsidence city block risk

A risk matrix is used to compute the differential subsidence city block risk. In the vertical axis of this matrix, we used the building volume developed by the German Aerospace Center (Esch et al. 2022). We use three threshold values to define this axis. The first threshold corresponds to those city blocks with a building volume lower than 55,000 m3; this volume value results from multiplying the average city block area by the average building height. The second threshold upper value is two times the city block average value, and the last upper value is the highest. The matrix horizontal axis is defined by the Limit States values, the first value (DO) or null risk are city blocks not exceeding the Limit State values, the D1, D2, and D3 represent city blocks exceeding between 1 and 2, 2 and 3, and more than 3 times the Limit States values, respectively. In the risk matrix, R0, R1, R2, R3, and R4 represent null, low, intermediate, high, and very high risk due to differential subsidence.

The differential subsidence risk map results are a useful tool for determining areas with higher differential subsidence and construction volume exposure; however, results may slightly vary depending on the threshold’s definitions of the risk matrix. We defined the differential subsidence risk based on the Limit States of differential subsidence from the CDMX construction code (GCDMX 2017; see Table 2) and the city block volumes. We defined the risk matrix with 12 cells and 5 classes (RO–R4) to maintain consistency with previous analysis, which made similar assumptions (e.g.Cigna and Tapete 2021a, b, 2022). However, in our research, we define R0 (null risk) for all the city blocks that do not exceed the Limit States, regardless of their volume size (Figs. 10 and 11).

4 Results and discussion

4.1 Cadastral values

4.1.1 Building use, class, and floors distribution

Building uses were assigned using the DENUE, the 2020 Household and Population Census, and Cadastral information, as explained in Sect. 3.1. Figure 4a shows the building use distribution per parcel of land in Mexico City. As a result, we observe that more than 95% of the parcels of land have households (HS; 48.5%) and commerce (CO; 46.9%) uses, where the sum of both HS and CO represent 1,021,314 out of 1,069,900 properties.

For class values calculation, the Characteristic Matrix of Mexico City’s Fiscal Code was used, resulting in intermediate classes (4, 3, and 5), the most common in Mexico City (Fig. 4b). The sum of classes 3, 4, and 5 is equal to 720,900 parcels of land out of a total of 1,069,900, representing 67.3%. The properties within classes 4, 3, and 5 are 251,236, 248,390, and 221,274, respectively (Fig. 4b). Therefore, most of the buildings in Mexico City have intermediate conditions regarding their construction finishes, services, and materials.

To determine the number of floors per land parcel, we used Mexico City’s Cadastral Information (Agencia Digital de Innovación Pública). The Cadastral Information reports the number of levels in 8 categories based on the number of levels (i.e., R1, R2, R5, R10, R15, R20, R99, RU; Fig. 4c) except for the RU category, which does not depend on the number of floors but building use (see Supplementary file 1). We can observe that R2 (1–2 levels high) and R5 (3–5 levels high) are the most common number of building’s floors in Mexico City, representing more than 96% of Mexico City’s constructions. In other words, in Mexico City, 9.6 out of 10 buildings have a total height equal to or lower than 12.2 m. Assuming each story has an average height of 2.44 m, where 77.5% and 19% of buildings have 1–2 floors and 3–5 floors, respectively (Fig. 4c). The obtained average buildings height match with previous research (e.g., Esch et al. 2022).

4.1.2 Cadastral values per city block

The cadastral value per property is the result of the sum of land value (LV) and construction value (CV), considering time depreciation and special building facilities (Fig. 3; see Sect. 3.1). Then, cadastral values were grouped into city blocks using polygons from Mexico City’s census (INEGI 2020), obtaining cadastral value per city block (Fig. 5a). The cadastral values per city blocks are presented with or without land value, and these are grouped into five categories considering the city block cadastral values as follows: (a) ≤ $5 million USD, (b) $5−10 million USD, (c) $10−30 million USD, (d) $30−50 million USD, and (e) ≥ $50 million USD (Fig. 5a and b).

Fig. 5
figure 5

Cadastral value per city block. a Considering construction and land value. b Only construction values. c Cadastral values of Mexico City and its municipalities considering land and construction values (green polygons) and excluding land value (grey polygons)

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In 2022, Mexico City has a total cadastral value of $171.3 billion USD, where $113.1 billion USD corresponds to the construction value and $58.2 billion USD accounts for land value. Only 4.5% of city blocks have a cadastral value higher than $10 million USD, and the top three municipalities with cadastral values are Iztapalapa $21.1 billion USD, Gustavo A Madero $19.3 billion USD, and Cuauhtémoc $19 billion USD. In contrast, municipalities with the lower cadastral value are Milpa Alta $854.9 million USD, Tlalpan $3.1 billion USD, and Magdalena Contreras $3.4 billion USD (Fig. 5c). Municipalities with the higher percentage of city blocks with a cadastral value exceeding $10 million USD are Cuauhtémoc, Miguel Hidalgo, and Cuajimalpa, with 19.2%, 19.1%, and 11.8%, respectively. Novelo-Casanova et al. (2022) found that Mexico City’s western sector has a lower socioeconomic vulnerability. Our research may suggest that a possible reason for a lower socioeconomic vulnerability in the western Mexico City portion is due to the proportionally higher construction cadastral value.

4.2 Mexico City subsidence

4.2.1 Vertical and horizontal velocity maps

Ascending and descending InSAR LOS velocity maps are obtained by processing Sentinel-1 A/B SLCs scenes covering October 2014 to June 2022 (see Sect. 3.2.1; Supplementary file 4). In order to calculate the vertical and horizontal E-W velocity fields, we combine the ascending and descending velocity fields and their acquisition geometries (see Sect. 3.2.2; Fig. 6a and b). Mexico City presents two well-defined areas where ground subsidence rates can exceed tens of centimeters per year.

Fig. 6
figure 6

Mexico City’s InSAR velocity using Sentinel-1 A/B scenes for the period 2014–2022. a Vertical velocity field; 1: The Angel of Independence, 2: Monument to the Revolution, 3: Cathedral, 4: Mexico City International Airport, 5 and 6: locations of maximum vertical velocity in the Texcoco and Chalco sub-basins, respectively. Zone I: Hill, Zone II: Transition, Zone III: Lake geotechnical zones (GCDMX 2017 ). b horizontal velocity map; 1 (Texcoco), 2 (Mexico City International Airport), and 3 (Peñón del Marqués) represent locations of maximum horizontal velocity. Black polygons are Mexico City’s municipalities (see Fig. 1)

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The largest vertical subsidence footprint is in the central northeast sector of the city (Fig. 6a). This footprint follows an approximate northeast-southwest orientation, a maximum length of ~ 28 km, and is located within the Lake (Zone III) geotechnical zoning. The fastest vertical velocity within this subsidence footprint is almost in the middle of this sector (point 5, Fig. 6a), in the surroundings of Caseta de Cobro Peñón-Texcoco, Nezahualcóyolt municipality, State of Mexico, where the vertical subsidence velocity is -52.3 cm/yr, the highest subsidence velocity recorded in the Mexico City Metropolitan Area, which matches the highest vertical subsidence and spatial location reported in previous research (Chaussard et al. 2021). Some of the city’s most significant historical and strategic buildings are in this vertical subsidence patch. For instance, the Angel of Independence (1), Monument to the Revolution (2), the Mexico City Cathedral (3), and the Mexico City International Airport (4) have maximum vertical subsidence of − 1.3 cm/yr, − 2.4 cm/yr, − 6.6 cm/yr and − 24 cm/yr, respectively (Fig. 6a, points 1, 2, 3, and 4).

The second vertical subsidence footprint is located between the southern flank of the Sierra Santa Catarina and borders the northern flank of the Sierra Chichinautzin (Fig. 6a). This zone has an east-west orientation, and its maximum length can be up to 24 km. Within this footprint, the fastest observed vertical subsidence rate is − 43.8 cm/yr in the suburb of Bosque de Xico, Valle de Chalco municipality, State of Mexico (Fig. 6a; point 6).

At the municipality level, the top five metropolitan area municipalities with the fastest recorded vertical velocity are Nezahualcóyolt (− 26.6 cm/yr), Venustiano Carranza (− 18.2 cm/yr), Valle de Chalco (− 17.5 cm/yr), Iztacalco (− 15.2 cm/yr), and Tláhuac (− 12.9 cm/yr). The municipality ranking with the fastest maximum subsidence rate is Nezahualcóyolt (− 52.3 cm/yr), Texcoco (− 46.6 cm/yr), Valle de Chalco (− 43.8 cm/yr), Tláhuac (− 41.1 cm/yr), and Xochimilco (− 38.8 cm/yr).

Even though using different SAR sensors, InSAR processing algorithms, and time windows, the obtained velocity field has similar deformation rates and spatial distribution than previous land subsidence research published for Mexico City (e.g., Cabral-Cano et al. 2008; López-Quiroz et al. 2009; Osmanoğlu et al. 2011; Fernández-Torres et al. 2020, 2024; Solano-Rojas et al. 2020b; Chaussard et al. 2021; Cigna and Tapete 2021a). Other analyses that used multi-sensor InSAR data and integrated total subsidence since the advent of SAR data indicate that Mexico City’s subsidence behavior has maintained a linear trend (Du et al. 2019; Chaussard et al. 2021).

The high subsidence rates recorded in Mexico City may intensify the effects of other natural hazards, such as the seismic response of subsoil (Ermert et al. 2023), and increase the flooding potential. In the case of seismic activity, ground subsidence has generated shortening of the vibration periods of soil (Avilés et al. 2006; Avilés and Pérez-Rocha 2010; Albano et al. 2016), rapid slip along subsidence associated faulting (Solano-Rojas et al. 2020a), and the increase of vulnerability to earthquakes in constructions over some parts of the Transition geotechnical zone (Ovando-Shelley et al. 2003). The high-ground subsidence velocities recorded in Mexico City have modified the terrain relief, promoting the development of negative relief areas susceptible to flooding events when extreme rain occurs (Novelo-Casanova et al. 2022). Precipitation could also collapse the drainage network, which has lost its optimal capacity due to the slope decrease of pipelines due to land subsidence, increasing the flooding potential affecting the central and northern parts of Mexico City (Novelo-Casanova et al. 2022).

Mexico City’s rapid subsidence velocity has induced changes in the subsoil properties, and in the silty clay upper aquitard. Ovando-Shelley et al. (2003) found that water content, density, strength, and compressibility are the subsoil properties that are more susceptible to changes due to land subsidence in Mexico City, which can produce a rearrangement of lacustrine volcanic components of the upper aquitard producing inelastic ground subsidence (Chaussard et al. 2021).

Mexico City’s subsidence may also produce migration of salts and other contaminants from the upper aquitard to the productive aquifer, causing a reduction in water quality, producing the potential for a water crisis in coming years (e.g., Ortega-Guerrero et al. 1993; Hernández-Espriú et al. 2014). Chaussard et al. (2021) forecasted that within 150 years, the upper aquitard would be completely compacted, which could eliminate the current natural protection of the productive aquifer from the contaminants due to urban activity and contribute to at least an additional 30 m of subsidence.

In the horizontal rates field, we can observe that the E-W velocities are comparatively lower than the vertical subsidence values (Fig. 6a and b). However, some municipalities in the eastern sector of the Mexico City metropolitan area show significant horizontal velocities. The maximum recorded horizontal velocities are in the surroundings of Caseta de Cobro Peñón-Texcoco, Texcoco (− 10.1 cm/yr), Mexico City International Airport, Venustiano Carranza (− 8.6 cm/yr), and the north flank of Peñón del Marqués, Iztapalapa (− 8.3 cm/yr), (Fig. 6b points, 1, 2, and 3, respectively). Our results are similar to those obtained by Cigna and Tapete (2021a).

We also observe that at the south flank of Sierra de Santa Catarina and the north flank of Sierra de Chichinautzin, their predominant horizontal velocities are toward the west and east, respectively, which suggests some topographic control of the horizontal movement in this portion of the city. The obtained horizontal velocity field may suggest that although the land subsidence in Mexico City is predominantly vertical, there is indeed a horizontal component of motion. The horizontal velocity could be due to groundwater extraction and tectonic movement (Osmanoğlu et al. 2011). Our results only show the East-West horizontal field because Sentinel-1 has a nearly polar acquisition path, considerably reducing the capability to detect North-South deformation (Torres et al. 2012).

Our velocity maps were calibrated by comparing the InSAR-SBAS LOS in ascending and descending acquisition modes with four GPS stations (MXAZ, MMX1, ICMX, and UFXN, see Supplementary file 4). In this calibration, we found a mean velocity difference of 0.3 cm/yr, and 0.4 cm/yr between ascending and descending velocity (LOS) time series and the cGGPS (LOS) time series. Therefore, we assume that the obtained velocity fields are accurate. Previous research also compared InSAR and GPS time series and obtained millimetric velocity differences, confirming the assumption that InSAR velocity fields provide precise measurement of land surface deformation (e.g., Cabral-Cano et al. 2008; Osmanoğlu et al. 2011; Yalvac 2020; Fernández-Torres et al. 2022, 2024).

4.2.2 Angular distortion and differential subsidence

We use the InSAR-vertical velocity (2014–2022) as input to the Neighborhood Slope Algorithm (NSA) to calculate angular distortion and differential subsidence. The NSA algorithm allows measuring the vertical and horizontal maximum change rate (see Eqs. 5 and 6, Sect. 3.2.2) and the angular distortion (\(\:\beta\:\)) and differential subsidence (ds). In Mexico City, the maximum differential vertical velocity change occurs in the eastern sector of the city, around the contact of the stable volcanic structures (e.g., Sierra de Chichinautzin, Sierra de Santa Catarina, Peñón del Marqués, Peñón de Los Baños; see Fig. 7a and b). Mexico City’s municipalities with the higher mean differential subsidence are Tháhuac (ds = 0.8 cm), Iztapalapa (ds = 0.6 cm), Venustiano Carranza (ds = 0.5 cm), Iztacalco (ds = 0.4 cm), and Xochimilco (ds = 0.4 cm). The four locations with the highest differential subsidence are in the surrounding of Line A, Peñón Viejo subway station, Iztapalapa (ds = 7.2 cm), between Line 12, Nopalera and Zapotitlán subway stations, Tháhuac (ds = 5.4 cm), and Tlalmelac, Xochimilco (ds = 4.4 cm), and around the Mexico City International Airport (ds = 3 cm) (Fig. 7b; locations P1, P2, P3 and P4, respectively, see Fig. 8a–c). On the other hand, the municipalities with the lower mean differential subsidence are Azcapotzalco (ds = 0.05 cm), Miguel Hidalgo (ds = 0.06 cm), and Álvaro Obregón (ds = 0.07 cm).

Fig. 7
figure 7

Angular distortion and differential subsidence based on InSAR vertical velocity (2014–2020), in Mexico City. a Angular distortion; b differential subsidence. Blue circles represent the four locations with the highest differential subsidence in Mexico City. P1: Peñón Viejo Line A subway station, Iztapalapa (ds = 7.2 cm), P2: between Nopalera and Zapotitlán Line 12 subway stations, Tháhuac (ds = 5.4 cm), P3: Tlalmelac, Xochimilco (ds = 4.4 cm), P4: Mexico City International Airport (ds = 3.0 cm)

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In Fig. 8a–c, we can observe three zoom-in areas with the highest differential subsidence and their respective cross sections. These figures show that in Mexico City, high values of differential subsidence and angular distortion are located along the contact between volcanic structures and lacustrine compressible deposits. Previous research has demonstrated that abrupt transition between materials with dissimilar mechanical behavior (i.e., volcanic, and lacustrine deposits) could be the leading cause of differential subsidence (e.g., Carreón-Freyre and Cerca 2006; Carreón-Freyre and Rodríguez-Quiroz 2010). Carreón-Freyre et al. (2006) pointed out that an additional contribution to differential deformation is also observed inside the silty clay aquitard sediments due to lateral and vertical heterogeneities in the geomechanical behavior that the mineralogical heterogeneity may produce, which could be controlled by the paleoenvironmental history of the sediments.

Fig. 8
figure 8

Zoom-in view of areas of interest with the higher values of differential subsidence and differential subsidence cross-sections (a), (b), and (c). The location of the zoom-in views are shown in Fig. 7b. MCIA: Mexico City International Airport City blocks exceeding the Limit States due to differential subsidence 

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High values of differential subsidence promote large tensile stress in the ground, increasing the vulnerability to developing subsidence-associated faulting (e.g., Holzer 1984; Rojas et al. 2002; Cabral-Cano et al. 2008; Carreón-Freyre 2010Sarychikhina et al. 2011; Solano-Rojas et al. 2020c; Cigna and Tapete 2021b; Fernández-Torres et al. 2022). Faulting associated with differential subsidence is responsible for considerable damages to constructions in Mexico City, including the subway system, urban infrastructure, historical buildings, and houses (e.g., Auvinet-Guichard et al. 2013, 2017b; Solano-Rojas et al. 2020b). In this context, Ovando-Shelley et al. (2003) suggest a scenario where most of the architectural heritage buildings of Mexico City may be severely damaged in the coming decades at the current differential subsidence rate.

4.3 Economic risk

4.3.1 City blocks exceeding Limit States due to differential subsidence

We combine city blocks’ cadastral value with the differential subsidence field to compute and compare the results with the Limit States under two assumptions (Fig. 2). In scenario 1, all city street blocks have masonry constructions with less than two floors, and scenario 2, civil structures are made of steel frame constructions less than four floors (see Sect. 3.3.1; Table 2; Fig. 9a–d).

Fig. 9
figure 9

City blocks and city block values that exceed differential subsidence Limit States assuming masonry structures with less than 2 floors, (a) and (c) respectively. City block and city block values that exceed differential subsidence Limit States assuming steel frame structures with less than 4 floors (b) and (d) , respectively. In panels a and b red and green polygons represents city blocks exceeding or not the Limit States, respectively 

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In scenario 1, we found that 24.6% of city blocks overpass the construction code differential subsidence Limit State value (0.0025 m; Table 2; Fig. 9a). This implies a cadastral value exposure of 44.4 billion and 32 billion USD if only constructions are considered. We also found that the municipalities with the higher number of city blocks exceeding tolerable differential subsidence assuming masonry constructions with less than two floors are Iztapalapa (5517), Gustavo A. Madero (2712), and Tláhuac (1796), and the municipalities with the lower number of city blocks that exceed the differential subsidence limit states are Miguel Hidalgo (0), Magdalena Contreras (4), and Azcapotzalco (5) (Fig. 9a). The top 3 municipalities with the highest cadastral values exceeding Limit States assuming masonry constructions typology are Iztapalapa $12.4 billion USD, Cuauhtémoc $7.7 billion USD, and Gustavo A. Madero $7.6 billion USD (Fig. 9c).

For scenario 2, we observed that 9.7% of Mexico City’s blocks exceed 0.006 m of differential subsidence (Table 2; Fig. 9b). The cadastral value of city blocks exceeding 0.006 m is $13.6 billion USD, where $9.9 billion USD represents only the civil structure cost. Municipalities with a higher number of city blocks exceeding 0.006 m are Iztapalapa (2908), Tláhuac (1,368), and Gustavo A. Madero (857). The municipalities with the highest cadastral value exceeding 0.006 m are Iztapalapa, Gustavo A. Madero, and Tláhuac with $5.5 billion, $2.1 billion, and $2 billion USD, respectively (Fig. 9d).

In scenarios 1 and 2, we obtained that $44 billion USD and $13.6 billion USD are the cadastral cost of city blocks exceeding Limit States, respectively. As a consequence, the economic exposure due to differential subsidence that exceeds the construction code Limit States represents 3.1% and 0.9% of the 2022 Mexico PIB ($1.41 trillion USD; the 14th largest economy of the world; World Bank 2023) for scenarios 1 and 2, respectively.

The obtained cadastral value exceeding the Limit States considers the differential deformation of construction for the 2014–2022 period, which is a small time window of the more than 100 years that Mexico City has undergone land subsidence (Gayol 1925). Therefore, the cadastral cost scenarios of civil structures exposed to differential subsidence are underestimated.

We used two scenarios to evaluate the city blocks exceeding the Limit States due to differential subsidence (i.e., masonry ≤ 2 floors and steel frame constructions ≤ 4 floors) because the information on building typologies is unavailable in Mexico City. However, these two construction scenarios represent the end members of the construction deformation spectrum, as was mentioned above. Our assessment was performed at the city block level because of the Sentinel-1 spatial resolution limitations, which may produce an underestimation of the Limit States due to differential subsidence.

Other Mexican cities, such as San Luis Potosi, Morelia, and Toluca, have evaluated the economic losses due to differential subsidence (Julio-Miranda et al. 2012; Hernández-Madrigal et al. 2015; Camacho-Sanabria et al. 2020). These studies did not consider the velocity and differential velocity fields. Instead, they used the spatial proximity to faulting associated with ground subsidence as the unique criteria to identify the properties with the highest exposure and only assumed an average construction cost, except for Camacho-Sanabria et al. (2020) in Santa Ana Tlapaltitlán Toluca, where they used the land and construction cadastral costs in their estimation of the economic losses due to differential subsidence.

4.3.2 Economic risk due to differential subsidence

A risk matrix based on average city block volume and a multiple of the Limit State threshold value was used to compute economic risk due to differential subsidence (Figs. 10 and 11). Five categories are defined to evaluate risk, which are null (R0), low (R1), intermediate (R2), high (R3), and very high (R4).

Fig. 10
figure 10

Economic risk due to differential subsidence assuming steel frame constructions with 4 or less floors. a City blocks with the economic risk value. b City blocks distribution per risk category. c Household distribution per risk category. e Cadastral values per risk category 

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Fig. 11
figure 11

Cadastral value per city block. a Considering construction and land value. b Only construction values. c Cadastral values of Mexico City and its municipalities considering land and construction values (green polygons) and excluding land value (grey polygons)

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If the scenario is based on the assumption that civil structures on all city blocks are masonry with 1–2 floors, we found that 7.6% of city blocks are under a high and very high risk. The number of properties and people living in those high and very high-risk city blocks are 215,000 and 738,000, respectively. As a consequence, the cost of civil structures at high and very high economic risk due to differential subsidence is $10.5 billion USD or 6.1% of Mexico City’s cadastral value (Fig. 10a–d).

When we assume that city blocks are made of constructions with steel frames with 4 or less floors, 2% of city blocks reach high economic risk, where 1.6% (48 thousand) and 1.9% (169 thousand) of Mexico City’s total households and population, reach high economic risk due to differential subsidence. In economic terms, $2.5 billion USD is the total cadastral value of city blocks with high risk or 1.4% of Mexico City’s cadastral value (Fig. 11a–d).

In Mexico City, other methodologies have been applied to evaluate risk due to land subsidence. Fernández-Torres et al. (2022) used a formula that includes socioeconomic vulnerability, vertical land subsidence, and subsidence horizontal gradient to determine socioeconomic risk due to land subsidence Cigna and Tapete (2021a) used a risk matrix that consists of properties density and angular distortion to compute subsidence-induce surface faulting. Both previous risk evaluations were made at AGEB level (i.e., a group of city blocks defined by INEGI), and in Cigna and Tapete (2021a), the analysis included adjacent municipalities of the State of Mexico.

Our results estimate the economic value of the civil structures that exceed the Limit States, based on Mexico City’s current construction code, and is most useful to compare the economic impact of differential subsidence with other phenomena such as seismic or volcanic activity. In addition, using the risk matrix, the building volumes instead of the property’s density considered the actual dimensions, including the civil structure height and not only the property amount. Our risk maps allow us to describe with higher spatial resolution the properties at high and very high economic risk.

Other research has previously combined land deformation from satellite geodesy data (e.g., InSAR) construction or cadastral values, and construction typologies to assess economic risk due to flooding, land subsidence, landslides, and sinkholes elsewhere (e.g., Peduto et al. 2018; Navarro-Hernández et al. 2023; Mastrantoni et al. 2023). However, our research is the first economic evaluation due to differential subsidence considering the State Limits, building typologies, cadastral information, construction volumes, and land deformation.

Although our economic risk assessment provides, for the first time, the economic damage cost within the context of differential subsidence in Mexico City, some limitations in this work should be considered in future research. Using higher resolution X-band SAR sensors will allow a more detailed evaluation at individual land parcel level scale. Fieldwork to document structural damage will allow the generation of fragility and vulnerability curves, which are useful to better define the severity of structural damage. Finally, we acknowledge that the cadastral value used in our analysis may underestimate the property’s real market value.

5 Conclusion

This study evaluated the economic risk due to differential land subsidence under two scenarios using different construction typologies. These two scenarios assumed that Mexico City constructions are built using masonry materials with 1–2 floors or steel frame constructions with 1–4 floors. In the first scenario, we obtained that 7.6% of the city blocks of Mexico City are at high and very high economic risk, exposing 738,000 people and 215,000 properties, which have a cadastral cost of $10.5 billion USD, which is equivalent to 6.1% of the Mexico City total cadastral value (i.e., $171.3 billion USD). For scenario 2, we obtained that the cadastral value of properties at very high risk is $2.5 billion USD or 1.4% of Mexico City’s total cadastral value, exposing 2% of Mexico City’s blocks, 48,000 properties, and 169,000 people.

The obtained vertical velocity spatial distribution presents two well-defined areas where the subsidence rate is faster than − 10 cm/yr toward the eastern and southeastern sector of the Mexico City metropolitan area with a maximum vertical velocity of -52.3 cm/yr within the Nezahualcóyolt municipality, State of Mexico, coinciding with previous research (Cabral-Cano et al. 2008; Chaussard et al. 2021; Cigna and Tapete 2021a). On the other hand, we detect that the metropolitan area undergoes horizontal velocities faster than − 8 cm/yr in places like Texcoco, the Mexico City International Airport, and Peñón del Marqués in Iztapalapa, suggesting that although the vertical velocity is the main velocity component, a horizontal component is also present in some places of the city as was previously reported by Cigna and Tapete (2021a). We also confirm that the highest values of differential subsidence are along the sharp boundaries between compressible lacustrine deposits and stable volcanic structures where the three locations with the highest differential subsidence are in the surroundings of Line A Peñón Viejo subway station, Iztapalapa (ds = 7.2 cm), between Line 12’s Nopalera and Zapotitlán subway stations, Tháhuac (ds = 5.4 cm), Tlalmelac, Xochimilco (ds = 4.4 cm), and Mexico City International Airport (ds = 3 cm).

This study is an analysis of the economic cost and risk due to differential land subsidence in Mexico City, one of the cities in the world with the highest land subsidence rate, population exposure, and long subsidence history. The methodology developed here can be applied to assess the economic risk due to differential land subsidence and other hazards (e.g., earthquakes, flooding, landslides) through Mexico or elsewhere.