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Geological Society of America Bulletin doi: 10.1130/B26001.1 2008;120;1556-1566 Geological Society of America Bulletin Sánchez-Zamora and Richard E. Carande Enrique Cabral-Cano, Timothy H. Dixon, Fernando Miralles-Wilhelm, Oscar Díaz-Molina, Osvaldo Space geodetic imaging of rapid ground subsidence in Mexico City Email alerting services articles cite this article to receive free e-mail alerts when new www.gsapubs.org/cgi/alerts click Subscribe America Bulletin to subscribe to Geological Society of www.gsapubs.org/subscriptions/ click Permission request to contact GSA http://www.geosociety.org/pubs/copyrt.htm#gsa click official positions of the Society. citizenship, gender, religion, or political viewpoint. Opinions presented in this publication do not reflect presentation of diverse opinions and positions by scientists worldwide, regardless of their race, includes a reference to the article's full citation. GSA provides this and other forums for the the abstracts only of their articles on their own or their organization's Web site providing the posting to further education and science. This file may not be posted to any Web site, but authors may post works and to make unlimited copies of items in GSA's journals for noncommercial use in classrooms requests to GSA, to use a single figure, a single table, and/or a brief paragraph of text in subsequent their employment. Individual scientists are hereby granted permission, without fees or further Copyright not claimed on content prepared wholly by U.S. government employees within scope of Notes © 2008 Geological Society of America on February 25, 2011 gsabulletin.gsapubs.org Downloaded from

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Geological Society of America Bulletin

doi: 10.1130/B26001.1 2008;120;1556-1566Geological Society of America Bulletin

 Sánchez-Zamora and Richard E. CarandeEnrique Cabral-Cano, Timothy H. Dixon, Fernando Miralles-Wilhelm, Oscar Díaz-Molina, Osvaldo Space geodetic imaging of rapid ground subsidence in Mexico City  

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official positions of the Society.citizenship, gender, religion, or political viewpoint. Opinions presented in this publication do not reflectpresentation of diverse opinions and positions by scientists worldwide, regardless of their race, includes a reference to the article's full citation. GSA provides this and other forums for thethe abstracts only of their articles on their own or their organization's Web site providing the posting to further education and science. This file may not be posted to any Web site, but authors may postworks and to make unlimited copies of items in GSA's journals for noncommercial use in classrooms requests to GSA, to use a single figure, a single table, and/or a brief paragraph of text in subsequenttheir employment. Individual scientists are hereby granted permission, without fees or further Copyright not claimed on content prepared wholly by U.S. government employees within scope of

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1556

ABSTRACT

Since the late 1950s, several areas of Mex-ico City have undergone accelerated ground subsidence and have developed associated fracturing and faulting. New interferometric synthetic aperture radar (InSAR) and global positioning system (GPS) data indicate that rates of current land subsidence in Mexico City exceed 350 mm/yr. These rates are close to historical maximum levels of the mid-twen-tieth century, when mitigation efforts were fi rst undertaken to reduce damage to urban infrastructure. The locus of maximum subsid-ence has shifted from its historical location in the old city center to the east. Correlation of our InSAR results with seismically mapped stratigraphic units suggests that subsidence is primarily controlled by compaction of Quater-nary lacustrine clays and silts. We also evalu-ate spatial gradients in subsidence and suggest that this, rather than subsidence magnitude, is the key factor in risk assessment. Subsidence represents a major geologic risk for Mexico City and imposes serious constraints to any further urban development.

Keywords: subsidence, interferometry, GPS, SAR, Mexico Basin.

INTRODUCTION

Many of Earth’s urban and suburban areas are subsiding due to excess withdrawal of fl u-ids, principally water, but also petroleum, natu-ral gas, and geothermal fl uids (Poland, 1984). While most subsidence rates are relatively low (<10 mm/yr) and local (<100 km2), much higher rates over larger areas are possible, increasing the risk of fl ooding, damage to infrastructure from differential subsidence, and damage to the fl uid reservoirs by overpumping and permanent porosity loss.

Since the late 1950s, several areas of Mexico City have undergone accelerated ground subsi-dence and associated shallow fracturing and faulting. These faults have mainly developed on the piedmont and talus deposits of older Qua-ternary volcanoes and other volcanic structures and have continuously damaged housing, utility works, and other urban infrastructure. The inte-grated economic damages of this process are large, rivaling those of a strong earthquake, but they have received less attention because of the longer time frame. The economic consequences of subsidence, while large, are generally fac-tored into yearly maintenance budgets rather than accounted for as unique natural disasters at a single point in time. As these integrated costs grow, it becomes increasingly important to assess the extent and magnitude of damage

in the Mexico City metropolitan area due to ground subsidence. Monitoring of the spatial and temporal patterns of surface deformation associated with fl uid withdrawal is an important fi rst step, and it is the focus of this paper.

No current single technique gives complete temporal and spatial sampling of subsidence. Here, we describe the recent subsidence of Mexico City due to groundwater withdrawal using a combination of interferometric synthetic aperture radar (InSAR) for high spatial resolu-tion and global positioning system (GPS) data for improved temporal information and cali-bration. We use a remote-sensing approach to defi ne regions where large differential subsid-ence results in large strain gradients, which thus require closer monitoring.

GEOLOGIC AND HYDROLOGIC BACKGROUND

The southern portion of the Basin of Mexico (Fig. 1) includes a low-relief lacustrine plain, formerly covered by shallow water bodies and wetlands, commonly referred to as the Val-ley of Mexico. This area at present has several small lakes, including Texcoco, Zumpango, and Chalco; the latter was completely drained at the turn of the twentieth century. These lakes, along with the Xochimilco canal system, are remnants of a large water body that encompassed about

For permission to copy, contact [email protected]© 2008 Geological Society of America

GSA Bulletin; November/December 2008; v. 120; no. 11/12; p. 1556–1566; doi: 10.1130/B26001.1; 10 fi gures.

Space geodetic imaging of rapid ground subsidence in Mexico City

Enrique Cabral-Cano†

Departamento de Geomagnetismo y Exploración, Instituto de Geofísica, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F. 04510, Mexico

Timothy H. DixonRosenstiel School of Marine and Atmospheric Sciences, University of Miami, 4600 Rickenbacker Causeway, Miami, Florida 33149, USA

Fernando Miralles-WilhelmDepartment of Civil and Environmental Engineering, Florida International University, 10555 West Flagler Street, Miami, Florida 33174, USA

Oscar Díaz-MolinaDepartamento de Geomagnetismo y Exploración, Instituto de Geofísica, Universidad Nacional 10 Autónoma de México, Ciudad Universitaria, México D.F. 04510, Mexico

Osvaldo Sánchez-ZamoraDepartamento de Sismología, Instituto de Geofísica, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F. 04510, Mexico

Richard E. CarandeNeva Ridge Technologies, 4750 Walnut Street, Suite 205, Boulder, Colorado 80301, USA

†E-mail: ecabral@geofi sica.unam.mx.

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Geological Society of America Bulletin, November/December 2008 1557

one-fourth of the total surface of the basin sev-eral thousand years ago.

The Mexico City metropolitan area, located in the southern section of the Mexico Basin, is a heavily populated urban area with ~17 million inhabitants (INEGI, 2000). Originally named Tenochtitlán, the capital of the Aztec empire, it was built over the former Lake Texcoco, parts of which survive east of the Mexico City metropol-itan area, in a high (2200 m elevation), closed basin ringed by mountains that can exceed 5000 m elevation (Fig. 1) and that provide natural recharge of basin groundwater (Ortega and Farvolden, 1989). The unusual location poses technical challenges for hydraulic management. Flooding in the sixteenth and seventeenth cen-turies led to artifi cial opening of the basin and construction of other hydraulic works in the late 1700s to divert fl ood water. Since then, a major hydraulic management network has been built and periodically upgraded, maintaining the fl ood-control function but also drastically reduc-ing natural groundwater recharge.

Mexico Basin stratigraphy is well described (Schlaepfer, 1968; Mooser, 1975; Vázquez-Sánchez and Jaimes-Palomera, 1989). GODF (2004) presented the most recent geotechnical classifi cation of the main surface and near-sur-face units: a hard rock unit, a transitional unit, and a lacustrine unit. The hard rock unit (Unit I in Fig. 2) corresponds to the slopes of surround-ing mountain ranges and includes basaltic lava fl ows and pumiceous tuffs and sandy/silty beds with a high percentage of gravel. The transi-tional unit (Unit II, Fig. 2) is a slope deposit; it represents the transition between the lacustrine beds and rock outcrops. It consists of progres-sively thicker sedimentary deposits overlying the uppermost clay-rich lacustrine beds with interbedded lacustrine and alluvial deposits. The lacustrine unit (Unit III, Fig. 2) includes depos-its from former Lake Texcoco, mainly soft and compressible silts and clays with relatively low permeability. A large percentage of the modern city is built over these beds, refl ecting the his-tory of urban development since the Spanish conquest. Unit III ranges up to 80 m in thick-ness and overlies coarser, more permeable beds that comprise the main aquifer, mainly alluvial sands and gravels, as well as Pleistocene-Recent volcanic rocks in the depth range 100–400 m.

The Mexico City metropolitan area con-sumes over 65 m3/s of water (JACMCW, 1995), and more than 70% of it comes from the aqui-fer beneath the city through a system of more than 380 water wells. The larger basin has more than 630 wells. In a typical year, consumption exceeds recharge, lowering the water table by 0.1–1.5 m/yr, reducing pore fl uid pressure in the aquifer and overlying aquitard, and leading

to compaction of lacustrine shales and surface subsidence. Drilling for groundwater started in the 1850s. Subsidence was eventually recog-nized as a serious problem (Gayol, 1925), but the link between groundwater extraction and clay compaction was only recognized later (Carrillo, 1948). By 1952, total subsidence (1891–1952) had reached 6.0 m in the down-town area (CHCVM, 1953). More recent sur-veys show up to 2.5 m of additional subsidence between 1952 and 1973. Other studies show an average subsidence rate of 90 mm/yr for the 20 yr period 1965–1985 in the downtown area (CAVM, 1975; Figueroa-Vega, 1984; Ortega et al., 1993). The decrease in subsidence rates after 1965 refl ects conservation measures instituted in the 1950s and 1960s, which included capping wells near the city center.

Consequences of the subsidence process are costly. Water sewage works must be constantly upgraded due to loss of gradient, and transi-tional areas between lacustrine beds and slope deposits are prone to severe differential subsid-ence, damaging housing and urban infrastruc-ture. However, the regional extent and spatial variation of subsidence, and seasonal and lon-ger-term variations, are not well monitored or understood, hampering effective mitigation.

DATA PROCESSING

InSAR has been used to study a variety of surface deformation processes, including sub-sidence from groundwater withdrawal, and the technique is well described (e.g., Massonnet et al., 1997; Galloway et al., 1998, 1999; Galloway and Hoffman, 2006; Fielding et al., 1998; Ame-lung et al., 1999). We used Synthetic Aperture Radar data from the European Remote Sensing Satellite (ERS) 1 and 2 (pre-2001) and from the Advanced Synthetic Aperture Radar (ASAR) onboard the Environment Satellite (ENVISAT; 2003 and later). ERS-1/2 data collected prior to 2001 was used, but many interferometric pairs yielded poor coherence, in some cases, due to the long time span between passes. Best results were obtained with image pairs spanning rela-tively short time spans. The following discus-sion is based on SAR images acquired in 1996 (1 and 2 February and 16 May), 1999, 2000 (7 January and 17 March), 2003 (10 October and 31 December), and 2005 (15 April and 24 June).

Topography data from the Shuttle Radar Topography Mission (SRTM) was used for the topographic correction. We assumed a constant rate of surface change to make a fi rst-order cor-rection for this effect and used a phase unwrap-ping algorithm to convert ambiguous fractional-phase measurements to continuous phase corresponding to range change (Goldstein et al.,

1988; Ghiglia and Pritt, 1998). In the interfero-grams (Fig. 2), one color cycle represents 28 mm of range change (one half the SAR wavelength) in the line of sight direction between the satel-lite and ground (23° from vertical in the case of ERS1/2 and 15°–45° for ENVISAT_ASAR). Although this range change is usually interpreted as vertical motion when considering fl uid with-drawal, reservoir contraction may induce hori-zontal motions as well. If the motion is purely vertical, 28 mm of range change corresponds to a true vertical motion of 30.4 mm. We then reg-istered the SAR interferogram to high-resolution optical image data from the Advanced Space-borne Thermal Emission and Refl ection Radi-ometer (ASTER) to improve georeferencing and facilitate feature matching, for example, the location of InSAR fringes with respect to water-well locations or major street intersections.

GPS analysis and error estimation proce-dures follow Dixon et al. (2000) and Sella et al. (2002). Permanent station UIGF (Ciudad Uni-versitaria) on the southwestern margin of the Mexico City metropolitan area has been occu-pied since 1997. Station AIBJ (Mexico City International Airport) was occupied for a total of 10 twenty-four hour sessions at the end of the dry season (May–June) between 1995 and 2001. A permanent GPS station located on the center of the historic downtown was installed April 2004, and more recent permanent GPS stations (MRRA, MPAA, and MOCS) have continuously recorded data since early 2005 in order to monitor subsidence with high temporal resolution. We fi t a weighted least-squares line to the GPS position data for each site to derive the average velocity and uncertainty over the entire observation period, and also considered subsidence over shorter intervals.

GPS data also allow calibration of InSAR measured subsidence. For example, the unad-justed 1996 interferogram agrees well with both GPS sites, implying minimal orbit error and/or atmospheric delay effects in this data set. On the other hand, the 1999–2000 interferogram predicts subsidence at UIGF 55 mm below that indicated by the GPS analysis at this site. The InSAR-derived profi le in Figure 3 is adjusted based on the UIGF data, allowing an InSAR-based estimate of subsidence within the study area relative to UIGF.

SUBSIDENCE ANALYSIS

The InSAR data (Fig. 2) suggest signifi cant range change across most of the Mexico City metropolitan area in the 1996, 1999–2000, 2003, and 2005 data sets. However, assuming these changes represent real surface displace-ment, do they indicate purely vertical motion, or

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5400 0 m98°20″

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Figure 2. Left: Study area shaded digital elevation model with geotechnical subsoil classifi cation (white lines; GODF, 2004). Red and yellow lines show the leveling transects described in the text and Figure 5. Global positioning system (GPS) sites referenced in the text are shown as blue triangles. Center: Interferometric synthetic aperture radar (InSAR) fringe maps of Mexico City metropolitan area for 1 February to 16 May 1996. Right: InSAR fringe maps of Mexico City metropolitan area for 16 July 1999 to 7 January 2000. Each color cycle phase represents 28 mm distance change between sensor and ground. The digital elevation and fringe images have been merged and registered with a high-resolution ASTER band 2 image.

Figure 1. Location map and shaded digital elevation model of study area in central Mexico. Rectangle shows the coverage of images in Figure 2.

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a mix of vertical and horizontal motion? A SAR interferogram from one look direction, as in our case, measures only the scalar length change in the satellite line of site direction and does not resolve the three orthogonal components of the displacement vector. Also, the imaged changes may include short-term (e.g., seasonal) changes, or could refl ect longer-term trends. The avail-able SAR data do not address the issue of high-resolution temporal variability.

We recorded negligible GPS vertical veloc-ity at UIGF, outside the subsidence affected zone, and high and constant subsidence at AIBJ, at an average rate of −291 mm/yr for the 1995–2001 period using campaign data. More recently installed GPS sites at MOCS, MPAA, and MRRA (Fig. 4) located on the high-sub-sidence region show rates that range from −168 to −255 mm/yr and display linear trends with no or very little annual variation. On the other hand, the UPEC site, located further to the west (Fig. 4) where lacustrine sediments are thinner, shows a lower subsidence rate (−84 mm/yr) but displays small seasonal variations.

Figure 3 plots InSAR displacement, assuming only vertical motion, and the vertical component of GPS displacement for a transect across the basin that intersects UIGF and AIBJ GPS sites, assuming that the longer-term average veloc-ity at the GPS sites (representing data spanning more than 6 yr at AIBJ) is representative of the average velocity over the 175 d (1999–2000) or 105 d (1996) InSAR period. The three subsi-dence estimates at AIBJ (two InSAR, one GPS) agree fairly well. The InSAR-based subsidence

estimate at AIBJ is 100 mm over 105 d (1996) and 148 mm over 175 d (1999–2000), equivalent to average annual rates of 347 mm/yr (1996) and 309 mm/yr (2000), compared to the 291 mm/yr derived from the GPS campaigns.

The agreement between the different data sets with different time spans suggests several important points:

(1) Most of the InSAR recorded ground motion is vertical. Independent analysis of the horizontal component GPS data at MRRA, MPAA, UPEC, and MOCS confi rms that hori-zontal motion at these sites is small.

(2) Short-term subsidence rates measured by SAR in 1996 and 1999–2000 are similar to the average rate for the period 1995–2001, the time span of campaign GPS measurements at AIBJ.

(3) It confi rms that extraordinarily high rates of surface subsidence are occurring within the Mexico City metropolitan area.

The general agreement of the various subsid-ence estimates for different time intervals and independent techniques (Fig. 4) indicates that the short-term SAR-based measured subsidence process does not have a signifi cant seasonal bias. The eastern part of Mexico City has been subsiding at a fast and essentially constant rate for at least the past 10 yr. While short-term GPS-based rates (better shown on UPEC site; Fig. 4) indicate fl uctuations spanning a few week’s period, these short-term fl uctuations are small compared to the long-term signal and probably account for the small discrepancies between the InSAR and GPS based estimates. For example, InSAR data indicate that the old city center sub-

sides at an average annual rate of 115 mm/year, while the current GPS rate is −84 mm/yr. These rates are less than the historical maximum at this location (Fig. 4), consistent with the capping of wells in the 1950s.

Figure 4 shows a multitechnique compos-ite plot of historical subsidence in the down-town area. Pre-1985 leveling data (Mazari and Alberro, 1991) were collected at selected city landmarks. The 1985–2002 data were derived from leveling of a modern benchmark network encompassing most of the city, surveyed at ~2 yr intervals by the former Dirección General de Construcción y Operación Hidráulica (1993; now Sistema de Aguas de la Ciudad de Mexico). Although benchmarks used in Figure 4 are not the same on the pre-1985 and post-1985 surveys, the closest modern benchmark to the location of the historical landmarks was selected, typically within just a few hundred meters distance. Con-tinuous GPS data (2004–2007) from the current permanent network (map on Fig. 2) are also dis-played in Figure 4.

Total subsidence of the downtown area (Alameda park) between the end of the nine-teenth century, when artesian fl ow from the local water springs ceased, and spanning the interval between the times fi rst water wells were drilled in the basin and present time is shown in Figure 4. Between 1895 and 2002, a total of 9.7 m subsidence occurred. The rates of subsidence since 1985 show sharp differ-ences with other areas east of downtown. Sub-sidence rates of ~−57 mm/yr (1960–1985) and −112 mm/yr (1985–1992) are comparable with the current rate of −84 mm/yr measured by GPS techniques at UPEC.

Subsidence rates of other eastern sites such as Airport SW (benchmark M[S01E03]05), which lies close to GPS site AIBJ, show similar rates to the GPS-derived rates of subsidence: −215 mm/yr at Airport SW (leveling) compared to −211 mm/yr, −255 mm/yr, and −287 mm/yr for the GPS sites MPAA, MRRA, and AIBJ, respec-tively. The daily sampled GPS data, and general agreement with rates derived from less frequent leveling data, suggest essentially constant sub-sidence with little seasonal fl uctuations.

We also compared several techniques to better characterize the post-1985 subsidence period. We used space geodetic data and com-pared them to the two main north-south leveling transects that run across the city (red and yel-low lines in Fig. 2). These are tied to reference benchmarks on rock outcrops and are assumed to be devoid of regional subsidence effects. A temporal comparison of these leveling transects (Fig. 5, top panels) indicates that except for a few benchmarks that exhibit anomalous behav-ior, the rate remains essentially constant over

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Figure 3. Elevation change versus distance (profi le UIGF to AIBJ, see Fig. 2 for location) for global positioning system (GPS) (triangles) and interferometric synthetic aperture radar (InSAR) (lines) for time periods of 1996 and 1999–2000 SAR interferograms. GPS displacement was calculated assuming constant rate for period 1995–2001, interpolated to time span of interferogram. The 1996 interferogram is unadjusted for orbit error; the 1999–2000 interferogram shown is adjusted to match GPS data at UIGF near the southwest edge of basin.

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time. We then constructed a relative subsidence plot following the same locations of benchmark transects using InSAR-derived subsidence mag-nitude maps (Fig. 5, bottom panels). The most relevant observations from this comparison are as follows:

(1) InSAR-based relative subsidence transects show ~8× better spatial resolution compared to leveling, and they are capable of resolving ver-tical motion for areas less than 100 × 100 m, well within average city block dimensions in a medium to high population density zone.

(2) Each technique has a characteristic time interval that needs to be considered in the inter-pretation, especially if subsidence has a time-varying rate, e.g., seasonal fl uctuations. The InSAR-derived transects represent an integrated measurement over the time span of the interfero-

metric pair. The continuous GPS data give daily measurements. Most of the continuous GPS sites show more or less continuous subsidence at an essentially constant rate; hence, the InSAR and GPS rates may be usefully compared, even if they were acquired at different times. The conventional leveling transects are carried out every 2 yr over a 2–4 wk period during normal working hours; the methodology includes a ref-erence benchmark of known (static?) elevation and assumes a static reference frame during the period of the survey. Therefore, any leveling sur-vey that is performed over high subsidence rate areas, such as the eastern part of Mexico City, with rates over 250 mm/yr, may be biased by up to ~9.5 mm in a typical 3 wk survey (differential subsidence between benchmarks at beginning and end of survey).

(3) Correspondence between the leveling and InSAR rates is better displayed on the eastern transect (Fig. 5, right middle and bottom pan-els) than on the western transect (Fig. 5, left middle and bottom panels). This is evidenced by the overall correspondence in magnitude and location of high and low values of both eastern leveling and InSAR plots (Fig. 5, right middle and bottom panels). This may be a consequence of the magnitude of the subsidence rate, which is higher on the western transect, and is located mostly over lacustrine clays (Unit III on Fig. 2), than on the eastern transect, located along the transitional zone (Unit II on Fig. 2).

Current maximum subsidence for the Mex-ico City metropolitan area (Figs. 6 and 7) is localized at Ciudad Nezahualcóyotl (on the eastern side of the Mexico City metropolitan

Mexico City Historical Subsidence

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Figure 4. Left: Multitechnique composite plot of the subsidence in the Mexico City downtown area since 1895. Pre-1985 leveling data were collected at selected city landmarks, whereas 1985–2002 data were derived from leveling of a modern benchmark network. See text for further explanation. Right: Vertical component time series for global positioning system (GPS) sites (red triangles) within the high subsidence region; see Figure 2 for their location. Map inset shows location of leveling benchmarks (blue circles) and GPS site UPEC (red circle).

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area), southeast of the historical maximum sub-sidence area. This area registered an average annual rate of 378 mm/yr, close to the highest annual subsidence rate in the downtown area recorded in the mid-twentieth century (~400 mm/yr; see Fig. 4). This shift is important and suggests that water extraction has not declined, but rather moved eastward. Compaction may now be affecting deeper units near the center of the basin.

Groundwater overdraft in the Iztapalapa-Nezahualcóyotl region is acute; there has been a sustained static piezometric level drop of −1.4 m/yr averaged over the past 20 yr (Lesser y Asociados, 2003; Ortega, 1999). The region

where current subsidence rates exceed a few mm/yr corresponds closely to the lacustrine unit (Unit III on Fig. 2). In contrast, the western part of the city, mostly built over alluvial-fan deposits and/or volcanic tephra, tuffs, and lava fl ows (Unit I), shows negligible motion. The high subsidence region corresponds closely to the boundary of old Lake Texcoco just prior to Spanish settlement, when a major change in agricultural practices and hydraulic manage-ment was initiated. The outer InSAR fringe in Figure 2 (2000 data panel) maps the location of the lake boundary at the time of Spanish conquest of the Aztec empire, when Mexico City was built over the ruins of old Tenochti-

tlán, and the lake was drained to build the new city, irrevocably changing the ecosystem and hydrologic balance.

Further evidence supporting the strong cor-relation between subsidence and thickness of clay-rich units is shown in Figure 8, where we superimpose the seismically derived depth of the Quaternary lacustrine clay unit (Perez-Cruz, 1988) and the subsidence magnitude estimated for 2000. This clay unit is thickest in the high subsidence region east of the Mexico City metropolitan area. This unit is 350 m thick in the Texcoco-1 deep well (Fig. 8) and can be seismically correlated under most of the Ciu-dad Nezahualcóyotl neighborhood.

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0

(mm

/yr)

Subsidence Rate Eastern Transect

Rate 1998–2000Rate 2000–2002Rate 1998–2002

Rate 1998–2000Rate 2000–2002Rate 1998–2002

Figure 5. Comparison of two north-south–trending leveling transects (top and middle panels) and the corresponding interferometric synthetic aperture radar (InSAR)–derived relative subsidence (bottom panels) along the same transects (location shown in Fig. 2). InSAR-based relative subsidence transects show ~8× better spatial resolution compared to leveling. Subsidence rate magnitude is higher on the western transect, which is located mostly over lacustrine clays (Unit III on Fig. 2), than on the eastern transect, which is over coarser-grain alluvial-fan deposits (Unit II on Fig. 2). See text for further details.

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1562 Geological Society of America Bulletin, November/December 2008

1996 2000 2003

N N N

0 Subsidence rate -400 mm/yr99°15′ W 99°00′

19°15′

0

2

4

6

8

10 km

0

2

4

6

8

10 km

0

2

4

6

8

10 km

mm/yr

0

-374

-187

N

0

1

2

3

4

5 km167

5TEC-2

243244123-126

110

107107107

1439

2666

942

2221

38

160

6 7 8 9 4

2728

442681

210645

2679

105

193

2161

2259

50192

162 2239

160

1911

165689

196380 2

190

14

1757

1078128 267

170

138

13

199

198

1857

2075

11953

6159152

185150

151164

2294

20382263

1978

51412581903

2380

2624

Airport

Ciudad Nezahualcoyotl

Calzada Zaragoza

Viaducto

Tlalp

an

Rio

Ch

uru

busc

o

AIBJ

19°26′45″ N

19°21′20″

99°00′30″99°09′45″ W

Div. del N

orte

Figure 6. Examples of annual interferometric synthetic aperture radar (InSAR)–derived subsidence maps for Mexico City for 1996, 2000, and 2003. White line shows the Distrito Federal political boundary.

Figure 7. Location of pilot wells used in the analytical subsidence calculation superimposed onto the 2003 interferometric syn-thetic aperture radar (InSAR) subsidence map. Major streets are show as white lines.

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Space geodetic imaging of rapid ground subsidence in Mexico City

Geological Society of America Bulletin, November/December 2008 1563

SUBSIDENCE GRADIENT

We computed the horizontal gradients of subsidence rate from the subsidence maps to investigate possible correlation with damage to infrastructure. Figure 9 shows the magnitude of maximum horizontal gradient, computed from the October–December 2003 ENVISAT-ASAR image pair. While there are minor differences between gradients computed from the various interferograms, all show four regions of large horizontal subsidence gradient:

(1) southern slopes of the Sierra de Guadal-upe, north of Mexico City;

(2) Peñón de Los Baños, immediately north of Mexico City International Airport;

(3) the Zaragoza corridor, which has a NW-SE feature running parallel to this major avenue between the Agricola Oriental and Aca-titla neighborhoods, including the Peñón del Marqués area, on the eastern part of the Mexico City metropolitan area; and

(4) a NE-SW corridor located immediately to the SE of Canal de Garay Avenue and into the Santa Cruz Meyehualco neighborhood, north of Calzada Ermita Iztapalapa.

All of these regions coincide with Quaternary volcanic features in close proximity to lacus-trine clay-rich sediments. These high-gradient zones mark the location of abrupt transitions between continuous subsidence of the lacus-trine beds and stable volcanic outcrops (Fig. 2).

These areas are known for extensive damage to housing and large civil engineering structures such as subways and large hydraulic infrastruc-ture. Detailed information on the location and extent of these zones from the InSAR-derived gradient maps provides a new and valuable tool to include in urban land use and mitigation of subsidence hazard.

ANALYSIS OF SUBSIDENCE DATA

The consolidation analysis (Terzaghi and Peck, 1967) establishes a relationship between those changes in effective stress caused by extraction pumping in an aquifer and the result-ing deformation of its porous matrix, as follows:

240

342454

149240342

149

240

149

149

149

342

240

Texcoco

Copilco

Tulyehualco

Mixhuca

Roma

Deep stratigraphic borehole

Seismic depth contour (m)

Municipal boundary

0 Subsidence rate -400 mm/yr0

1

2

3

4

5 km

19°30′07″ N

19°14′00″98°59′00″99°11′51″ W

Figure 8. Seismically derived depth (black contours) of the Quaternary lacustrine clay unit from Perez-Cruz (1988) superimposed onto the interferometric synthetic aperture radar (InSAR)–measured subsid-ence magnitude for 2000. Stars show location of PEMEX deep wells.

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1564 Geological Society of America Bulletin, November/December 2008

dV

Vdh= α γ ,

(1)

where V is the aquifer porous matrix bulk vol-ume, α is the porous media compressibility, γ is the specifi c weight of water, and h is the piezo-metric head (groundwater table elevation) in the aquifer. Assuming that deformation of the porous matrix occurs predominantly in the verti-cal direction and solving for the thickness of the aquifer as a function of the change in piezometric

head, this equation can be rewritten in terms of the land subsidence (b

0 – b), where b

0 and h

0 are

the reference (datum) conditions, i.e., b(h0) = b

0.

This equation assumes that the surface responds instantly to changes in piezometric head.

b b

bh h0

001

− = − − −[ ]exp ( )α γ . (2)

Figure 10 compares the InSAR-measured subsidence values to those analytically derived

subsidence values following Equation 2 at those water-well locations shown in Figure 7, using compressibility (α) values that correspond to clay, silt, and sand soils (Freeze and Cherry, 1979). We used a value for the specifi c weight of water of γ = 9800 N/m3 and a reference aqui-fer thickness of b

0 = 80 m (Ortega et al., 1993).

This analysis suggests that the land subsidence observed in the vicinity of these wells can be represented with soil parameters that correspond to a spatial composite of silt and clay. The offset

19°17′00″ W 99°00′00″

19°14′00″

19°30′00″ N

N

0.04

0.00

2

4

6

8

10 km

Figure 9. Horizontal subsidence gradient for the Mexico City metropolitan area calculated from the 2003 subsidence magnitude map. High gradient (nondimensional) values depict areas where structural damage risk to housing and other civil engineering structures is higher due to intense surface fracture and faulting. These areas coincide with transitional piedmont zones between Cenozoic volcanic structures and clay-rich Quaternary lacustrine deposits.

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Space geodetic imaging of rapid ground subsidence in Mexico City

Geological Society of America Bulletin, November/December 2008 1565

between observed and modeled values (e.g., 5 cm offset between zero calculated subsidence and 5 cm observed subsidence) may refl ect the infl uence of fi ne-grained clays, which retard the migration of water and consequent attainment of equilibrium. Hence, areas with no current change in water levels still experience subsi-dence due to past overdraft. Furthermore, the estimated order of magnitude of aquifer com-pressibility compares favorably with the histori-cal observations of land subsidence reported by Ortega et al. (1993) for a total land subsidence of 7.5 m in the old downtown area of Mexico City during the period 1940–1985, and to the 9.7 m (this work) for the period 1940–2007.

DISCUSSION AND CONCLUSIONS

The spatial correspondence between subsi-dence and the location of young lacustrine beds identifi ed here, combined with the high and essentially constant subsidence rate, implies that subsidence is due mainly to pressure loss in the shallow aquitard (clay-rich lake sediments) asso-ciated with groundwater overdraft (withdrawal in excess of recharge). This poses important impli-cations for water management in the Mexico City metropolitan area because compaction of clay-rich aquitards is often associated with per-manent loss of porosity and reservoir capacity (Holzer, 1984). Our data suggest that mitigation activities have not had a signifi cant effect on the long-term compaction of the lacustrine beds. Our

data also suggest that subsidence is not primar-ily seasonal. Long-term, inelastic compaction and shrinkage of the lacustrine unit are continu-ing at high rates, close to maximum historical values. This impermeable layer currently limits surface pollutants from reaching the underlying aquifer. However, as this layer shrinks, fractur-ing and faulting may occur, enabling pollutants to percolate down and contaminate the underly-ing aquifer (Rudolph et al., 1991).

Economic assessment of damage to urban infrastructure due to subsidence will benefi t from detailed mapping of the horizontal gradient pre-sented here. Continued monitoring of the spatial and temporal patterns of surface deformation within the Mexico City metropolitan area by the techniques outlined here can lead to the imple-mentation of stronger mitigation actions, which are necessary to preserve the aquifer beneath the Mexico City metropolitan area.

ACKNOWLEDGMENTS

This work was funded by the Offi ce of Naval Research (ONR), the National Aeronautics and Space Administration (NASA), Universidad Nacio-nal Autónoma de Mexico (UNAM) Projects Papiit IN-121515 and IN-114907, and Geofi sica-Cardi. European Remote Sensing satellites (ERS)-1, 2, and Envisat data were provided by the European Space Agency (ESA) Projects AO-3 441 and CAT-1 1409. NASA’s Earth Observing System provided Advanced Spaceborne Thermal Emission and Refl ection Radi-ometer (ASTER) imagery through the Unites States Geological Survey Earth Resources Observation and Science Data Center Land Processes Distributed

Active Archive Center (EDC-DAAC). We thank Francisco Correa-Mora, Gerardo Cifuentes-Nava, Esteban Hernández-Quintero, Teodoro Hernandez-Treviño, and Mario Mártinez-Yáñez for fi eld sup-port, and F. Amelung, D. Galloway, T. Holzer, D. Eaton, and other anonymous reviewers for their com-ments, which improved this paper. This paper is pub-lication 12 from the Center for Southeastern Tropical Advanced Remote Sensing (CSTARS).

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Observed InSAR subsidence (m)

0.2

0.15

0.1

0.05

0

0 0.05 0.1 0.15 0.2

An

alyt

ical

su

bsi

den

ce (

m) α = 10–7 Pa–1 (silt)

α = 10–6 Pa–1 (clay)

α = 10–8 Pa–1 (sand)

Figure 10. Plot of interferometric synthetic aperture radar (InSAR)–mea-sured land subsidence versus analytically derived subsidence values based on Terzaghi and Peck (1967) for water wells shown on Figure 7. We applied compressibility values that correspond to clay, silt, and sand soils (Freeze and Cherry, 1979), a specifi c weight value of water of γ = 9800 N/m3, and a refer-ence aquifer thickness of b0 = 80 m (Ortega et al., 1993).

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