Today, some tens of million years after its creation by the collision between India and Asia, the Tibetan Plateau is the highest and largest plateau on Earth. Results of geological and tectonic studies indicate that the plateau is extending. However, almost no quantitative evidence shows whether the plateau is still uplifting or thickening nowadays. Herein, we present geodetic evidence of mass loss beneath the Tibetan Plateau and increasing crust thickness. Combined absolute gravity and Global Positional System (GPS) measurements at three stations in southern and southeastern Tibet during two decades reveal uplifting of the Tibetan Plateau at a millimeter-per-year level, but its underlying mass is diminishing, indicating that the crustal thickness is increasing at an annual millimeter to decimeter level.
 The Tibetan Plateau, the highest and largest plateau on Earth with mean elevation of 4.5 km and width of about one km, began rising about 50 million years ago [Tapponnier et al., 2001]. The continued northward movement of the Indian subcontinent deformed a large part of the plateau crust through folding and various faulting mechanisms. The high rate of seismicity along the Himalaya reflects that a collision between India and Asia is still thrusting the Tibetan Plateau upward. The huge mass of Asia to the west and north blocks the northward movement of the plateau crustal material. Consequently, northward movement on deep-seated thrust faults is transferred laterally to the east and southeast roughly along the east–west trending strike-slip faults. The nearly north–south trending strike-slip faulting in eastern Tibet and western Sichuan and the rotation of Indochina southeastward into the South China Sea can be interpreted as eastward and southeastward extrusion of Tibetan crustal blocks. The horizontal displacements obtained by GPS measurements in China show that crustal shortening accommodates most of the Indian penetration into Eurasia [Wang et al., 2001]. The Tibetan Plateau undergoes substantial internal shortening at the contraction rate of ca. 38 mm/yr between northern India and the rigid Alashan block. A continuum deformation appears to characterize the active tectonics of the Tibetan Plateau. However, this continuum deformation is apparently confined to the plateau itself. It is absorbed by crustal thickening, which causes vertical crustal movement, i.e., elevated topography of the Tibetan Plateau and a subsided crustal bottom at depth. The seismological tomographic evidence showing that the lithospheric crust under south Tibet has doubled to 80 km thickness [Chen and Yang, 2004] supports this hypothesis.
 This report presents geodetic evidence of the increasing crustal thickness by gravity observations in the plateau area: a gravity change can reflect material transport accompanying vertical movements at the surface and on the crustal bottom, as described above. The vertical displacements add an additional gravity change; they must therefore be eliminated from the observed gravity at the surface to isolate the signal from mass changes. Combined absolute gravity and GPS measurements at three stations in southern and southeastern Tibet during two decades reveal uplifting of the Tibetan Plateau, but its underlying mass is diminishing. As the crust thickens, the mass of a column of rock beneath the station decreases because mantle is displaced by crust, causing a reduction in gravity. Continuous GPS measurements during 9–12 years reveal uplift, and negative gravity change rates are shown for 13–17 years. Removing the contribution of surface vertical displacement, gravity values on the deformed earth surface are transformed to those of a fixed point. Thereby, residual gravity changes reflect only the interior mass distribution.
2. Absolute Gravity and GPS Observation Stations
 Because both GPS and gravity measurements are necessary, we specifically examine data obtained at three unique stations—Lhasa (29.66°N, 91.10°E), Kunming (25.13°N, 102.76°E), and also Dali (25.61°N, 100.25°E)—from which data of two types are available (Figure 1 (left)). These stations are managed as part of the Chinese National Geodetic Observation Network. Station Lhasa has two observation points: both belong to the Surveying and Mapping Bureau of Tibet, but are located respectively within the capital city of Lhasa (3,643 m a.s.l. and 3,645 m a.s.l.; separated by ca. 800 m) in the southern plateau. The GPS station is located near the gravity stations, about 2,000 m distant. Because of their proximity, they can be assumed to have the same crustal deformation properties: they might be considered as one station. The other two stations (Kunming seismic station and Dali seismic station) are located in southeastern Tibet, with slightly lower respective elevations of 1,952 m and 1,958 m. The GPS station in Kunming is located about 8,900 m south of the gravity station; the GPS station in Dali is located at the same site as the gravity station. At the three stations, both GPS and gravity measurements have been performed for a decade or more. Continuous GPS observations have been made from 1995 or 1998 to the present. Absolute and relative gravity measurements have been carried out regularly since the early 1990s.
3. Gravity Measurements Indicate a Negative Change Rate
 The earliest absolute gravity measurements were made at the three stations in 1990; they were repeated in 1992 and 1995, respectively, under Sino-Finnish and Sino-German joint observations [Mäkinen et al., 1993]. For those studies, JILAG-3 and JILAG-5 absolute gravity meters were used. Observations at each station were usually carried out during 1–2 days. The measurements comprised 10–20 sets; each set included 100 free-fall drops. The standard deviation for each set was about 10–60 μgal; the standard deviation of the total set gravity was about 1–5 μgal. Since 1996, these stations have been revisited by the Institute of Geodesy and Geophysics of the Chinese Academy of Sciences, China, with their absolute gravimeter (FG5#112; Micro-g Solutions Inc.), by a joint observation of China and the United States in 1998 using a FG5#107, and by a joint observation of China and Japan in 2004 using FG5#210 [Takemoto et al., 2006]. The measurements at each station comprised 24–28 sets within 24 h; each set included 100 free-fall drops. The standard deviation for each set was about 7–12 μgal. The standard deviation of the total gravity set was about 1–2 μgal. The gravity gradient at each station was measured using LaCoste-Romberg G type relative gravimeters [Zhang and Wang, 2004; Wang et al., 2004]. In 2005, the FG5#212 absolute gravimeter belonging to the Earthquake Research Institute (ERI) of The University of Tokyo was reinstalled at the Dali station based on a cooperative project between ERI, the Institute of Seismology (IOS), and the Yunnan Seismological Bureau of the China Earthquake Administration. In all, about 10,000 drops, or 100 sets of gravity measurements were made; the observation accuracy was good. The standard deviation of the final gravity set is less than 1.0 μgal. In 2007, this station was measured again for the same project, but then using a FG5#232 owned by IOS.
 The Olivia and g-soft programs are used in data processing; some physical corrections were made to compensate for earth tides, polar motion, and ocean loading. All gravity values are transformed from the observation point at 1.3 m height from the ground. Finally, summarizing the observations described above, we plot temporal gravity changes at the three stations in Figure 2 (left). Results show negative gravity change rates: −1.97 ± 0.66 (sum of the first two rows), −1.42 ± 0.38, and −0.41 ± 0.24 μgal/yr, respectively, for the Lhasa, Kunming, and Dali stations. The rate of change lines (red) are obtained using least-squares fitting. The standard deviation following the gravity rate of change number indicates one sigma, with reliability of 67%. The gravity data at Dali show a period signal, but the GPS displacement data do not. This phenomenon is considered to result from an annual water level change (with no secular change) in the Erhai Lake [Zhang and Wang, 2005], which is only 100 m from the Dali station. The effects of an annual or seasonal signal will be reduced by averaging data over a long period of time. Therefore, the estimated rate of change of gravity is considered reliable. The same reasoning applies for the loading corrections from snow accumulation and melt, hydrology, and the atmosphere.
4. GPS Data Reveal Uplift of the Tibetan Plateau
 We use GPS data at the three stations to obtain the vertical displacement rate. Since the early 1990s, several GPS networks for tectonic studies have been established in China and neighboring regions [Wang et al., 2001]. Especially, 25 permanent GPS stations have been established and continuous observations have been made to the present day [Gan et al., 2007] The Lhasa, Kunming, and Dali stations belong to parts of the permanent network; high-quality data are obtained. Here we use GIPSY software to reduce phase and pseudorange data into a site position. The GPS data collected at ca. 20 IGS stations throughout Asia and 18 continuous sites within China are organized into discrete 24 h segments and are processed simultaneously to yield a daily network solution. The precise satellite orbit and clock are fixed to the non-fiducial products provided by the JPL. We solve for 3D coordinates, clock biases, and atmospheric refraction per site with loose constraints. Phase ambiguities are also estimated, but no ambiguity resolution was done (phase ambiguities are estimated as real number and not fixed to integers). We apply azimuth and elevation-dependent antenna phase center models, following the tables recommended by the IGS. We select a subset of IGS sites with a longer time span for definition of reference frame, and rotate the loosely constrained daily solutions onto the ITRF2000 by seven-parameter similarity transformation. We then obtain a time series of vertical components of each site. The time series is then fit in a weighted least-squares sense to a linear function that includes the initial coordinate plus the secular motion rate. Furthermore, assuming a time series characterized by a white noise process, we derive a post-fit RMS of 1.1–1.5 mm for the vertical component of site position and standard deviation of <0.1 mm/yr (1 sigma) for the vertical rate. The rate uncertainty might be overoptimistic because of neglect of the time-correlated noise inherited in the geodetic time series. The rate error might be underestimated by a factor of 5–11 if a pure white noise model is assumed for the coordinate time series [Mao et al., 1999]. Zhang et al.  found that the rate uncertainty might be 2–4 time larger than that for fractional white noise and 3–6 for white plus flicker noises. We adopt a moderate scale factor of five because the time-correlation noise averaged down gradually over time. Multiplying the standard deviation of 0.1 mm/yr by five engenders the rate uncertainty of ca. 0.5 mm/yr, which is comparable with vertical rate precision of 0.4–0.6 mm/yr assigned by Prawirodirdjo and Bock  and Calais et al. . Finally, we obtain the aggregate station coordinates of the three stations and plot them in Figure 2 (right). Results show that all three stations exhibit positive displacements vertically, implying that the Tibetan Plateau is continuing its uplift. The uplift rates are, respectively, +0.8 ± 0.5, +2.3 ± 0.5 and +0.5 ± 0.5 mm/yr for Lhasa, Kunming, and Dali. Such a mean vertical displacement rate of 1.2 mm/yr agrees well with the conclusion (1.14 mm/yr) obtained on a geological scale [Rowley and Currie, 2006].
5. Gravity Rate of Change at Space-Fixed Point
 The observed gravity change rates g1) described above are presented in Table 1. These gravity change rates are obtained on the deformed earth surface. They can therefore be decomposed into three contributions associated with crustal vertical displacement, surface denudation, and internal mass change. We consider them separately to interpret the gravity changes. We first eliminate the contribution from the surface movement as determined by GPS. The gravity gradient for a mean spherical earth model is known to be −3.08 μgal/cm [Heiskanen and Moritz, 1967]. This gradient applies for free air correction in case the observation point moves vertically in space with no mass change. However, if the gravity measurement is performed on the deformed earth surface, the observation point moves together with the earth surface: the free air gradient is no longer applicable. Instead, the Bouguer gradient must be used. According to an earlier study [Heiskanen and Moritz, 1967], the Bouguer correction can be estimated as +1.1 ± 0.1 μgal/cm based on the local crustal density ρ = 2.7 − 2.9 g/cm3 [Chen and Yang, 2004]. Thus the Bouguer gradient is obtained as −1.9 μgal/cm. Multiplying the Bouguer gradient by the corresponding vertical displacements inferred from GPS measurements (Figure 2 (right)), we obtain the Bouguer gravity change rate corrections as −0.16 ± 0.02, −0.44 ± 0.02, and −0.10 ± 0.02 μgal/yr for the three stations, respectively (g2) in Table 1).
Table 1. Gravity Change Rates at Lhasa, Kunming, and Dali Stationsa
Where g1) is the observed gravity change rates; g2) is the gravity rates by vertical displacement; g3) indicates denudation-caused gravity change rate; and g4) = g1)−g2)−g3). (unit: μgal/yr).
−1.97 ± 0.66
−0.16 ± 0.1
−0.25 ± 0.1
−1.56 ± 0.67
−1.42 ± 0.38
−0.44 ± 0.1
−0.25 ± 0.1
−0.73 ± 0.40
−0.41 ± 0.24
−0.10 ± 0.1
−0.25 ± 0.1
−0.06 ± 0.27
−1.26 ± 0.46
−0.23 ± 0.1
−0.25 ± 0.1
−0.78 ± 0.48
 Next, we consider the gravity rate of change contributed from the surface denudation of the Tibetan Plateau. Because of erosion, much mass is denuded from the mountains over the whole plateau and is subsequently transported by rivers to the Indian Ocean, the East China Sea, and adjacent basins [Westaway, 1995]. Most of the denudation is considered happening below the observation points, this mass loss decreases gravity, it must be evaluated. Westaway  pointed out that the most concentrated denudation of the Tibetan Plateau occurs at its eastern and southeastern margins, within and around its Yunnan area. The combined sediment flux indicates an amount of 0.8 km3/yr. The average denudation rate would be 1.5 mm/yr if this denudation were to occur over the 600 × 800 km area for which the gravity measurements were carried out. That study also estimated that 0.4 km3/yr is eroded from the Himalayas and transported by rivers to the Indian Ocean and that 0.5 km3/yr is taken northward from Tibet. The equivalent loss rate of the mass layer is about 0.8 mm/year if this 0.9 km3/yr erosion is assumed to occur over the entire Tibetan Plateau. Overall, the 2.3 mm/yr denudation rate is an important factor of the gravity value reduction. This denudation rate has been confirmed by another independent study by Métivier et al. , which estimated the total denudation amount of the Tibetan Plateau as 1.5 km3/yr. Other studies [Lal et al., 2004] also found a high denudation rate of 2 mm/year in the Kunlun area and the Tibetan Plateau's eastern margin. Assuming the 2.3 mm/year denudation as a simple Bouguer layer, its contribution to the gravity changes is −0.25 μgal/yr. The uncertainty can be assumed as ±0.1 μgal/yr. The resultant g3) is listed in the fourth column in Table 1.
 Subtracting the gravity changes attributable to the vertical displacement and the denudation from the observed gravity changes rates, i.e., g4) = g1)−g2)−g3), we obtain the gravity change rates for the three stations as −1.56 ± 0.67, −0.73 ± 0.39, and −0.06 ± 0.26 μgal/yr, respectively, which are free of crustal motion (Table 1). The final gravity change rates are attributed to the mass change beneath the observation points. The negative gravity changes suggest that the total mass under the observation stations is diminishing gradually. The mean gravity decline rate for the three stations is −0.78 ± 0.47 μgal/yr.
6. Mass Loss Inferred From Crustal Thickness Change
 A review of the plateau's growth and rise to its present topography is useful to interpret the mass loss occurring beneath the Tibetan Plateau. Nearly 200 million years ago, the Indian plate is known to have moved northward, closing the Tethys Sea. About 55 million years ago, it began to collide with Asia at the geologically high rate of 5 cm/year. During this process, based on the physics of isostasy, some of the Indian subcontinent's lighter continental mass was subducted below the Asian continental mass before “locking up” and transmitting India's movement to the Asian crust. Consequently, the Asian crust was shortened and thickened by surface folding, large-scale overthrusting, and plastic flow at depth. The crust of the Tibetan Plateau thickened, thereby lifting up the crust surface. The bottom of the crust moves downward. Simultaneously, the plateau's area expands laterally, with its mass flowing sideward, because the lateral pressure gradient within the lower crust will tend to drive material out from beneath regions that have thickened, as detected using the GPS measurements described above [Wang et al., 2001]. According to the isostatic theory, the lower crust is usually sufficiently weak to be regarded as a fluid. Its flow is governed by variations in pressure at the base of the brittle layer. Subsequently, the heavier mantle is pushed sideward and the crustal bottom sinks. Gravity is not sensitive to the horizontal flow of mass. Therefore, the contribution to the gravity change is mainly (the uncertainty remains to be investigated) attributable to vertical movement of the crust, including the surface and bottom of the crust. Consequently, the gravity is expected to decrease, due to crustal thickening.
 After removing the effect of crustal deformation on gravity change, the residual gravity change −0.78 ± 0.47 μgal/yr is attributed to lowering Moho at depth by crustal thickening, as presented in Figure 1 (right). In that illustration, the additional crust on the crustal bottom is portrayed as a single layer with uniform thickness h. Assuming a crustal density of 2.6 g/cm3 and mantle density of 3.4 g/cm3 [Chen and Yang, 2004], with density contrast of Δρ = 0.8 ± 0.2 g/cm3, the gravity change related to this Bouguer layer can be expressed simply as 2πGΔρh = 0.78 μgal. The thickening rate—that of crustal expansion downward—is inferred as 2.3 ± 1.3 cm/yr. Compared to the mean surface uplift of 1.2 mm/yr, as determined by GPS, the 2.3 ± 1.3 cm/yr of crustal subsiding on the Moho seems reasonable in light of the mean elevation of 4.5 km of the Tibetan Plateau and the crustal thickness of 70 km below it.
7. Discussion and Remarks
 For the discussion presented above, we assumed a constant crustal density. This assumption is reasonable because, over a long time scale, the stress and strain accumulation caused by the collision is released primarily by frequent earthquakes in a shallow layer of the lithospheric crust. In addition, although several quantitative studies of Tibetan extension have relied upon the assumption that prolonged shortening in and around Tibet has caused the crust to thicken, no observational evidence has been provided so far. This study provides geodetic evidence of increasing crust thickness. The crustal thickening rate of 2.3 ± 1.3 cm/yr described above is based on one sigma of the gravity data, i.e., the crust thickens from 1.0 to 3.6 cm/yr with a reliability of 67%. If we consider two sigmas, the thickening rate is from −0.3 to 4.9 cm/yr, with 95% reliability. This thickening rate can be confirmed from the present-day volume flux balance for the Indian-Eurasia collision. The total convergent volume flux is estimated as 4.4 km3/yr [Westaway, 1995], which is equivalent to a 7 mm Bouguer layer if we assume the plateau bottom size as 1000 cm × 600 km, the same order as that derived in this study. The glacial isostatic adjustment in the Tibetan Plateau might affect the trends in the above geodetic data, but it is considered to be much less influential than the crustal motion caused by the Indian plate collision. Kaufmann  argued that gravity change from glacier isostatic adjustment could exceed 0.3 μgal/yr and uplift rate is about 3 mm/yr. However, according to the above GPS and geological rate [Rowley and Currie, 2006], it seems that Kaufmann's  results were overestimated. It is also noted that the above conclusion is based on measurements at three points on the plateau. Since two of the three sites are in the southeast part of the plateau, which are considered having a different tectonic history and topographic height, we may consider them separately. In this case, it is inferred that the crustal thickening rate beneath Lhasa is 4.4 ± 2.6 cm/yr and average thickening rate of the Dali and Kunming area is 1.1 ± 0.6 cm/yr.
 In addition, the relation between GPS observed uplift rate and surface height deserves some comment. Geodetic techniques provide present surface heights; repeat measurements can detect the displacement of benchmarks on the surface. However, displacements of the benchmarks do not necessarily enable the determination of the change of surface height because of erosion. The GPS-determined vertical displacement indicates the uplifting of rocks. Because the geodetic markers are placed on rocks that are not eroded away between surveys, the mean surface may lower with time relative to the geodetic points if there is rapid erosion, whether or not the mean surface elevation changes with time. Table 1 shows that the mean gravity changes caused by uplift and denudation are almost identical. That is to say, the uplift compensates the denudation. However, areas with slow erosion move along with the uplift rate detected using GPS.
 This study was financially supported by a Japanese JSPS research-in-add project. Helpful comments by Makoto Uyeshima and anonymous reviewers are acknowledged and appreciated.