One century of tectonic deformation along the Sumatran fault from triangulation and GPS surveys

Abstract

An analysis combining historical triangulation and recent Global Positioning System (GPS) survey measurements in west and north Sumatra, Indonesia, reveals a detailed slip history along the central part of the Sumatran fault. The arc-parallel components of the combined velocity field are consistent with slip rates inferred from GPS data, ranging from 23 to 24 mm/yr. Between 1.0°S and 1.3°N the Sumatran fault appears to be characterized by deep locking depths, of the order of 20 km, and the occurrence of large (MW~7) earthquakes. The long-term (1883-1993) strains show simple right-lateral shear, with rates similar to GPS-measured, 1989-1993 strain rates. Coseismic deformation due to the 1892 Tapanuli and 1926 Padang Panjang earthquakes, estimated from triangulation measurements taken before and after the events, indicates that the main shocks were significantly larger than previously reported. The 1892 earthquake had a likely magnitude of MW~7.6, while the 1926 events appear to be comparable in size to the subsequent (M~7) 1943 events and an order of magnitude higher than previously reported.

Full text

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. B12, PAGES 28,343-28,361, DECEMBER 10, 2000
One century of tectonic deformation along the Sumatran fault
from triangulation and Global Positioning System surveys
L. Prawirodirdjo, Y. Bock, and J. F. Genrich
Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Inslitution of Oceanography
University of California, San Diego
$. $. O. Puntodewo, J. Rais, C. Subarya, and S. Sutisna
National Coordination Agency for Surveying and Mapping, Cibinong, Indonesia
Abstract. An analysis combining historical triangulation and recent Global Positioning
System (GPS) survey measurements in west and north Sumatra, indonesia, reveals a detailed
slip history along the central part of the Sumatran fault. The arc-parallel components of the
combined velocity field are consistent with slip rates inferred from GPS data, ranging from
23 to 24 mm/yr. Between 1.0øS and 1.3øN the Sumatran fault appears to be characterized by
deep locking depths, of the order of 20 km, and the occurrence of large (M,•, ~ 7)
earthquakes. The long-term (1883-1993) strains show simple right-lateral shear, with rates
similar to GPS-measured, 1989-1993 strain rates. Coseismic deformation due to the 1892
Tapanuli and 1926 Padang Panjang earthquakes, estimated from triangulation measurements
taken before and after the events, indicates that the main shocks were significantly larger
than previously reported. The 1892 earthquake had a likely magnitude of M w -- 7.6, while
the 1926 events appear to be comparable in size to the subsequent (M - 7) 1943 events and
an order of magnitude higher than previously reported.
1. Introduction
The first geodetic measurements of coseismic deformation
were made by serendipity on the island of Sumatra during the
course of a triangulation survey [M•itler, 1895]. These data,
which indicated right-lateral motion in a NW-SE direction,
were later referenced by Reid [1913] as evidence for his
elastic rebound theory of the earthquake cycle. The
triangulation survey was part of an extensive geodetic
network established by the Dutch colonial government in the
1880s and 1890s. The entire triangulation network consisted
of more than 2000 primary, secondary, and tertiary sites,
coveting most of the island [TrianguIatiebrigade van den
ropographischen Dienst, 1916; War Research Institute,
1944]. Construction of a concrete pillar and subsequent
initial surveys often took several weeks at each site. Because
triangulation involved point-to-point optical direction
readings through a theodolite, most stations were situated on
mountain tops. The Sumatran fault (SF) extends over the
entire length of the island (-1600 km) through the Bukit
Barisan Mountains and the volcanic chain (Figure 1) and was
thus conveniently well-spanned by the triangulation network.
We initiated Global Positioning System (GPS) geodetic
surveys in Sumatra in 1989 [Bock et aI., 1990; McCaffrey et
al., 1990] as part of a larger campaign which included the
entire Indonesian archipelago [Puntodewo et al., 1994;
Genrich et aI., 1996; Prawirodirdjo et al., 1997; Stevens et
al., 1999]. In this paper, we describe crustal deformation in
Copyright 2000 by the American Geophysical Union.
Paper number 2000JB900150.
0148-0227/00/2000JB900150509.00
the vicinity of the SF inferred from triangulation and GPS
data spanning a period of over 100 years. The triangulation
data were available to us from historical archives and
provided the intriguing opportunity to test whether recent
GPS-measured deformation rates are consistent with longer-
term rates if we could reoccupy some of the triangulation
pillars with GPS. Many of the triangulation monuments are
in remote areas that even with modem logistics represent a
formidable challenge for state-of-the-art, space-based
geodetic surveys. Furthermore, as we discovered during the
reconnaissance phase of the project, the state of preservation
of the triangulation pillars usually correlated inversely with
accessibility.
The GPS network on Sumatra came to include 22
historical triangulation sites, and was surveyed from 1989 to
1993 [see also Genrich et aI., this issue]. The subset of
triangulation sites we call the "west Sumatra" network
(Figure 2 and Table l a), established between 1883 and 1896
at 1.5øS to 2øN latitude, is especially useful for comparing
crustal deformation rates because many of its sites were
surveyed at more than one epoch with triangulation and were
also surveyed during the 1989-1993 GPS campaigns. In
addition, we used several sites from the "north Sumatra"
network (north of 2øN, Figure 2 and Table lb), established
between 1907 and 1918, which were reoccupied with GPS.
Several studies [e.g., Shay and Drew, 1989; Grant, 1990]
have shown it feasible to combine space geodetic and
terrestrial survey data to derive an unambiguous velocity
field. Dong [1993] and Dong et aI. [1998] subsequently
developed a theoretically rigorous method for combining
heterogeneous geodetic data sets based on the work of Hein
[1986] and Collier et al. [1988]. This mett•od, which we
28,343

28,344 PRAWIRODIRDJO ET AL.' TRIANGULATION AND GPS ON SUMATRAN FAULT
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- løS
_ 3øS
- 4øS
- 5øS
,' 6os
95øE 96øE 97øE 98øE 99øE 100øE 101 øE 107E 103øE 104øE
Figure 1. Map of the west and north Sumatra region with bathymetry (500-m contour intervals), tectonic
features, and inset showing geographic location. The Sumarran fault trace is based on data collected by Sieh
and Natcm'idjaja [this issue], and fault segmcnts discussed in the text are labeled in bold italics with names
and dates of earthquake occurrences. Arrows in the Indian Ocean and at the trench show the direction and
rates of convergence of the Australian plate relative to Southeast Asia. Open arrows show slip orientation on
the Sumarran fault, with slip rates from GPS measurements reported by Gertrich et al. [this issue].
applied here, was implemented in the software package
FONDA developed by Dong [1993].
The ability to combine heterogeneous data sets with
widely differing measurement epochs and scen•ios is
important for two reasons. First, it allows us to extend the
relatively short temporal coverage of space geodetic data by
combining them with terrestrial geodetic data, which in
Sumatra date as early as the late nineteenth century.
Furthermore, the addition of space geodetic data lets us
eliminate the rank deficiencies inherent in terrestrial geodetic
data without applying arbitrary external constraints, such as,
for example, the "inner coordinate" constraint [Segcdl and
Matthews, 1988].
We performed a network adjustment of the combined
triangulation and GPS data to obtain an averaged
deformation field over the last 100 yem's, which we then
compare to the short-term (4-year) GPS-derived deformation.
We examined whether our combined velocity field is
consistent with slip rates and locking depths inferred from
GPS measurements and geological observations. In addition,
we estimated the coseismic deformation caused by the 1892
[Reid, 1913], 1926 (M s = 6.5 and 6.8 [Gutenberg and Richter,
1954]), and 1943 (M s = 7.1 and 7.4 [Pacheco w•d Svl, es,
1992]) earthquakes. We discuss our results in the context of a
recent, comprehensive geological study of the SF by Sieh
Natawidjaja [this issue], and compare them to results from
the GPS surveys reported by Gertrich et al. [this issue] with
further analysis by McCaffrey et al. [this issue].

PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT 28,345
14
i- 4øN
Plll
P 109/DSIM
P1
Lake Toba
P065
)63
2øN
O Pt
150 km
P062
P055/BINA
1892
)63
West Sumatra
Network 0
)43
P0,•(
P027/AJUN
P023
P022/TANJ
P021
1926,1943
PO02
PO03,
P026
PO42/PAUH
P017
Sianok
6
5
SUmani
P014
P032
÷13
P033
2øS
98OE 100øE 102øE
Figure 2. Historical triangulation and GPS networks in Sumatra. Sites connected by solid lines indicate
triangulation sites used in this study. Solid crosses indicate triangulation sites with more than one epoch of
observation. Circles indicate GPS survey sites. Shaded areas are rupture zones of the 1892, 1926, and 1943
earthquakes. Sites discussed in the text are labeled with site names. Some of the triangulation sites which
were resurveyed with GPS were renamed in the process (see Table 2). These sites are labeled with both
triangulation and GPS site codes, separated by a slash. Sites belonging to the "north Sumatra" and "west
Sumatra" networks are listed in Table 1. Subnetworks are labeled in bold.
2. Sumatra Tectonics
Sumatra experiences active deformation and large
earthquakes due to subduction of the Australian plate beneath
Southeast Asia [e.g., Newcomb and McCa/m, 1987]. From
velocity vectors derived t¾om regional GPS data
[Prawirodirdjo, 2000] the pole of rotation for the Australian
plate relative to Southeast Asia is located in East Africa (9.64
+- 1.44øN, 51.38 + 2.03øE), with an angular rotation rate of
0.677 + 0.016ø/Myr. Thus, southwest of Sumatra, the
convergence of the Australian plate occurs obliquely, ranging
from 60 mm/yr, N17øE azimuth at (6øS, 102øE), to 52
mm/yr, N10øE azimuth at (2øN, 95øE) (Figure 1). The
oblique convergence is p•titioned into subduction at the
trench which is nearly perpendicular to the •c, and arc-
parallel motion of the forearc along the SF [Fitch, 1972'
McCaffrey, 1991 ]. McCaffrey [ 1991 ] further demonstrated
from earthquake slip vector deflections and plate

28,346
Table la. West Sumatra Triangulation Network: Station Coordinates (WGS84) and
Calendar Years of Survey
Site Code Lat., øN Lon., øE Triangulation Survey Years GPS Survey Years
P001 -0.8992 100.5337 1883,1884,1885,1927,1930 1991,1993
P002 -0.9560 100.2308 1883,1884,1885,1927,1930 1991,1993
P003 -1.1166 100.4293 1883,1884,1885,1927,1930 1990,1993
P004 -1.1769 100.7504 1885,1886,1887,1927,1930 1991,1993
P005 -0.7159 100.7037 1883,1885,1886,1927,1930 1991,1993
P006 -0.7256 100.4582 1883,1885,1927,1928 -
P007 -0.3245 100.6731 1885,1886,1887,1928 1991,1993
P008 -0.3899 100.3311 1885,1886,1928 1991,1993
P009 -0.5724 100.2368 1884,1885,1927 -
P010 -1.3677 100.6090 1885,1887 -
P011 -1.2777 100.8021 1885,1887 -
P012 - 1.2465 101.0131 1886,1887,1888, -
P0!3 -0.9879 101.0827 1885,1886,1917,1930 -
P014 -0.5861 100.9833 1886,1930 -
P015 -0.3612 100.8985 1885,1886,1887,1928 1991,1993
P016 -0.2323 100.7850 1885,1886,1887,1928 1991,1993
P017 -0.0075 100.6538 1885,1887,1928 1990,1993 (as DING)
P018 0.0753 100.3893 1885,1886,1887,1888,1928 -
P019 -0.2452 100.1309 1885,1886,1930 -
P020 -0.4112 100.1794 1885,1886,1930 -
P021 -0.5959 100.0748 1885,1930 -
P022 -0.4444 99.9867 I885,1886, I930 1989,1990,1991,
1993 (as TANJ)
P023 -0.2662 99.8846 1885,1886,1930 -
P024 -1.5980 101.0098 1887,1888,1889,1917,1918 -
P025 -1.6079 100.6414 1885,1887,1888 -
P026 -I.8474 100.8503 1887,1888,1889,1890,1918 -
P027 -0.1584 99.7655 1885,1886,1890 1989,1990,1991,
1993 (as AJUN)
P028 0.0787 99.9839 1885,1886,1888,1890 -
P030 -1.9006 101.1387 1887,1888,1889,1890,1917,1918 -
P031 -1.0189 101.2732 1886,1887,1888 -
P032 -0.7751 101.2399 1886,1917 -
P033 -1.3242 101.3418 1886,1887,1888,1917 -
P034 -1.6778 101.4280 1887,1888, 1917,1918 -
P035 0.3093 100.1904 1887,1888,1891 -
P036 0.7364 100.2429 1887,1888,1891 -
P037 a 0.7018 99.8199 1888,1890,1891, 1892 -
P038 -2.1010 101.2631 1889,1890,1904 -
P039 -2.1604 101.1209 1888,1889,1890,1904 -
P040 0.2226 99.3879 1885, 1890,189 ! 1989,1990,1991,
1993 (as AIRB)
P041 a 0.4770 99.6513 1885,1888,1890,1891,1892,1893 1993 (data are bad)
P042 0.2372 100.8324 1886,1887 I989,1990,1991,
1993 (as PAUH)
P043 0.4097 100.6978 1887,1888,1891 -
P047 -2.5413 101.4393 1890, 1904 -
P049 a 0.7562 99.2753 1890,1891,1892,1893,1894 -
P050 1.4782 99.2096 1893,1894,1895 -
P051 a 0.9439 99.6261 1890,1891,1892,1893,1894 1991,1993
P052 0.3439 99.1288 1890,1891,1893 -
P053 0.8388 98.9818 1891,1893,1894 -
P054 1.7859 98.8779 1894,1895 1990,1993
(as GADI)
P055 1.4489 99.7553 1894,1895 1989,1990,1991,
1993 (as BINA)
P056 1.9599 98.9682 1894,1895,1908,1913 -
P057 1.2710 98.8258 1893,1894 -
P058 1.7572 99.5604 1894, I895,1930 -
P059 1.8756 99.1724 1894,1895, -
P060 2.0830 99.5083 1894,1895,1930 -
P061 2.1770 99.1364 1895,1908,1912 1989,1990,1993
P062 1.6480 99.8344 1894,1895,1930 -
P063 2.0605 99.7981 1894,1895,1930 -
P104 -2.2277 101.4272 1890,1917,1918 -
S059 a 0.6861 99.5393 1890,1891,1892,1893 1990,1993
(as MERA)
S063 a 0.8605 99.7678 1891,I892,1893 -
S080 a 0.7686 99.6401 1891,1892,1893 -
S174 -1.8980 101.7749 1887,1917,1918 -
aSites comprising Mtiller's survey network that spanned the 1892 Tapanuli earthquake.

PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT 28,347
Table lb. North Sumatra Triangulation Network: Station Coordinates (WGS84) and
Calendar Years of Survey
Site Code Lat., øN Lon., øE Triangulation Survey Years GPS Survey Years
P064 2.3782 99.6871 1895,1913,1930 -
P065 2.5083 99.5534 1913 -
P066 2.4524 99.3570 1912,1913 -
P106 2.4622 98.7463 1908,1912 1989,1990,1993 (as DOLO)
P107 2.5982 99.0654 1908,1909 -
PI08 2.6854 98.6090 1908,1909 -
P109 3.0130 98.9036 1908,1909 1990, 1993 (as DSIM)
P110 2.9259 98.5354 1908,1909 -
Pill 3.2474 98.5006 1909,1910,1914,1915 -
Pl12 3.1376 98.!267 1909,1910 -
P121 2.1958 98.5976 1908,1913 -
S103 2.1726 99.3616 1913 -
S104 2.0763 98.8257 1908,1913 -
S200 2.0922 98.6153 1908,1913 1990.1991,1993 (as SIGL)
convergence vectors that the forearc sliver plate located
between the trench and the SF is not rigid but instead
undergoes arc-parallel stretching, requiring a northwestward
increase in slip rate along the SF. Slip rates estimated at two
locations by Sieh et al. [1991] from stream offsets incised in
Quaternary volcanic tuffs, and at several locations by BeIlier
and Sgbrier [1995] from SPOT satellite images of stream
offsets, support an increase in slip rates from SE to NW.
However, recent GPS surveys [Gertrich et al., this issue]
show only a marginal increase.
The spatial and temporal variations in slip rate and
seismicity along the SF are still only poorly known. The
spatial variations are just beginning to be revealed by
geodetic and geologic observations. While it is confirmed
that the oblique convergence is generally partitioned into
subruction at the trench and transcurrent shear along the SF,
modeling of geodetic data shows that this simple scenario is
complicated by many intriguing details. There appears to be a
north-south segmentation in the pattern of strain
accumulation along the subruction zone [Prawirodirdjo et
aL, 1997]. The southern half of the forearc is moving roughly
in the same direction as the convergence between the
Australian plate and Southeast Asia, while the northern half
is moving in a direction more closely parallel to the arc. The
division of the forearc velocity field coincides with the
boundary between the rupture zones of the 1833 and 1861
(M w > 8) thrust earthquakes postulated by Newcomb and
McCann [1987] and is thus probably related to the
subruction zone's rupture kinematics. Also, the inferred slip
rate on the SF is about 1/3 less than the full arc-parallel
component of plate motion [McCaffrey et al., this issue]. To
account for 20 km of offset on the SF since the Oligocene
[Sieh and Natawidjaja, this issue], an additional 20 mm/yr of
strike-slip is required west of the SF and probably takes place
seaward of the Mentawai Islands [McCaffrey et al., this
issue].
Our goal in this study, together with those presented by
Genrich et al. [this issue] and McCaffrey et aI. [this issue], is
to gain some insight into the spatial and temporal details of
the dynamics along the SF. Moreover, since rupture
kinematics along the SF and in the forearc are strongly
correlated with structural features, it is important that we
formulate interpretations of our geodetic data consistent with
geological observations such as those made by Sieh and
Natawidjaja [this issue]. Throughout this paper, in referring
to various regions along the SF, we use the fault segment
names proposed by Sieh and Natawidjaja [this issue].
3. Data
3.1. Triangulation Data
The original triangulation monuments consisted of
concrete pillars- 1.5 m high, with embedded bronze markers
(Plate 1). Horizontal angles from a central station to a set of
surrounding stations were measured using micro theodolites,
from Pistor and Martins and Wegener and Wanschaff, and
heliotropes placed on the pillars with their axes in the plumb
line of the bronze markers [War Research Institute, 1944].
We used 391 horizontal angle measurements from the
west and north Sumatra networks, defining 106, roughly
equilateral triangles (Figure 2), with sides measuring 20 to 70
km long. For each network, there were also available one
distance measurement and one azimuth measurement,
intended to fix the scale and orientation of the network. The
distance measurements were not precise enough, however, to
constrain the scale to within less than several hundred parts
per million (ppm). Nor are the azimuth measurements useful
to us, since they were taken at sites where we do not know
the coordinates precisely. Instead, we fixed scale and
orientation by linking GPS and triangulation horizontal
positions and velocities at well-determined, collocated
stations, as described in section 5.1.
The initial survey of the west Sumatra network began in
!883 and was completed in 1896. The north Sumatra network
was surveyed in 1907-1916. After the 1926 Padang Panjang
earthquake (Figure 2), sites around the rupture area were
resurveyed in 1927-1930. At the Angkola segment of the SF
(IøN latitude, Figure 2), an earthquake occurred in 1892
while a second-order survey was underway, displacing the
triangulation monuments [M•iIter, 1895; Reid, 1913]. Sites
near the rupture area were later surveyed again over the next
2 years (1892-1894). For reasons unknown to us, repeat
measurements were also performed in 1917 and 1918 at a
few sites in the west Sumatra network (Figure 2) and in 1930
in the north Sumatra network (Figure 2). Table I summarizes
the triangulation sites and their dates of survey.

28,348 PRAWIRODIRDJO ET AL.' TRIANGULATION AND GPS ON SUMATRAN FAULT
(A)
P106
PI09
(c)
S200
ß ':. (D) S58
?.lBg' '
(E) Poe5
Plate 1. Photographs showing different types of Sumatra triangulation monuments surveyed with GPS. (a)
and (b) Primary pillars (P106 and P I09) that have remained intact since the 1880s, including their brass
survey markers. Shape and height of the pillars often required metal extension rods (shown in Plate l a) lbr
the survey tripods in order to center the antenna accurately above the survey mark. (c) A well-preserved
secondary pillar (S200). (d) At other sites like S58, pillar still erect but damaged, with no trace of bronze
marker. We placed stainless steel pins at the center ot' the top surface to serve as the GPS survey mark. (e)
Monument P005 which suffered heavy damage over the years. In such cases tt new concrete monument was
reconstructed over the still recognizable l:oundation of the original pillar. Horizontal location of the original
survey marker could often be identified and "recovered" to within tens of centimeters.

PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT 28,349
The original raw data were reduced by one of us (S.
Sutisna) to one measurement for each angle and then used as
input to a least squares adjustment of station coordinates
using the software package CHAOS (School of Surveying,
University of New South Wales). The ancillary distance and
azimuth measurements mentioned above were used to
nominally constrain the scale and orientation of the network.
The result of this adjustment was a set of station coordinates
referenced to the GRS67 ellipsoid. We used these as a priori
triangulation site coordinates. The GRS67 is based on the
geocentric equipotential ellipsoid, with ellipsoid parameters
(ellipticity f = 1/298.2472 and semiaxis length a =
6,378,160.00 m [h•ternational Associatio/i of Geodesy,
1971]) significantly different from the WGS84 ellipsoid 0 r =
1/298.257223563, a = 6,378,137.00 m [Defense Mapping
Agency, 1987]), to which our GPS geodetic coordinates are
referenced. Hence, before combining the data we
transformed the triangulation coordinates into the WGS84
system by converting them into geocentric Cartesian
coordinates and converting them back to geodetic
coordinates using the WGS84 ellipsoid parameters.
3.2. GPS Data
Our analysis is based on GPS data from geodetic surveys
performed in Sumatra in 1989, 1990, 1991, and 1993. Some
sites in south and east Sumatra were surveyed in 1994, but
these measurements are not used in this analysis. Neither did
we use data from the near-field arrays, discussed by Genrich
eta!. [this issue], which were part of the Sumatra GPS
surveys. A detailed description of the GPS campaigns in
Sumatra is given by Prawirodirdjo [2000], and the complete
GPS velocity field is documented by Genrich et al. [this
issue].
Dual-frequency carrier phase and pseudorange
observations were combined with improved orbits [Fang a•d
Bock, 1996] to compute daily solutions consisting of site
coordinates, satellite state vectors, tropospheric zenith delay
parameters, and phase ambiguities by weighted least squares
using GAMIT version 9.40 [King and Bock, 1995]. The daily
solutions were then combined using GLOBK version 4.12
and GLORG version 4.04 [Herring, 1997] to estimate site
coordinates and velocities. North and east velocity
components have a typical formal one standard deviation
(assuming a white noise stochastic model for the estimated
site coordinates [see Zhang et aI., 1997]) of 1-2 and 3-4
mm/yr, respectively.
Of the more than 70 GPS sites surveyed, 22 were located
on triangulation sites. A 4-day GPS survey of a well-
preserved site typically required a 1-day vehicle drive to the
nearest village, assembly of a team of local guides and
porters, a 1-3 day ascent to the site on previously nonexisting
or barely established narrow mountain trails, several hours of
site perimeter clearing to gain reasonable satellite visibility,
the actual 4-day GPS survey, and a 1-2 day return trip to the
village.
The triangulation sites that were reoccupied during the
GPS campaigns fall roughly into three categories:
1. Monuments which were sufficiently intact were
resurveyed directly over the original bronze mm'ker (Plates
la-!c). At least four sites, P106/DOLO, P109/DSIM,
S059/MERA, and S200/SIGL (Figure 2 and Table 2), fall
within this category. We refer to these as the "core" sites.
2. At monuments which were still erect but had sustained
some damage, including removal of the bronze marker, the
GPS antenna was set up over the remains of the monument
(Plate l d), approximating the location of the triangulation
marker to within a few tens of centimeters.
3. Monuments which had sustained heavy damage or had
been completely destroyed required construction of a new
monument over the likely location of the original mark. GPS
reoccupation was performed within ! m of the estimated
original mark (Plate l e).
In addition, in an attempt to tie in eight more triangulation
sites, we established new monuments placed as close to the
original sites as local logistics permitted (up to several km).
Although GPS vectors were measured from these eight
eccentric sites to the respective triangulation sites, the
measurements were, unfortunately, not precise enough to
serve as ties in our analysis. We used one of these eccentric
sites (DEMU) to establish a reference frame in the northern
part of the network by linking its horizontal velocity to that
of its corresponding triangulation monument (P065). Table 2
summarizes the relationships between the triangulation and
GPS stations.
The triangulation stations which were resurveyed with
GPS were used to update the a priori triangulation site
coordinates. Using FONDA, we used the GPS-measured
ve!ocities of the collocated stations to propagate back in time
to estimate coordinates of the collocated stations during the
triangulation epochs and used the angle measurements to
estimate coordinates for all other triangulation stations not
resurveyed with GPS. This process, described in more detail
in section 4.2, yielded improved coordinates for all the
triangulation stations and allowed us to assume, in
subsequent analyses, that the coordinates for most of the
triangulation stations are well determined. In this manner,
information from the GPS measurements allowed us to
eliminate the rank deficiencies of the triangulation data.
4. Analysis
Our analysis of the triangulation and GPS measurements
was based on the method developed by Dong [1993] and
Dong et al. [1998] to analyze trilateration and GPS data in
southern California. This method is implemented in the
software package FONDA [Dong, 1993], a sequential least
squares (Kalman filter) estimation in which station positions
are estimated as a function of time, taking into account
secular velocities and, where appropriate, episodic and
stochastic station displacements. The method is briefly
reviewed here.
First, loosely constrained estimates of geodetic parameters
are obtained from an analysis of individual experiments to
serve as "quasi-observations" for the combined solution.
Here we derived loosely constrained estimates of site
positions from the 1989-1993 GPS observations and the
angle measurements f¾om triangulation surveys. The quasi
observations are then combined using FONDA. Unknown
episodic (coseismic) site displacements at a subset of
specified sites are modeled as step functions in the site
positions. General constraints on position and site velocity
were imposed on the solution to remove the rank deficiency
in the triangulation data and to define a uniform reference
frame through well-determined stations common to all data
sets. Including data from a global network in the analysis of

28,350 PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT
Table 2. North and West Sumatra Historical Triangulation Sites Resurveyed with GPS in 1989-
1993
Estimated Offset Between
Site Code Relation of GPS Survey Uncertainty of GPS Triangulation and Eccentric Site b
Mark to Original Survey Mark Relative
Triangulation Mark to Triangulation
Triangu- GPS Mark a, cm Azimuth, Distance, km
lation deg
P001 c P001 monument reconstructed
P002 c P002 monument reconstructed
P003 ½ P003 monument reconstructed
P004 c P004 monument reconstructed
P005 ½ P005 new monument
reconstructed over center
of foundation' s remains
P007 c P007 monument reconstructed
P008 c P008 original monument, no
bronze marker
P015 c P015 monument reconstructed
P016 P016 monument reconstructed
P017 ½ DING monument reconstructed
P022
P027 ½
P037
P035
P040 c
P042 c
P050
P051
P054
P055 c
P059
P061 e
P065
P 106 ½
P 109 c
S059 c
S200 c
ULUA eccentric point to P017
TANJ monument reconstructed
AJUN monument reconstructed on
foundation remains
P37E eccentric point to P037
PETO eccentric point to P035
AIRB monument reconstructed
PAUH original monument
SIBI eccentric point to P050
P051 monument reconstructed
GADI original monument found
tilted
PISA eccentric point to P054
BINA monument reconstructed
PANT eccentric point to P059
P061 monument reconstructed
over original foundation
DEMU original monument
destroyed - eccentric point
constructed to P065
DOLO original monument
MART eccentric point to P!06
DSIM original monument
MERA original monument
SIGL original monument
10
10
10
10
100
10
10
!0
20
10
-
10
10
297 5
- 327 8.75
- 124 10
10 - -
5 - -
- 225 4
l0 - -
- 125 13.75
50 - -
- 1!6 14
10 ~ -
291 8
_
- 141 12.25
5 -
5 - -
5 - -
aFor collocated sites; not applicable to eccentric sites.
bOnly applicable to eccentric sites.
cSites which were used to estimate transformation parameters between the triangulation and GPS coordinates.
primary GPS observations renders the GPS solution
unambiguous on the regional scale. Thus, by linking GPS
and triangulation estimates of horizontal velocities of well-
determined, collocated stations we removed the dilatation
and rotation ambiguity inherent in the triangulation surveys
[Dong et al., 1998].
FONDA's estimation procedure yields site coordinates,
velocities, and episodic (in this case, coseismic)
displacements simultaneously. However, we chose not to
estimate all the desired parameters in one large solution
involving all the triangulation and GPS data. We opted
instead for a slightly distributed approach, with the goal of
minimizing the effect of any systematic shifts on the
displacement and velocity estimates. For example, to
using the GPS measurements). To estimate long-term
interseismic strain, we used the first-epoch triangulation
measurements and GPS data, accounting for coseismic
displacements by applying corrections based on the
coseismic estimation. More detailed descriptions of the
procedures used at each step are given in sections 4.1 and
4.2.
4.1. Assessment of Triangulation Data Quality
To estimate the error in the triangulation (angle)
measurements, we inverted the triangulation data set for
station coordinates only. Holding fixed the coordinates of
two arbitrarily chosen sites, P037 and P042 (Figure 2),
eliminates the rank deficiency due to scale and orientation. h
estimate coseismic displacements spanned by triangulation. this inversion we did not include measurements taken by
surveys, we used only subsets of angle measurements from MiiIler [1895] in the epicentral area immediately after Be
before and after the earthquake (and site coordinates updated 1892 earthquake, since we expected them to contain lax'g,

PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT 28,3>1
140
120
• 1oo
80
z
60
4O
20
0
-3 -2 -1 0 1 2 •
Residuals (arc seconds)
Figure 3. Histogram of residuals from adjustment of 374 horizontal angles in the 1883-1896 survey,
calculated with P037 and P042 fixed (see text). Solid line represents a normal distribution with zero mean
and standard deviation of 0.4 arc sec.
contributions from the earthquake. Figure 3 shows the
distribution of angle residuals fi'om this adjustment of 374
angle measurements from 82 sites. We found that repeating
this adjustment while holding coordinates o1' different pairs
of sites fixed did not significantly affect the distribution of
residuals. With the exception of angles measured from
station P009, the roofmean-square (rms) residuals of angles
measured from each station all fall below 0.5 arc sec. The
standard deviation of the residuals is 0.4 arc sec. This
corresponds to - 2 ppm in triangle misclosure [Davies et al.,
1997], the difference between the sum of three angles in a
given triangle and 180 ø plus the spherical excess [Bomford,
1980; Yu and Segall, 1996]. This level oi' precision is
adequate to detect regional strains, which are expected to be
a few tens o1' ppm over 100 years (the interval between
triangulation and GPS surveys) or several ppm over--- 45
years (the interval between repeated triangulation
measurements in the region of the 1926 and 1943
earthquakes, Figure 2).
4.2. Updating Site Coordinates
First, we estimated four transformation parameters (three-
dimensional translation and rotation about one axis) based on
the collocated sites indicated in Table 2. A coordinate
transformation was then performed to align the a priori
triangulation site coordinates with the GPS coordinate
system. This first step serves as a large-scale correction to
the a priori triangulation site coordinates, while still
disregarding the temporal variations in site positions.
Next, we used FONDA to adjust the triangulation site
coordinates, using all the angle measurements. In this
adjustment, the positions and velocities of the four core sites
(Pi06, PI09, S059 and S200) are tightly constrained to their
GPS-determined values. In addition, velocities (but not
positions) of triangulation sites where the GPS rcsurveys
were within tens of centimeters of the original mark were
constrained to their GPS-determined values. Beginning with
strict outlier identification criteria, we repeated the
adjustment a few times, updating coordinates and loosening
the outlier identification criteria after each iteration. In the
final adjustment we constrained the horizontal coordinates of
the GPS-resurveyed triangulation sites to within 20 cm and of
the four core sites to within I cm of their GPS-determined
positions (the coordinate constraints were loosened up again
when we began estimating deformation rates). By thus using
the GPS-measured velocities of the collocated stations,
FONDA propagates back in time to estimate coordinates of
the collocated stations during the triangulation epochs, and
uses the angle measurements to estimate coordinates for all
other triangulation stations not resurveyed with GPS. This
process yielded improved coordinates for all the triangulation
sites to be used in the velocity field estimation.
Our final adjustment included 357 angle measurements
87 stations. All angle measurements were given equal
weight. We did not estimate vertical velocities, and vertical
positions (heights) were given tight constraints. After the
final iteration the postfit nns of the angle measurements was
0.9 arc sec. This level of error, higher than the 0.4-0.5 arc sec
obtained fi'om our initial adjustment of angle measurements,
suggests that some stations may have experience coseismic
as well as secular motion. Nevertheless, these updated
coordinates m'e sufficient in quality to be used as a priori

28,352 PRAW!RODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT
values in the studies that follow. Three measurements, all
taken from site S080, were discarded due to large angle
residuals.
5. Results and Discussion
5.1. Interseismic Deformation Rates Obtained by
Combining Triangulation and GPS Measurements
By performing a solution combining first-epoch
triangulation measurements for the west and north Sumatra
networks with GPS measurements, we estimated the long-
term interseismic deformation rates. International Terrestrial
Reference Frame 1996 (ITRF96) [SilIard et al., 1998] -based
locations served as a priori coordinates for the GPS sites, and
the set of updated coordinates described above served as
those for the triangulation sites. Since the interval between
the triangulation and GPS surveys also spans the 1943
earthquake, we solved for coseismic displacements at sites
near the 1943 rupture zone along with the interseismic
deformation rates (see section 5.3.3).
As quasi-observations for the GPS-reoccupied sites (listed
in Table 2), we used loosely constrained coordinates obtained
from analysis of the entire GPS data set. For sites surveyed
both by triangulation and GPS, our goal was to obtain the
long-term (1880s to 1990s) velocities from the a priori
triangulation coordinates, angle measurements, and current
GPS positions. To minimize dependence on the short-term
(GPS-measured) velocity signal, we did not want to include
GPS-measured velocities as quasi-observations (although
note that the GPS velocities have been used to update the
triangulation site coordinates). However, we included the
GPS-measured velocity for one site, DEMU, as a quasi-
observation in our adjustment. This site is eccentric to P065,
and we constrained P065 to have the same velocity as
DEMU to install a frame of reference for velocities in the
northern part of the triangulation network. Both sites, only 8
km apart, are located in the back arc basin, where strain rates
are very small (- 0.01 gstrain/yr [McCaffrey et aI., this
issue], Table 3). As input from the triangulation surveys, we
used all available first-epoch angle measurements for the
west and north Sumatra networks. This included several sites
which were surveyed only once, which are needed for
triangle closure (we did not estimate their velocities).
Following Dong's [1993] approach, we first combined the
triangulation and GPS observations in a loosely constrained
solution. We then applied constraints to P042 and P065. We
constrained the position and horizontal velocity of P042,
which is located on the back arc, to their GPS-derived,
ITRF96 values. As mentioned above, we also constrained
P065 to have the same velocity as DEMU but did not
constrain its position. The constraints on P042 and P065
placed the estimated velocity field in the ITRF96 reference
frame and allowed us to make a direct comparison between
the long-term velocities derived here and the GPS-measured
velocities. In this process, the only assumptions we made are
that two sites (DEMU and P042/PAUH) located on the back
arc have had a constant velocity (as measured by GPS)
during the period between the triangulation and GPS surveys
and that P065 moves at the same (constant) velocity as
DEMU.
The velocity field for 1883-1993 obtained from the
combined solution of triangulation and GPS measurements is
shown in Figure 4, plotted relative to the Eurasian plate pole
of rotation. This does not include the measurements made in
1927-1930. For comparison, the short-term GPS-derived
velocities have also been included.
At sites P005, P015, P017, P106 and P109, long-term and
short-term rates agree within their 95% confidence regions
(Figure 4). The long-term velocities south of the equator
clearly show right-lateral shear across the SF. Sites located
around the Suliti and Siulak segments (south of 1.5øS) are
only weakly connected to the rest of the west Sumatra
network, yet the velocity field in this area clearly shows
fight-lateral shear across the SF. The velocities in the
northern back arc (north of 1.5øN) have large uncertainties,
but the uniformity of the vectors suggests lack of internal
deformation in that region of the back arc.
Genrich et al. [this issue] inferred slip rates and locking
depths along the SF by fitting GPS-measured velocities to
Savage and Burford's [1973] 1-D elastic dislocation model
for a locked strike-slip fault. In this model, velocities located
far (>100 km) from the fault trace largely constrain the slip
rate, while velocities near the fault constrain the locking
depth. Vectors from the combined triangulation and GPS
solution all lie within 150 km of the SF, are sparsely
distributed, and have large uncertainties; hence they only
loosely constrain slip rate and locking depth. Therefore we
Table 3. Horizontal Interseismic Strain Rates
•;11, •22, 0,
Region 10 '6 yr-1 10 '6 yr -1 deg
N Source of Estimate
10 '6 yr-1 10-6 yr-1
Sumani -0. i0+0.04 0.09_+0.07 24.8_+10.9
Sumani -0.09_+0.03 0.14+0.03 32.4+2.9
Sumani - - 31.0-+ 12.9
Back arc -0.01+0.03 0.02-+0.08 168.1+12.6
Northern - - not well
Back are determined
0.13-+0.09 -0.15_+0.08
0.09_+0.02 -0.3+_0.02
0.08-+0.08 -0.15-+0.07
0.03-+0.07 0.014_+0.06
0.03_+0.12 0.06_+0.09
16 1989-1993 GPS McCa. ffrey
et al. [this issue]
9 1883-1885 to 1989-1993
triangulation and GPS
21 1883-1885 to 1927-1930
triangulation
8 1989-1993 GPS McCa. ffrey
et al. [this issue]
6 1893-1895 to 1930
triangulation
Strain rates are expressed in terms of the axes of maximum compression ( •l• ) and extension ( •;22 ) and the
engineering shear strain rates 'iq and •/2; 0 is the azimuth of maximum contraction; N is the number of sites
used in the stxain estimation. Quoted uncertainties are forrnal standard errors.

PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT 28,353
•. ..... .:- ..... .:
2øN -
(•• .......... ':'. PAND
D957 u ..'..... BINT
IøN , 3
"""•"D952
0ø- D9 4
:..
2ø$-
30 mm/yr
150 km
63
;P055
BLMS ¸
DUR•
•PASI
SIKA ;E RUMB
P(
D947
D937.•
ß . (•PO42
P027 P016
P0(
P00' -
P003
•2
P039 P038
3øS • • I •
97øE 98øE 99øE 100øE 101 øE 102øE
Figure 4. Interseismic velocity field (solid arrows) derived fi'om a combination of triangulation and GPS
observations. Open arrows are 1989-1993 GPS-derived velocities from Ge/•rich et al. [this issue], shown for
comparison. Ellipses indicate 95% confidence levels
did not attempt to infer slip rates or locking depths from our
combined velocities, but in Figure 5 we compare them to the
slip rates and locking depths estimated by Gertrich et al. [this
issue]. Because convergence between the Australian plate
and the forearc is nearly perpendicular to the trench, strain
accumulation on the subduction zone mainly afi:ects the arc-
normal components of the vectors, while the arc-parallel
components reflect slip along the SF [Prawirodirdjo et al.,
1997]. Hence we plotted (Figure 5) the arc-parallel velocities
for tbur regions across the SF corresponding to segments
reported by Sieh and Namwidjaja [this issue], with curves
reflecting slip rates and locking depths estimated by Gertrich
et al. [this issue] from GPS data at the appropriate latitudes.
Our combined velocities at the Toru segment (approximately
2 ø to 3.5øN) are consistent with a slip rate of 24 mm/yr and a
locking depth of 9 km reported by Gets rich et al. [this issue]
for this region (Figure 5a).
Between 0 ø and 1.8øN, the SF splits into two major
strands (the Barumun and Angkola segments, Figure 1), and
thus cannot be modeled by a simple fit to Savage and
Butford's [1973] model. Assuming locking depths of 10-20
km and treating the vectors as the sum of surface deformation
due to slip on both fault branches, Gertrich et al. [this issue]
estimated slip rates of 2-4 mm/yr on the eastern (Barumun)
branch and 19-2! mm/yr on the western (Angkola) branch. In
this region, all our combined vectors have large uncertainties.
Within the 95% confidence level the arc-pm'allel components
of our vectors at P040 and S059 are consistent with either the

28,354 PRAWlRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT
50 ...... 50
40
20
10
Tom
,
, . ,
Slip rate --- 24 mm/yr
Locking depth = 9 km
-10
-!5o -lOO -50 0 50 113o 150
40
30
20
-10
-150 -lO0
Barumun/Angkola
b Slip rates = 20 and 3 mm/yr
Locking depths = 20 km
-50 0 50 100 150
• 40
• 30
.• 20
• lO
I
< o
Sianok
,
Slip rate = 23 mm/yr
Locking depth = 24 km
-10
-150-lf•3 -5; 0 50 100 150
50
40
30
20
Sumani
Slip rate = 23 mm/yr
Locking depth = 22 km
-50 0 50 100 150
50
40
3O
2O
-I0
-150 -1(•0
Suliti-Siulak
[ Slip rate = 23 mm/yr
iLocking depth = 22 km
! I !
-50 0 50 100 150
Distance from geologic trace of SF, SW to NE (km)
Figure 5. Fault-parallel components of velocities derived from triangulation and GPS data (circles) with
associated formal one standard deviation as a function of orthogonal distance across segments of the
Sumarran fault. Solid lines are fault-parallel velocity profiles from Gertrich et al. [this issue], reflecting the
best fitting (in a least squares sense) slip rates and locking depths infen'ed from GPS data. The velocity field
is divided into sections corresponding to fault segments as reported by Sieh and Natawidjaja [this issue] (see
Figure 1): (a) Toru, (b) Barumun/Angkola, (c) Sianok, (d) $umani, and (e) Suliti-Siulak.
GPS-measured values or with zero slip (Figure 5b). The large
discrepancy at P051 may indicate that we underestimated the
error in locating the former triangulation site.
Along the Sianok and Sumani segments (approximately
!.0 ø to 0.5øS), our velocity vectors are also scattered and
include a few anomalously high velocities, noticeably at
P001, P002, P004 and P027. Our results suggest slip rates
closer to Genrich et at. 's [this issue] estimate of 23 mm/yr
(Figures 5c and 5d) than Natawidjaja and Sieh's [1994]
estimate of 12 mm/yr at these latitudes. Our data at Sumani
and Sianok appear to favor locking depths of the order of 20
km.
South of iøS, along the Suliti and Siulak segments,
velocity estimates are available only from the triangulation
data. In Figure 5e we plot the fault-parallel velocities in this
region, along with a curve showing the same slip rate and
locking depth as the Sumani segment Oust north of Suliti).
Although the uncertainties are large, our velocity field for the
Suliti-Siulak segments is similar to our combined velocity
field for the Sumani segment, suggesting a slip rate als0

PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT 28,355
closer to ~20 mm/yr or higher instead of ~ !0 mm/yr as
reported by Sieh et al. [1991] and Natawidjaja and Sieh
[1994] for this region.
Deep locking depths inferred by Gertrich et al. [this issue]
in the Sumani, Sianok, and Angko!a regions are consistent
with the occurrence of M s > 7 earthquakes in 1822, 1892,
1926 and 1943 [MiilIer, 1895; Visser, 1927; Untung et al.,
1985; Natawidjaja et aI., 1995]. Analyses of the triangulation
data, in combination with GPS measurements, support the
results suggested by Gertrich et aI. [this issue] that on time
scales of ~ 100 years the SF can be characterized by deep
locking depths which result in large (M•v > 7) earthquakes.
5.2. Strain Rates
As mentioned before, parts of the triangulation network
have more than one epoch of angle measurements. These
include sites around the Sianok and Sumani segments which
were surveyed in 1883-1885 and agai• in 1927-1930, and
sites in the northern back arc, just SE of Lake Toba, which
were surveyed in the 1890s and again in 1930. For these
intervals we could not determine an unambiguous velocity
field, but we estimated strain rates which we then compared
to strain rates computed from GPS measurements.
Five sites around the Suliti and Siulak segments (P024,
P026, P030, P033 and P034; Figure 2) also have two epochs
of angle measurements, from 1887-!890 and 1917-1918.
Also in this region and connected to those stations, P038 and
P039 were surveyed twice, once in 1888-!890 and again in
1904. However, data from this region along the Suliti and
Siulak segments were not enough to yield a meaningful strain
solution.
5.2.1. Sumani region. For the region around the Sumani
segment, we estimated strain rates for the period 1883-1930
from two epochs of triangulation data, and for the period
1883-1993 from triangulation and GPS data. Strain rates from
the two epochs of triangulation data (1883-1885 and 1927-
1930) were computed from the angle measurements using the
program ADJCOORD [Bibby, 1982; Crook, 1992] and are
expressed in terms of the "engineering" shear strain rates 'h
and •2 [Feig! et al., 1990] (Table 3). Scale and orientation
were fixed by constraining the horizontal coordinates of P001
and the azimuth and distance from P001 to P007. These
triangulation measurements across the Sumani segment for
1883-1930 span the 1926 earthquakes. However, effects of
the earthquakes are not evident in the shear strains listed in
Table 3. The values of •,• and ?2 are consistent with strain
rates estimated by McCaffrey et al. [this issue] from GPS
measurements (Table 3).
Strain rates from 1883 to 1993 spanned by the
triangulation and GPS data were computed by fitting a
surface strain rate tensor to the velocity field (described in
section 5.1.), then finding the magnitudes and directions of
the principal strain rate components [FeigI et al., 1990]. The
strain rates are given in Table 3. We note, however, that the
tensor components are not uniquely determined by the
triangulation measurements and are dependent on our
assumptions about the GPS data. Therefore we interpret only
the engineering strains • and •2- Strain rates across the
8umani segment computed from 1883-1885 triangulation and
1989-1993 GPS data are consistent with right-lateral shear
strain parallel to the SF. Furthermore, the shear strain rates
•! and 'i'2 are consistent, within the uncertainties, with those
estimated by McCaffrey et al. [this issue] from GPS
measurements (Table 3). Since measurements from 1927 to
1930 were not included in the estimation, strain rates for this
period (1883-1993) are probably even less sensitive to effects
of the 1926 earthquake than the 1883-1927 strain rates and
are likely to reflect the long-term interseismic strains. Since
the GPS-measured strain rates are consistent with these strain
rates, we infer that the GPS-measured strain rates are a good
indication of the long-term, interseismic deformation.
5.2.2. Northern back-are. We estimated strain rates
from the two epochs (1894-1895 and 1930) of angie
measurements taken in the northern back arc region (stations
P055, P058, P060, P062, P063 and P064; Figure 2) using
ADJCOORD, constraining the horizontal position of P062
and the azimuth and distance from P062 to P064. The error
estimates are much larger than the strain rate estimates
(Table 3), so we cannot draw any firm conclusions. However,
the results suggest that the strain rates are probably much
smaller than strain rates at the Sumani segment. A similar
level of strain (-0.01 gstrain/yr) is estimated by McCaffrey et
al. [this issue] for the central back arc (Table 3), suggesting
that the back arc region east of the SF is relatively free of
deformation. This result was also reflected in the velocity
field for the northern back arc region (Figure 4).
5.3. Estimation of Coseismic Deformation
5.3.1. The 1892 earthquake. For the 1892 earthquake a
direct estimate of the coseismic deformation from monument
displacements is available from surveyors at the scene
[MiiIler, 1895; Reid, 1913], but there exists no reliable
estimate of the event's magnitude. One of our goals in
analyzing these data was to estimate the size of the 1892
earthquake. Triangulation surveys in the region of the
Angkola segment (Figure 1) were started by Miiller in 1890.
After the 1892 Tapanuli earthquake, sites surrounding the
epicentral region were resurveyed from 1892 through 1895.
Mtiller's measurements in this area were later connected to
the rest of the Sumatra networks by only one measurement
and thus form a semi-independent data set (they were
published as such by MiiIIer [1895]). To estimate the 1892
coseismic displacements, we performed an adjustment of
Mtiller's 1890-1895 Tapanuli measurements for seven sites in
the region (Figure 6a), solving for surface coseismic
displacements. We used coordinates for these sites which
have been updated using GPS measurements (see section
4.2). Making the assumption that the GPS-measured
velocities are representative of the long-term, we fix scale
and orientation by constraining the coordinates of five
stations (all but S063 and S080) to their updated values.
Stations S063 and S080 were not included in the preliminary
network adjustment performed by S. Sutisna and were not
surveyed with GPS (attempts to locate these two sites were
unsuccessful), so we do not have good a priori coordinates
for them. Hence coordinates for S063 and S080 were given
looser constraints (0.5 m) in the adjustment.
Since all measurements included in the adjustment were
taken within a time span of 3 years (and most measurements
were taken within only 1 or 2 years), we expected the
accumulated interseismic displacements to be small
compared to the coseismic displacements. Therefore we
constrained secular velocities for all sites to be zero. Our
analysis using FONDA then yields the coseismic
displacements given in Table 4a and plotted in Figure 6a. All
reported coseismic displacements are relative to the far field.

28,356 PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT
150 km
2 meters
,
Figure 6a. Sites comprising Miiller's [1895] survey network (triangles) overlying a radar image of the
region sun'ounding the Sumarran fault equatorial bifurcation. Radar image courtesy o1' BAKOSURTANAL,
Indonesia. The 1892 Tapanuli earthquake displacements are computed from triangulation taken before and
after the earthquake (shaded arrows), with 95% confidence ellipses. Open arrows show restilts of our elastic
dislocation modeling. Heavy solid lines indicate the trace ot' the model fault plane. Model parameters are
explained in the text and in Table 5. Nurncrical values ot' the coseismic displacements are given in Table 4.
99 ø 30'E 100 ø 00'E 1000 30'E 1010 00'E
0 ø 00'
P016,:
0 ø 30's
1 ø 00'S
2 rneters
100 km
Figure 6b. The 1926 Padang Panjang earthquake displacements, computed from triangulation
measurements taken before and after the event (solid arrows). Open and gray shaded arrows show results of
our elastic dislocation modeling (see text for explanation). The first main shock in 1926 ruptured between
Alahan Panjang and Lake Singkarak, and the second ruptured between Lake Singkarak and Sipisang.

PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT
0 ø
los -
2øS
99øE 100øE 101 øE
•. .
ß
..9
••umani '11':•A•
abuh
..
0 km
102øE
Figure 6c. Coseismic displacements for the 1943 Padang earthquake computed from triangulation and GPS
measurements (solid arrows). Open arrows show results of our elastic dislocation modeling. The first main
shock ruptured between Muara Labuh and Alahan Panjang, and the second ruptured between Alahan
Panjang and Sumani.
28,357
We obtained similar restilts for the coseismic displacements
(within 0.1 m) when we constrained secular velocities for all
sites to values obtained by combining GPS and triangulation
data. Displacement at site P049 was not estimated because
0nly one epoch of measurements was taken at P049 (after the
earthquake).
We estimated a total of 4.0 + 0.6 m of coseismic
displacement across the SF (Figure 6a and Table 4a) due to
the 1892 earthquake. This estimate is significantly higher
than the 2-3 m coseismic displacement reported by Reid
[1913] based on the same surveys performed by Miiiler
[1895]. Some of this discrepancy may be due to the poor
quality of available coordinates for S063 and S080. It is also
possible that Reid [1913] underestimated the coseismic
displacements by constraining the positions of stations too
dose to the fault (P037, P051 and S063).
To assess the magnitude of the 1892 earthquake based on
our estimate of surface displacements, we solved for the
average coseismic slip on the fault by weighted least squares
inversion of the data using Okada's [1985] formulation of
elastic dislocation along a strike-slip fault. We assumed that
the 1892 earthquake ruptured the entire main fault zone of
the Angkola segment (Figure 1), which we modeled as a
vertical (90 ø dip) fault system consisting of two segments of
Table 4a. The 1892 Tapanuli Earthquake Coseismic
Horizontal Displacements
Site East Component, m North Component, m
P037 0.3 + 0.3 -0.6 _+ 0.3
P041 0.2 _+ 0.4 -0.2 + 0.5
P051 0.5 + 0.3 -0.1 + 0.4
S059 -1.5 _+ 0.4 2.4 + 0.3
$063 -0.3 _+ 0.4 -0.1 _+ 0.5
S080 0.8 + 0.3 -1.4 _+ 0.3
Quoted uncertainties represent one standard deviation.
equal downdip width, measuring 90 and 56 km along-strike
(Figure 6a). The assumed fault lengths were based on the
fault segmentation determined by Sieh and Natawidjaja [this
issue]. We treated our measurect surface coseismic
displacements as the sum of the effect of coseismic slip on
both fault segments. The east and west components of the
surface displacements were weighted by their inverse
variances in the inversion. We assumed complete rupture
along both segments from a specified fault depth to the
surface. We varied this fault depth fron• 5 to 20 km in 5-kin
increments. The modeling results are given in Table 5a, and
show that the data cannot resolve the depth of coseismic
rupture. Figure 6a compares surface displacements predicted
by the model for a 5-km rupture depth to those derived fi'om
the triangulation data.
We used the estimated coseismic slip and assumed fault
plane dimensions to estimate a moment magnitude for the
1892 earthquake using the relationship [Kanamori, 1977]:
M w = 2/3 log10 M 0 - 6.0,
where M 0 is the earthquake moment given by [Brune, 1968]
M 0 = • Alt,t. (2)
Table 4b. The 1926 Padang Panjang Earthquake
Coseismic Horizontal Displacements
Site
East Component, m North Component, m
P007 0.8 +_ 0.2 -0.4 _+ 0.4
P008 -0.2 + 0.3 0.8 _+ 0.4
P009 -0.6 _+ 0.5 0.3 _+ 0.9
P015 0.0 + 1.0 0.1 _ 0.5
P016 0.1 + 0.8 -0.2 _+ 0.7
P017 0.2 + 0.3 0.4 + 0.4
P019 0.6 + 0.8 0.9 _+ 0.7
P022 -0.1 + 0.3 0.2 _+ 0.5
Quoted uncertainties represent one standard deviation

28,358
PRAWIRODIRDJO ET AL.' TRIANGULATION AND GPS ON SUMATRAN FAULT
Table 4c. The 1943 Padang Earthquake Coseismic
Horizontal Displacements
Site East Component, m North Component, m
,,
P001 0.3 -+ 0.2 0.8 +_ 0.3
P004 0.7 ___ 0.3 •0.1 _+ 0.2
P005 -0.1 +_ 0.1 0.0 + 0.2
Quoted uncertainties represent one standard deviation.
Here •'7 is the average coseismic slip on the fault system, A is
the area of the fault plane, and g is the shear modulus (0.4 x
l0 ll Pa).
For fault depths ranging from 5 to 20 km we computed an
earthquake moment of M 0 = (3.4 + 1.0) x 1020 N m,
corresponding to moment magnitudes of M w = 7.6 to 7.7.
This estimate is consistent with the comparison of the
reported radius of ground-shaking during the 1892
earthquake [Visser, 1922] to ground-shaking during nearby
earthquakes of known magnitudes, which suggests that the
1892 event had a magnitude of M s = 7.7 or larger [D. H.
Natawidjaja, oral communication, 1999]. The quality of our
data is not sufficient to resolve the down-dip extent of the
seismogenic portion of the fault but is adequate to constrain
the moment magnitude of the 1892 earthquake to M w ~ 7.6.
5.3.2. The 1926 earthquakes. The 1926 earthquakes of
Padang Panjang impelled the Dutch colonial government to
resurvey sites around the rupture area. Triangulation taken
from P001 in 1927 [Topografische Dienst, 1927] and from
P007 in !928 [Topografische Dienst, 1929], revealed up to 5
arc sec change in angle measurements. To estimate coseismic
displacements due to the 1926 earthquake, we used
triangulation measurements from the west Sumatra network,
consisting of the measurements taken in !883-1896 and
postseismic measurements taken in 1927-1930 in the
epicentral region. To fix the orientation and scale of the
network, we constrained the positions of the triangulation
stations which were surveyed with GPS (P001, P002, P003,
P004, P005, P007, P008, P015, P016, P017, P022, P027 and
P042), making the assumption that their GPS-updated
coordinates are accurate to within half a meter. Since this
interval spans a considerable interseismic period, we
furthermore assigned secular velocities to the GPS-
resurveyed stations, based on the long-term velocities
Table 5a. Coseismic Slip on Fault Surfaces Estimated by
Weighted Least Squares Inversion of Surface
Displacements for 1892 Earthquake
Downdip Fault u l, u 2, Weighted RMS, m
Width, km m m
5 2_+8 12_+4 1.2
10 1_+6 8+_.4 1.4
15 1+_5 6-+3 1.5
20 1 +_. 5 6 -+ 3 1.6
Quoted uncertainties represent one standard deviation. Positive
values for ;7 1 (average coseismic slip on southern segment) and
• 2 (average coseismic slip on northern segment) indicate right-
lateral slip. Both fault segments are assumed to be vertical (dip =
90 ø) and of equal downdip width. Model parameters are discussed
further in the text.
Table 5b. Coseismic Slip on Fault Surfaces Estimated by
Weighted Least Squares Inversion of Surface
Displacements for 1926 Events
Downdip Fault u l, u 2, Weighted RMS, m
Width, km m m
5 7 +9 12+_7 2.4
10 9-+9 9_+6 1.9
15 9+8 8+4 1.7
20 8 -+ 8 7 _+ 4 1.5
Uncertainties are forrnal one standard deviation. Positive
values for [ I (average coseismic slip on southern segment) and
•'7 2 (average coseismic slip on northern segment) indicate right-
lateral slip. Both fault segments are assumed to be vertical (dip =
90 ø) and of equal downdip width. Model parameters are discussed
further in the text.
computed from combining the triangulation and GPS
measurements (described section 5.1). We estimated
interseismic velocities for all other sites, while solving for
coseismic displacements at eight sites located near the
rupture zone (P007, P008, P009, P015, P016, P0!7, P019 and
P022). We thus assumed that the sites remeasured using GPS
have interseismic velocities which are well represented by
the combined (GPS plus triangulation) solution.
Our best estimates of the 1926 coseismic deformation are
given in Table 4b and plotted in Figure 6b. We estimated 1.7
+ 1.0 m of fight-lateral displacement across the SF, as shown
by the motion of P007 relative to P008 (Figure 6b).
Performing this solution using half or twice the interseismic
velocities for the sites in question changes the coseismic
displacements by up to 1 m in the east component and up to
0.5 m in the north component. The displacement of P007 is
best determined because it has the largest number of
measurements. Displacements at P008 and P009 are not well
constrained because P008 and P009 were only sighted from
P(307 and other stations before the earthquake, and each have
only one angie measurement associated with them during the
second epoch. This means that in principle only one
component of the displacement at P008 and P009 can be
determined. The coseismic displacements reported in Figure
6 represent the best fit to the data, using the stated
assumptions for the positions and velocities of the GPS-
resurveyed stations.
Recent reinterpretation of Visser's [1927] detailed report
of the 1926 earthquake, together with independent fieldwork
and interviews conducted by Natawidjaja et al. [1995]
provide us with reasonable limits for the rupture lengths. The
August 4, 1926 event consisted of two main shocks of nearly
equal magnitude and appears to have ruptured adjacent fault
segments in the vicinity of Lake Singkarak and Lake
Maninjau (Figure 7B). Gutenberg and Richter [1954]
estimated magnitudes of M s = 6.75 and M s = 6.5 for the first
and second shocks, respectively. Natawidjaja et at. [1995]
constrained the rupture zone of the first shock to the 58-m
fault segment between Alahan Panjang and Lake Singkarak
and the second shock to 64 km between Lake Singkarak and
Sipisang, NW and adjacent to the first shock (Figure 6b).
Relying on Natawidjaja et aI. 's [1995] estimates of fault
rupture length, we estimated coseismic slip by weighted least
squares inversion of our estimated 1926 coseismic surface
displacements. Again we assumed that rupture occurred on a

PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT •,359
vertical fault from a specified depth to the surface, and we
varied this depth from 5 to 20 km. We performed the
inversion using surface displacements for the eight sites
listed in Table 4b weighted by their inverse variances.
Results of our inversion are presented in Table 5b, and the
deformation field predicted by the model for a fault
extending down to 15 km is plotted (open arrows) in Figure
6b. From the estimated coseismic slips we computed
earthquake moments of M 0 = (2.4 +__ 1.6) x 1020 N m for the
first shock, and M o = (2.6 _+ 1.1) x 1020 N m for the second
shock. These moments correspond to M w = 7.3-7.7 and M w =
7.4-7.7 for the first (southern) and second (northern) shocks,
respectively.
The surface coseismic displacements due to the 1926
earthquake are not well constrained by the tdata; thus we
cannot conclusively place bounds on the moment magnitudes
of the events based on the data alone. Natawidjaja et aI.
[1995] concluded from their field surveys that the surface
coseismic displacements near the fault were - 2-3 m, similar
to the 1943 event, which also consisted of two main shocks
with corrected magnitudes of M s = 7.1 and M s = 7.4
[Pacheco and Sykes, 1992]. Compared to Natawidjaja et al. 's
[1995] estimates of coseismic displacements, our estimates
of coseismic slips and moment magnitudes from the data
inversion are probably too high. Figure 6b also plots (shaded
arrows) the surface coseismic displacement• that would
result from 4 m of slip on both the northern and southern
segments (for a fault extending down to 15 km depth).
Models with 4-5 m of coseismic slip on each fault segment
result in weighted rms (wrms) misfits of 2.2-2.7 for depths
ranging from 5 to 20 km and correspond to a moment
magnitude for each main shock ranging from M w = 7.1 to M w
= 7.5, respectively. These estimates are more consistent with
Natawidjaja et al.'s [1995] field survey results and are still in
reasonable agreement with our data. In summary, our
geodetic results suggest that the 1926 main shocks were
significantly larger than previously reported (M w ~ 7 instead
of the M w ~ 6 reported by Gutenberg and Richter [1954]) and
comparable in magnitude to the 1943 events.
5.3.3. The 1943 earthquakes. The interval between the
triangulation and GPS measurements span three M w > 6
earthquakes on the SF: the' 1943 Padang JUntung et aI.,
1985], 1977 Pasaman (Harvard centroid moment tensor
(CMT) catalog), and 1987 Tarutung [Untung and Kertapati,
19871 earthquakes. We therefore began our combined
estimation by including parameters that allow coseismic
displacement at sites located near these three rupture zones.
However, the 1977 and 1987 events were not resolvable by
our data. Coseismic displacements at P001, P004, and P005
due to the 1943 earthquakes were estimated by constraining
the interseismic velocities at those sites to their GPS-
determined values. The consistency of this solution is
checked by applying the coseismic displacement at those
three stations as coseismic corrections in a solution where
long-term interseismic velocities for all sites are estimated, as
well as small adjustments to the coseismic displacements.
Figure 6c summarizes our estimated coseismic
displacements at the three sites due to the 1943 earthquake.
The deformation is. statistically significant only at P001,
where we estimate 0.9 + 0.3 m of displacement (Figure 6c
and Table 4c). Natawidjaja et al. [1995] reported that the two
main shocks (June 8 and 9) of the 1943 event ruptured two
adjacent fault segments from south to norih, similar to the
1926 event, and estimated rupture lengths of 54 km for the
northern event and 46 km for the southern event.
Our estimate of the 1943 coseismic deformation suggests
some left-lateral motion at P004 and some fault-normal
motion at P001 and P004 (Figure 6c). Untung et al. [1985]
reported that the coseismic displacements during the 1943
earthquake included significant vertical "scissoring" motion
in this area, supporting the notion that faulting in 1943
included a significant dip-slip or thrust component.
The uncertainties of our surface coseismic displacements
were too large to allow inversion to estimate fault slip.
Therefore, to describe the estimated coseismic deformation
field in terms of s•ismic slip on the fault zone, we
implemented Okada's [1985] formulation of elastic
dislocation in a forward model. We used the rupture fault
lengths estimated by Narawidjaja et al. [1995], assumed
(arbitrarily) that the fault surfaces dip 60 ø to the NE, and set
the fault depth for both segments at 20 km. Varying the
amount of strike slip and thrust slip, we found that 3 m of
left-lateral strike-slip and 0.5 m of thrust slip on the southern
segment, and 2.3 m of right-lateral strike slip and 1.7 m of
thrust slip on the northern segment yield a reasonable fit to
the data. The surface displacements predicted by this 60 ø-
dipping fault model are plotted in Figure 6c. However, none
of the fault parameters are uniquely constrained by our data.
6. Conclusions
By combining triangulation with GPS data we obtained
long-term, near-field velocities along the northern half of the
SF. This combined velocity field is consistent with slip rates
ranging from - 23 to --- 24 mm/yr, as inferred from the
regional GPS data for the region between 1 øS and 2øN, and
are within 5 mm/yr of estimates based on earthquake slip
vector deflections [McCaffrey et al., this issue]. These rates
are fairly consistent with geological estimates by Sieh and
Natawidjaja [this issue] in the north but are up to twice as
high as their slip rate estimates in the south. The long-term
velocity field is also consistent with locking depths on the
order of 20 km on the SF. These deep locking depths are
consistent with historically high seismicity rates along the SF
in the vicinity of the Sumani, Sianok, and Angkola segments
and point to continued significant seismic potential in those
regions.
Strain rates in the northern back arc are low, suggesting
that the northern back arc is relatively free of deformation.
Strain rates for the Sumani region for the period 1883-1930
are similar to the long term (~ 100 year) rates, as well as the
short-term, GPS-measured rates.
From epochs of triangulation data collected before and
after the 1892 and 1926 earthquakes we estimated coseismic
displacements and moment magnitudes. Our results indicate
that these events were larger than previously reported. The
1892 earthquake had a moment magnitude of M w • 7.6, and
the 1926 main shocks were probably of the order of M w - 7,
comparable in size to the 1943 main shocks, instead of M w .•
6 as previously reported. We also estimated coseismic
displacements for the 1943 earthquake from the combined
triangulation and GPS solution, but the fault parameters for
this event are poorly constrained by the data.
Acknowledgments. We are indebted to the late Paul Suharto,
deputy and later director of the National Coordination Agency for
Surveying and Mapping (BAKOSuRTANAL), who passed away in

28,360
PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT
1999, for his encouragement and support of our work in Indonesia.
Site monumentation and data collection for this study could only
have been accomplished with the help of many Indonesian, U.S.,
and Japanese surveyors. In particular, we would like to mention
Agus Soedomo, Chris Bagandi, Hem Derajat, Djawahir, Endang,
Nyamadi, Ponimin, Rustandi Poewariardi, Untung Santoso,
Barnbang Susilo, Widiyanto, and Didi Wikayardi from Indonesia
and Eric Calais, Heather Chamberlain, Dan Johnson, Dalia Lahav,
Rob McCaffrey, Brennan O'Neill, Craig Roberts, Jennifer Scott,
Bruce Stephens, Briann Wolf, and Peter Zwick from U.S.-based
institutions. The 1989 survey was conducted as a joint effort in
conjunction with a research project by Ichiro Murata from Tokyo
University. We thank him and the team of Japanese scientists,
including Eiji Kawai, Fumiaki Kimata, Satoshi Miura, Shuhei
Okubo, and Mikio Satomura, for the excellent collaboration. We are
grateful to James Stowell and his staff at the UNAVCO Boulder
facility (Bruce Stephens and Mike Jackson) for training and
providing field engineers. Joe Bearden at Caltex provided logistical
support and GPS receivers for surveys in the Rumbai area, and some
welcome R&R at the Caltex facility in Rumbai. From the earliest
stages of this project, we are indebted to Ruth Neilan 'for
consolidating the triangulation data, made available to us through
BAKOSURTANAL. Klass Villanueva and Joenil Kahar from ITB
helped with logistical and other support. We thank Eric Calais, Paul
Tregoning, and Shimon Wdowinski for their input to the data
analysis. Australian tracking data were organized and provided by
Ken Alexander, Fritz Brunner, Martin Hendy, John Manning, and
Paul Tregoning. Miranda Chin and Gerry Mader helped collect
regional tracking data during the 1989 Asia-Pacific Experiment
(APEX) coordinated with Mike Bevis, and provided CIGNET data.
Our IGS colleagues provided global tracking data since 1992. We
thank Kerry Sieh and Danny Natawidjaja for useful discussions on
many geological aspects of the Sumatran fault, and Rob McCaffrey
and Shimon Wdowinski for their constructive comments on this
paper. John Beavan computed strain rates using ADJCOORD for us.
Comments from Jeff Freymuel!er, Thora Xrnad6ttir, and one
anonymous reviewer helped to improve the manuscript. Figures
were drawn with GMT [Wessel and Smith, 1991]. Supported at SIO
by NSF grants EAR-8817067 and EAR-9004376, NASA grant
NAGW-2641, and by the Indonesian government.
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(Received May 17, 1999; revised April 14, 2000;
accepted April 19, 2000.)