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Fractal geometry of the sumatra active fault system and its geodynamical implications
J. Geodynamics
Pergamon PII: SO264-3707(%)00015-4
Vol. 22. No. 112, pp. 1-9. 1996 Copyright 0 1996 Elsevier ScienceLtd Printedin Great Britain. All tights reserved 0264-3707196 $15.00+0.00
FRACTAL GEOMETRY OF THE SUMATRA ACTIVE FAULT SYSTEM AND ITS GEODYNAMICAL IMPLICATIONS SIGIT SUKMONO,‘*+ M. T. ZEN,’ W. G. A. KADIR,’ L. HENDRAJAYA,’ D. SANTOSO’ and J. DUBOIS2 ’ Teknik Geofisika-Institut Teknologi Bandung, Jl .Ganesha 10 Bandung 40132, Indonesia * Inst. de Physique du Globe de Paris, 4 place Jussieu, B89,75252 Paris Cedex, France (Received 30 November 199.5; accepted in revisedform
9 March 19%)
Abstract-The Sumatra active fault system is a 1650 km long northwest trending dextral active strikeslip fault which accommodates the oblique convergence between the Indo-Australian and the Eurasian plates. It consists of 11 fault segments connected northward to the Andaman extensional back arc basin and southward to the extensional fault zone of the Sunda Strait. The geometries of the 11 segments are quantified using a fractal approach and it is found that their fractal dimensions (D) range from 1.00+0.03 to 1.24~0.03. Larger D values are associated with more irregular fault geometry. There are six discontinuities, reflected by sharp changes of fractal dimensions, observed along the segments. The locations of the discontinuities correspond to sites of major structural breaks in Sumatra mainland and its fore arc and back arc. The discontinuities and variations of D values suggest that the Sumatra mainland is not rigid. Instead it appears to be segmented into several blocks which may correlate to the segmentation in the Sumatra fore arc. This segmentation may explain the large discrepancy among the displacements and velocities of the Andaman Sea opening, the Sumatra fault motion and the Sunda Strait opening. This research also demonstrates the applicability of the fractal approach for analyzing the variations of fault geometry due to geodynamic processes. Copyright 0 1996 Elsevier Science Ltd
INTRODUCTION The Sumatra fault system (SFS) is a 1650 km long northwest trending dextral spike-slip fault zone which cut the entire length of Sumatra-Indonesia. The SFS accommodates the oblique convergence between the Indo-Australian and Eurasian Plates and is widely known as one of the greatest active faults in the world (Fig. 1). It extends in a succession of en echelon segments and is connected northward to the Andaman extensional back arc basin and southward to the extensional fault zone of the Sunda Strait. There is a correlation in time between the Sunda Strait and the Andaman Sea opening during the Pliocene (Lassal et al., 1989). However, the total displacement measured within the Andaman Sea is 460 km (Curray et al., 1979) and cannot be * Author to whom correspondence should be addressed. ’ Tel. 62-22-2509167; Fax: 62-22-2509169; e-mail: [email protected] 1
S. S&mono
2
et al.
explained entirely by the displacement along the SFS, estimated to be about 180 km north of Sumatra (Page er al, 1979), and even less, namely 50-70 km extensional motion in the Sundra Strait (Lassal et al., 1989). Furthermore, recent studies along the southern end of the SFS estimate its northwestward velocity at 6 mm/yr (Bellier et al., 199 1) which is much smaller than the 40 mm/yr opening rate of the Andaman Sea (Cut-ray et al., 1979). The area located between the SFS and the Sumatra trench is part of the Burma plate (Curray et al., 1979) and has also been called the Sumatra fore arc sliver (Jarrard, 1986). The northward motion of the sliver would
I
1.4 F _ _
100 E
105'E
5F I’
___
1
0
/. A D=l.OI-1.02
n
I ”
Indo-Australia 1 ’
X21M.03
\RI
1914
I=
I
4
Fig. 1. Sumatra active fault segments, their fractal dimensions (D), discontinuities in D (I&..) and extent of subduction-related great earthquake ruptures (M>7.5) that occurred in the last two centuries (earthquake ruptures adopted from Newcomb and McCann, 1987). MFZ=Mentawai fault zone.
Fractal geometry of the Sumatra active fault system
3
explain the opening of the Sundra Strait (Huchon and Le Pichon, 1984) and an extension parallel to the SFS. This extension is also accompanied by a rotation of blocks and suggests an internal deformation of the fore arc sliver plate which can explain the discrepancy between the Andaman Sea and the Sunda Strait openings (Diament et al., 1992). It has been noted that knowledge of fault system geometry is a primary requisite to a better understanding of the mechanics of faulting. Ring (1983) shows that earthquake faulting and brittle deformation of the lithosphere in general, fracture toughness, critical stress intensity and the Griffith fracture energy are not material properties but properties of fault system geometry. Sholz (1990) observed that faults are not perfectly planar on any scale and the effects of fault geometrical irregularity on faulting mechanics are extreme. If geometrical irregularity is an important parameter, then it is useful to be able to quantify the degree of fault irregularity. Because of their rough appearance over many length scales, the faults’ geometrical irregularity can be quantified by the fractal dimension D. The D values then can be related to other parameters of faulting mechanics such as stress condition, degree of faulting and fracturing energy density (Velde er al., 1990; Nagahama and Yoshii, 1994). This paper presents some results of a treatment of Sumatra active fault geometry as a fractal set. Following a discussion on the geometry of the Sumatra “active” faults, the D values of 11 Sumatra fault segments are presented and discussed in relation to its geodynamical implications.
DATA AND RESULTS The definition
of a fractal distribution
is given by N,=CI$
(1)
where Ni is the number of objects with a linear dimension ri, D is the similarity dimension (also known as the fractal dimension), and C is a constant of proportionality (Mandlebrot, 1982). For the determination of Sumatra fault segments D values, we have constructed 1 : 250,000 maps showing traces of Sumatra active faults (e.g. Sumatra faults which were active throughout the Quatemary). SAR images (scale 1 : 50,000, 1 : 250,000) and aerial photographs (1 : 50,000) are used to examine surface features like fault scarps, sag ponds, stream offsets and fault ridges to infer the active fault geometry. By making inferences on the complexity of the geometry of mapped faults and its relation to fault mechanics, the study relies on the degree to which the surface expressions of faulting reflect deeper fault traces. Actually, it is possible that the mapped fault pattern is strictly an effect of the properties of materials which constitute the uppermost crust, and that the faults appear as smoother surfaces at depth. Seismicity studies, however, suggest that complex fault structures do indeed extend to depths of the order of 12 or 15 km (Eaton et al., 1970). Earthquake fault plane solution studies by Zwick and McCaffrey (1991) and aftershock observation of the February 1994 Liwa earthquake that occurred on the Ranau segment by Harjono er al. (1994), confirm that the strike-slip earthquakes on the Sumatra Fault System do extend to a depth of 15 km. We therefore use 15 km as an upper cutoff length, whereas with the active fault map drawn to a scale of 1 : 250,000, 1.0 km is used as the lower cuttoff length. With the upper cutoff of 15 km, we define that the extent of the active fault traces lie within a 30 km wide band centered about the primary fault traces (Fig. l), and only faults lying within this band are included in the D value determination. Identificatoin of segments of the Sumatra active fault are mainly based on their geometric character. Examples of geometric character
4
S. Sukmono et al.
include fault intersections (branch faults or cross faults), fault zone features (en echelon segments, separation, attitude change) and fault terminations. Eventually 11 segments can be distinguished (Fig. 1) and their D values are determined according to the method discussed by Okubo and Aki (1987). Circles of a chosen radius r are drawn in order to cover the fault traces using a minimum number N(r) for such circles. The fault length estimates L”(r) can be obtained by multiplyting N(r) with the diameter of a single circle L”(r)=2N(r)
r
(2)
Lengths L”(r) are plotted as a function of the measured radius r on log-log axes, and the fractal dimension D can be estimated from the slope b of the best straight-line fit to the data as D=l-b
(3)
D is thus a measure of the rate of change of log(fault length) with respect to log(measurement resolution). With a range of measuring radii from the upper cutoff of 15 km to the lower cutoff of 1.O km, the fault length is measured as a function of measuring radius in the same manner as described earlier. Logs of fault length and measuring resolution are plotted in Fig. 2. Fractal dimensions of the segments are estimated from the slopes of straight-line least square fits to these data and range from 1.00+0.03 to 1.24+0.03.
DISCUSSION The geometrical
irregularity differences of 11 Sumatra active fault segments are reflected by the variations in their D values which range from 1.00+0.03 to 1.2420.03. Larger values of D are associated with more complicated fault geometry. Comparison between the defined segments and a map of complete Bouguer anomaly (Fig. 3) shows a good agreement: each segment has a characteristic anomaly pattern which is different to the adjacent segments and separated by strong discontinuities. It is observed also that there are six discontinuities along the segments in which the fractal dimension values sharply change from one segment to its adjacent segments. The locations of these discontinuities coincide with the sites of sharp changes in gravity anomaly and formation density valueswith the boundaries of major basins in the Sumatra fore arc and back arc, and sites of major structural breaks on Sumatra (Fig. 4). The discontinuities I and II roughly correspond to the locations of major changes along the Mentawai fault zone (MFZ) and in the strike of the trench. The discontinuity II corresponds also to the location of a major tectonic boundary between the northern and southern part of the Sumatra fore arc, and the location of Sumatra’s volcanic line offset which is suggested to be the effect of a split in the descending oceanic plate along the continuation of the Investigator Ridge transform fault (Page et al., 1979). The discontinuities II to VI coincide also with the boundaries of the 1833, 1861, 1907 and 1914 subduction-related great earthquake ruptures (M>7.5) that occurred in the last two centuries (Fig. 1). The moment magnitudes M, of the 1833 and 1861 events were estimated to be 8.7-8.8 and 8.3-8.5, respectively, and the events can be included in the world’s largest earthquakes (Newcomb and McCann, 1987). Therefore it seems obvious that the discontinuities II, III and VI, which have acted as dominant barriers of the 1833 and 1861 ruptures, are major structural breaks in Sumatra possibly corresponding to deeper important structures. These three major discontinuities coincide also with major changes in the density distribution at 5 km depth throughout Sumatra obtained by Kadir et al. (1995) and boundaries of Sumatra fore arc and back arc basins (Fig. 4). Natawidjaja and Sieh (1994) have also suggested the existence of these three
5
Fractal geometry of the Sumatra active fault system
1.60
0.00
1 .oo
0.50
1.50
kg L=2.49-0.06bfj r
0.00
0.50
elr
ii1 0.00
1.50
1.00
1.50
hlr
_yr
(
1 .oo
0.50
1.00
1.50
0.00
0.50
loOr
2.60
2.60 2.40 1 jj
2.20
log1.~1.69-0.01 k&l
I
i
ad =+0.02
logL=1.99-9.01~r
2.00
2.00 i
,
1.60
1.80 JV 0.00
2.40 2.20
0.50
1.00
1.50
0.00
0.50
2.60 2.40
0.50
1.50
loOr
@Jr
0.00
1.00
1.00
1.50
1 log
L=2.264.21log
_
0.00
r
sd =+0.02
0.50
1.00
Fig. 2. Plots of log(L) over log(r) of 11 Sumatra active fault segments (sd=standard dimension). L-length of fault, r-radius.
1.50
deviation of fractal
S. Sukmono et al.
6
major discontinuities from observations of the dramatic increases of the fault slip rates along them. Previous studies have shown that the variation in the fracture geometry fractal dimension can be related to the variation of material properties (strength, uniformity coefficient, age and density), stress intensity and stress direction. Further investigations are required to determine precisely what causes the variations of fractal dimensions in Sumatra’s fault segments. The preliminary conclusion that can be drawn here is that the D value variations of Sumatra fault segments and the discontinuities between regions of different D values suggest that the Sumatra
E
100 E I
-. \
-.. . .
105 E
Fig. 3. Relationships of discontinuities in D, Bouguer gravity anomaly (solid contours, in mgal) and bathymetry (dashed contours, in km).
7
Fractal geometry of the Sumatraactive fault system
mainland is not rigid. Instead it appears to be segmented into several blocks in which each block is separated from adjacent blocks by structural discontinuities. The discontinuities may be directed in a northeast to southwest direction as reflected by the gravity anomaly pattern (Fig. 3). McCaffrey (1991) noted that the nodal planes of strike-slip earthquakes, which reflect the deformation in the Sumatra fore arc, also strike in this direction. The similarities of discontinuities and earthquake nodal plane directions, and the coincidence of discontinuity locations with sites of major structural breaks in the Sumatra fore arc, suggest that the
I
I
I
15 E
105 E
100 E z
-500
5E
1OOE I
\
km
105 E
I
Fig. 4. Relationships of discontinuities in D, density (p) distribution of Sumatra at 5 km depth and boundaries of major basins in Sumatra fore arc and back arc (density distribution map adopted from Kadir et al., 1995).
8
S. Sukmono et al.
segmentation and discontinuities in Sumatra mainland, as observed in this study, may well be correlated with the segmentation and internal deformation in the Sumatra fore arc. This segmentation may explain the large discrepancy between the displacements and velocities of the Andaman Sea opening, the Sumatra fault motion and the Sunda Strait opening. The study shows also that the fractal approach can be a powerful tool for analyzing the variations of fault geometry due to geodynamic processes. AcknowledgemenrsSupported by the National Research Council “Riset Unggullan Terpadu II” project under PDNMPBakosurtanal Contract No. 20. IO/PDNMD/IV/1994. We thank BAKOSURTANAL for providing us with raw gravity data, F. Hehuwat and D. H. Natawidjaja for their help, and Professor W. Jacoby and two reviewers for their valuable comments.
REFERENCES Bellier O., Sebrier M. and Pramumijoyo S. (1991) La grande faile de Sumatra: Geometrie, cinematique et quantite de deplacement mises en evidence par l’imagerie satellitaire. Academic des Sciences-Paris 312, 12 19- 1226. Curray J. R., Moore D. G., Lawyer L. A., Emmel F. J., Raitt R. W., Henry M. and Kieckhefer R. M. (1979) Tectonics in the Andaman Sea and Burma. In Geological and Geophysical Investigations of Continental Margins (Watkins, J. S., Montadert L. and Dickerson P. W., eds). American Association of Petroleum Geologists Memoir, Vol. 29, pp. 189-198. Diament M., Hatjono H., Karto K., Deplus C., Dahrin D., Zen M. T., Gerard M., Lassal O., Martin A. and Malod J. (1992) Mentawai fault zone off Sumatra: A new key to the geodynamics of western Indonesia. Geology 20,259-262. Eaton J. P., O’Neill M. E. and Murdock J. N. (1970) After shocks of the 1966 Parkfield-Cholame earthquake: A detailed study. Bull. Seismol. Sot. Am. 60, 115 l-l 197. Harjono H., Widiwijayanti Ch., Handayani L., Deverchere J., Sebrier M., Diament M., Suwijanto, Surono, Pramumijoyo S., Gunawan H. and Lumbanbatu U. (1994) The 1994 Liwa earthquake: a preliminary result of aftershocks observation. In Prosiding Tridawawarsa Puslitbang Geoteknologi-LIP1 v.2 (Hantoro W. S., Wirdsantosa S., Utomo E. I?, Soebowo E., Kumoro Y. and Riyanto A. M., eds). Geoteknologi-LIP1 Indonesia, pp.I1162-11168. . Huchon P. and Le Pichon X. (1984) Sunda Strait and Central Sumatra fault. Geology 14, 780-783. Jarrard R. D. (1986) Relation among subduction parameters. Rev. Geophys. Space Phys. 24, 127-284. Kadir, W. G. A., Zen M. T., Hendrajaya L. and Santoso D. (1995) Depth estimation of gravity anomalies by using deconvolution filter. Proc. of XX Indonesian Association of Geophysicist Annual Convention, 48. King G. (1983) The accommodation of large strains in the upper lithosphere of the earth and other solids by self-similar fault system: the geometrical origin of b-value. Pageoph 121, 761-815. Lassal O., Huchon P. and Harjono H. (1989) Extension crustale dans le detroit de la Sonde (Indonesie). Donnes de la sismique relextion (campagne Krakatoa). Academic des Sciences, Compte Rendus 309,881-884. Mandlebrot B. B. (1982) Fractals Geometry of Nature. W. H. Freeman, San Francisco. McCaffrey R. (1991) Slip vectors and stretching of the Sumatra fore arc. Geology 19, 881-884. Nagahama H. and Yoshii K. (1994) Scaling laws in fragmentation. In Fractals and Dynamic System in Geosciences (Kruhl, J. H., ed.). Springer Verlag, Berlin, pp. 25-36. Natawidjaja D. H. and Sieh K. E. (1994) Neotektonik sistem sesar Sumatra. In Prosiding Hasil Penelitian Puslitbang Geoteknologi LIPI, Geoteknologi LIP1 Indonesia, pp. 145-161.
Fractal geometry of the Sumatra active fault system
9
Newcomb K. R. and McCann W. R. (1987) Seismic history and seismotectonics of the Sunda arc. J. Geophy. Rex 92,421439. Okubo, P G. and Ati K. (1987) Fractal geometry in the San Andreas Fault System. J. Geophy. Res. 92,345-355. Page B. G. N., Bennett J. D., Cameron N. R., Bride D. McC., Jeffrey D. H., Keats W. and Thaib J. (1979) A review of the main structural and magmatic features of northern Sumatra. Geological Sot. Land, J. 136,569-579. Scholz C. (1990) The Mechanics of Earthquakes and Faulting. Cambridge University Press, Cambridge. Velde B., Dubois J., Touchard G. and Badri A. (1990) Fractal analysis of fractures in rocks: the Cantor’s Dust method. Tectonophysics 179,345-352. Zwick P. and McCaffrey R. (1991) Seismic slip rate and direction of the Great Sumatra fault based on earthquake fault plane solutions. EOS trans. AGU 72,20 1.
Pergamon PII: SO264-3707(%)00015-4
Vol. 22. No. 112, pp. 1-9. 1996 Copyright 0 1996 Elsevier ScienceLtd Printedin Great Britain. All tights reserved 0264-3707196 $15.00+0.00
FRACTAL GEOMETRY OF THE SUMATRA ACTIVE FAULT SYSTEM AND ITS GEODYNAMICAL IMPLICATIONS SIGIT SUKMONO,‘*+ M. T. ZEN,’ W. G. A. KADIR,’ L. HENDRAJAYA,’ D. SANTOSO’ and J. DUBOIS2 ’ Teknik Geofisika-Institut Teknologi Bandung, Jl .Ganesha 10 Bandung 40132, Indonesia * Inst. de Physique du Globe de Paris, 4 place Jussieu, B89,75252 Paris Cedex, France (Received 30 November 199.5; accepted in revisedform
9 March 19%)
Abstract-The Sumatra active fault system is a 1650 km long northwest trending dextral active strikeslip fault which accommodates the oblique convergence between the Indo-Australian and the Eurasian plates. It consists of 11 fault segments connected northward to the Andaman extensional back arc basin and southward to the extensional fault zone of the Sunda Strait. The geometries of the 11 segments are quantified using a fractal approach and it is found that their fractal dimensions (D) range from 1.00+0.03 to 1.24~0.03. Larger D values are associated with more irregular fault geometry. There are six discontinuities, reflected by sharp changes of fractal dimensions, observed along the segments. The locations of the discontinuities correspond to sites of major structural breaks in Sumatra mainland and its fore arc and back arc. The discontinuities and variations of D values suggest that the Sumatra mainland is not rigid. Instead it appears to be segmented into several blocks which may correlate to the segmentation in the Sumatra fore arc. This segmentation may explain the large discrepancy among the displacements and velocities of the Andaman Sea opening, the Sumatra fault motion and the Sunda Strait opening. This research also demonstrates the applicability of the fractal approach for analyzing the variations of fault geometry due to geodynamic processes. Copyright 0 1996 Elsevier Science Ltd
INTRODUCTION The Sumatra fault system (SFS) is a 1650 km long northwest trending dextral spike-slip fault zone which cut the entire length of Sumatra-Indonesia. The SFS accommodates the oblique convergence between the Indo-Australian and Eurasian Plates and is widely known as one of the greatest active faults in the world (Fig. 1). It extends in a succession of en echelon segments and is connected northward to the Andaman extensional back arc basin and southward to the extensional fault zone of the Sunda Strait. There is a correlation in time between the Sunda Strait and the Andaman Sea opening during the Pliocene (Lassal et al., 1989). However, the total displacement measured within the Andaman Sea is 460 km (Curray et al., 1979) and cannot be * Author to whom correspondence should be addressed. ’ Tel. 62-22-2509167; Fax: 62-22-2509169; e-mail: [email protected] 1
S. S&mono
2
et al.
explained entirely by the displacement along the SFS, estimated to be about 180 km north of Sumatra (Page er al, 1979), and even less, namely 50-70 km extensional motion in the Sundra Strait (Lassal et al., 1989). Furthermore, recent studies along the southern end of the SFS estimate its northwestward velocity at 6 mm/yr (Bellier et al., 199 1) which is much smaller than the 40 mm/yr opening rate of the Andaman Sea (Cut-ray et al., 1979). The area located between the SFS and the Sumatra trench is part of the Burma plate (Curray et al., 1979) and has also been called the Sumatra fore arc sliver (Jarrard, 1986). The northward motion of the sliver would
I
1.4 F _ _
100 E
105'E
5F I’
___
1
0
/. A D=l.OI-1.02
n
I ”
Indo-Australia 1 ’
X21M.03
\RI
1914
I=
I
4
Fig. 1. Sumatra active fault segments, their fractal dimensions (D), discontinuities in D (I&..) and extent of subduction-related great earthquake ruptures (M>7.5) that occurred in the last two centuries (earthquake ruptures adopted from Newcomb and McCann, 1987). MFZ=Mentawai fault zone.
Fractal geometry of the Sumatra active fault system
3
explain the opening of the Sundra Strait (Huchon and Le Pichon, 1984) and an extension parallel to the SFS. This extension is also accompanied by a rotation of blocks and suggests an internal deformation of the fore arc sliver plate which can explain the discrepancy between the Andaman Sea and the Sunda Strait openings (Diament et al., 1992). It has been noted that knowledge of fault system geometry is a primary requisite to a better understanding of the mechanics of faulting. Ring (1983) shows that earthquake faulting and brittle deformation of the lithosphere in general, fracture toughness, critical stress intensity and the Griffith fracture energy are not material properties but properties of fault system geometry. Sholz (1990) observed that faults are not perfectly planar on any scale and the effects of fault geometrical irregularity on faulting mechanics are extreme. If geometrical irregularity is an important parameter, then it is useful to be able to quantify the degree of fault irregularity. Because of their rough appearance over many length scales, the faults’ geometrical irregularity can be quantified by the fractal dimension D. The D values then can be related to other parameters of faulting mechanics such as stress condition, degree of faulting and fracturing energy density (Velde er al., 1990; Nagahama and Yoshii, 1994). This paper presents some results of a treatment of Sumatra active fault geometry as a fractal set. Following a discussion on the geometry of the Sumatra “active” faults, the D values of 11 Sumatra fault segments are presented and discussed in relation to its geodynamical implications.
DATA AND RESULTS The definition
of a fractal distribution
is given by N,=CI$
(1)
where Ni is the number of objects with a linear dimension ri, D is the similarity dimension (also known as the fractal dimension), and C is a constant of proportionality (Mandlebrot, 1982). For the determination of Sumatra fault segments D values, we have constructed 1 : 250,000 maps showing traces of Sumatra active faults (e.g. Sumatra faults which were active throughout the Quatemary). SAR images (scale 1 : 50,000, 1 : 250,000) and aerial photographs (1 : 50,000) are used to examine surface features like fault scarps, sag ponds, stream offsets and fault ridges to infer the active fault geometry. By making inferences on the complexity of the geometry of mapped faults and its relation to fault mechanics, the study relies on the degree to which the surface expressions of faulting reflect deeper fault traces. Actually, it is possible that the mapped fault pattern is strictly an effect of the properties of materials which constitute the uppermost crust, and that the faults appear as smoother surfaces at depth. Seismicity studies, however, suggest that complex fault structures do indeed extend to depths of the order of 12 or 15 km (Eaton et al., 1970). Earthquake fault plane solution studies by Zwick and McCaffrey (1991) and aftershock observation of the February 1994 Liwa earthquake that occurred on the Ranau segment by Harjono er al. (1994), confirm that the strike-slip earthquakes on the Sumatra Fault System do extend to a depth of 15 km. We therefore use 15 km as an upper cutoff length, whereas with the active fault map drawn to a scale of 1 : 250,000, 1.0 km is used as the lower cuttoff length. With the upper cutoff of 15 km, we define that the extent of the active fault traces lie within a 30 km wide band centered about the primary fault traces (Fig. l), and only faults lying within this band are included in the D value determination. Identificatoin of segments of the Sumatra active fault are mainly based on their geometric character. Examples of geometric character
4
S. Sukmono et al.
include fault intersections (branch faults or cross faults), fault zone features (en echelon segments, separation, attitude change) and fault terminations. Eventually 11 segments can be distinguished (Fig. 1) and their D values are determined according to the method discussed by Okubo and Aki (1987). Circles of a chosen radius r are drawn in order to cover the fault traces using a minimum number N(r) for such circles. The fault length estimates L”(r) can be obtained by multiplyting N(r) with the diameter of a single circle L”(r)=2N(r)
r
(2)
Lengths L”(r) are plotted as a function of the measured radius r on log-log axes, and the fractal dimension D can be estimated from the slope b of the best straight-line fit to the data as D=l-b
(3)
D is thus a measure of the rate of change of log(fault length) with respect to log(measurement resolution). With a range of measuring radii from the upper cutoff of 15 km to the lower cutoff of 1.O km, the fault length is measured as a function of measuring radius in the same manner as described earlier. Logs of fault length and measuring resolution are plotted in Fig. 2. Fractal dimensions of the segments are estimated from the slopes of straight-line least square fits to these data and range from 1.00+0.03 to 1.24+0.03.
DISCUSSION The geometrical
irregularity differences of 11 Sumatra active fault segments are reflected by the variations in their D values which range from 1.00+0.03 to 1.2420.03. Larger values of D are associated with more complicated fault geometry. Comparison between the defined segments and a map of complete Bouguer anomaly (Fig. 3) shows a good agreement: each segment has a characteristic anomaly pattern which is different to the adjacent segments and separated by strong discontinuities. It is observed also that there are six discontinuities along the segments in which the fractal dimension values sharply change from one segment to its adjacent segments. The locations of these discontinuities coincide with the sites of sharp changes in gravity anomaly and formation density valueswith the boundaries of major basins in the Sumatra fore arc and back arc, and sites of major structural breaks on Sumatra (Fig. 4). The discontinuities I and II roughly correspond to the locations of major changes along the Mentawai fault zone (MFZ) and in the strike of the trench. The discontinuity II corresponds also to the location of a major tectonic boundary between the northern and southern part of the Sumatra fore arc, and the location of Sumatra’s volcanic line offset which is suggested to be the effect of a split in the descending oceanic plate along the continuation of the Investigator Ridge transform fault (Page et al., 1979). The discontinuities II to VI coincide also with the boundaries of the 1833, 1861, 1907 and 1914 subduction-related great earthquake ruptures (M>7.5) that occurred in the last two centuries (Fig. 1). The moment magnitudes M, of the 1833 and 1861 events were estimated to be 8.7-8.8 and 8.3-8.5, respectively, and the events can be included in the world’s largest earthquakes (Newcomb and McCann, 1987). Therefore it seems obvious that the discontinuities II, III and VI, which have acted as dominant barriers of the 1833 and 1861 ruptures, are major structural breaks in Sumatra possibly corresponding to deeper important structures. These three major discontinuities coincide also with major changes in the density distribution at 5 km depth throughout Sumatra obtained by Kadir et al. (1995) and boundaries of Sumatra fore arc and back arc basins (Fig. 4). Natawidjaja and Sieh (1994) have also suggested the existence of these three
5
Fractal geometry of the Sumatra active fault system
1.60
0.00
1 .oo
0.50
1.50
kg L=2.49-0.06bfj r
0.00
0.50
elr
ii1 0.00
1.50
1.00
1.50
hlr
_yr
(
1 .oo
0.50
1.00
1.50
0.00
0.50
loOr
2.60
2.60 2.40 1 jj
2.20
log1.~1.69-0.01 k&l
I
i
ad =+0.02
logL=1.99-9.01~r
2.00
2.00 i
,
1.60
1.80 JV 0.00
2.40 2.20
0.50
1.00
1.50
0.00
0.50
2.60 2.40
0.50
1.50
loOr
@Jr
0.00
1.00
1.00
1.50
1 log
L=2.264.21log
_
0.00
r
sd =+0.02
0.50
1.00
Fig. 2. Plots of log(L) over log(r) of 11 Sumatra active fault segments (sd=standard dimension). L-length of fault, r-radius.
1.50
deviation of fractal
S. Sukmono et al.
6
major discontinuities from observations of the dramatic increases of the fault slip rates along them. Previous studies have shown that the variation in the fracture geometry fractal dimension can be related to the variation of material properties (strength, uniformity coefficient, age and density), stress intensity and stress direction. Further investigations are required to determine precisely what causes the variations of fractal dimensions in Sumatra’s fault segments. The preliminary conclusion that can be drawn here is that the D value variations of Sumatra fault segments and the discontinuities between regions of different D values suggest that the Sumatra
E
100 E I
-. \
-.. . .
105 E
Fig. 3. Relationships of discontinuities in D, Bouguer gravity anomaly (solid contours, in mgal) and bathymetry (dashed contours, in km).
7
Fractal geometry of the Sumatraactive fault system
mainland is not rigid. Instead it appears to be segmented into several blocks in which each block is separated from adjacent blocks by structural discontinuities. The discontinuities may be directed in a northeast to southwest direction as reflected by the gravity anomaly pattern (Fig. 3). McCaffrey (1991) noted that the nodal planes of strike-slip earthquakes, which reflect the deformation in the Sumatra fore arc, also strike in this direction. The similarities of discontinuities and earthquake nodal plane directions, and the coincidence of discontinuity locations with sites of major structural breaks in the Sumatra fore arc, suggest that the
I
I
I
15 E
105 E
100 E z
-500
5E
1OOE I
\
km
105 E
I
Fig. 4. Relationships of discontinuities in D, density (p) distribution of Sumatra at 5 km depth and boundaries of major basins in Sumatra fore arc and back arc (density distribution map adopted from Kadir et al., 1995).
8
S. Sukmono et al.
segmentation and discontinuities in Sumatra mainland, as observed in this study, may well be correlated with the segmentation and internal deformation in the Sumatra fore arc. This segmentation may explain the large discrepancy between the displacements and velocities of the Andaman Sea opening, the Sumatra fault motion and the Sunda Strait opening. The study shows also that the fractal approach can be a powerful tool for analyzing the variations of fault geometry due to geodynamic processes. AcknowledgemenrsSupported by the National Research Council “Riset Unggullan Terpadu II” project under PDNMPBakosurtanal Contract No. 20. IO/PDNMD/IV/1994. We thank BAKOSURTANAL for providing us with raw gravity data, F. Hehuwat and D. H. Natawidjaja for their help, and Professor W. Jacoby and two reviewers for their valuable comments.
REFERENCES Bellier O., Sebrier M. and Pramumijoyo S. (1991) La grande faile de Sumatra: Geometrie, cinematique et quantite de deplacement mises en evidence par l’imagerie satellitaire. Academic des Sciences-Paris 312, 12 19- 1226. Curray J. R., Moore D. G., Lawyer L. A., Emmel F. J., Raitt R. W., Henry M. and Kieckhefer R. M. (1979) Tectonics in the Andaman Sea and Burma. In Geological and Geophysical Investigations of Continental Margins (Watkins, J. S., Montadert L. and Dickerson P. W., eds). American Association of Petroleum Geologists Memoir, Vol. 29, pp. 189-198. Diament M., Hatjono H., Karto K., Deplus C., Dahrin D., Zen M. T., Gerard M., Lassal O., Martin A. and Malod J. (1992) Mentawai fault zone off Sumatra: A new key to the geodynamics of western Indonesia. Geology 20,259-262. Eaton J. P., O’Neill M. E. and Murdock J. N. (1970) After shocks of the 1966 Parkfield-Cholame earthquake: A detailed study. Bull. Seismol. Sot. Am. 60, 115 l-l 197. Harjono H., Widiwijayanti Ch., Handayani L., Deverchere J., Sebrier M., Diament M., Suwijanto, Surono, Pramumijoyo S., Gunawan H. and Lumbanbatu U. (1994) The 1994 Liwa earthquake: a preliminary result of aftershocks observation. In Prosiding Tridawawarsa Puslitbang Geoteknologi-LIP1 v.2 (Hantoro W. S., Wirdsantosa S., Utomo E. I?, Soebowo E., Kumoro Y. and Riyanto A. M., eds). Geoteknologi-LIP1 Indonesia, pp.I1162-11168. . Huchon P. and Le Pichon X. (1984) Sunda Strait and Central Sumatra fault. Geology 14, 780-783. Jarrard R. D. (1986) Relation among subduction parameters. Rev. Geophys. Space Phys. 24, 127-284. Kadir, W. G. A., Zen M. T., Hendrajaya L. and Santoso D. (1995) Depth estimation of gravity anomalies by using deconvolution filter. Proc. of XX Indonesian Association of Geophysicist Annual Convention, 48. King G. (1983) The accommodation of large strains in the upper lithosphere of the earth and other solids by self-similar fault system: the geometrical origin of b-value. Pageoph 121, 761-815. Lassal O., Huchon P. and Harjono H. (1989) Extension crustale dans le detroit de la Sonde (Indonesie). Donnes de la sismique relextion (campagne Krakatoa). Academic des Sciences, Compte Rendus 309,881-884. Mandlebrot B. B. (1982) Fractals Geometry of Nature. W. H. Freeman, San Francisco. McCaffrey R. (1991) Slip vectors and stretching of the Sumatra fore arc. Geology 19, 881-884. Nagahama H. and Yoshii K. (1994) Scaling laws in fragmentation. In Fractals and Dynamic System in Geosciences (Kruhl, J. H., ed.). Springer Verlag, Berlin, pp. 25-36. Natawidjaja D. H. and Sieh K. E. (1994) Neotektonik sistem sesar Sumatra. In Prosiding Hasil Penelitian Puslitbang Geoteknologi LIPI, Geoteknologi LIP1 Indonesia, pp. 145-161.
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Newcomb K. R. and McCann W. R. (1987) Seismic history and seismotectonics of the Sunda arc. J. Geophy. Rex 92,421439. Okubo, P G. and Ati K. (1987) Fractal geometry in the San Andreas Fault System. J. Geophy. Res. 92,345-355. Page B. G. N., Bennett J. D., Cameron N. R., Bride D. McC., Jeffrey D. H., Keats W. and Thaib J. (1979) A review of the main structural and magmatic features of northern Sumatra. Geological Sot. Land, J. 136,569-579. Scholz C. (1990) The Mechanics of Earthquakes and Faulting. Cambridge University Press, Cambridge. Velde B., Dubois J., Touchard G. and Badri A. (1990) Fractal analysis of fractures in rocks: the Cantor’s Dust method. Tectonophysics 179,345-352. Zwick P. and McCaffrey R. (1991) Seismic slip rate and direction of the Great Sumatra fault based on earthquake fault plane solutions. EOS trans. AGU 72,20 1.