Faults Evolve

Amir Sagy1, Emily E. Brodsky1 and Gary J. Axen2

1Dept. of Earth Sci., UC Santa Cruz, Santa Cruz, CA

2Dept. of Earth and Environmental Sci., New Mexico Inst. of Mining and

Technology, Socorro, NM

Principal slip surfaces in fault zones accommodate most of the displacement during

earthquakes. The topography of these surfaces is integral to earthquake and fault

mechanics, but is practically unknown at the scale of earthquake slip. We map

exposed fault surfaces using new laser-based methods over 10 µm-120 m scales.

These data provide the first quantitative evidence that fault surface roughness

evolves with increasing slip. Furthermore, we observe elliptical bumps ~10-20 m

long on large-slip faults. Identifying these bumps with seismological asperities

implies that the nucleation, growth and termination of earthquakes on evolved

faults are fundamentally different than on new ones.

The amplitude and wavelength of bumps, or asperities, on fault surfaces affect all

aspects of fault and earthquake mechanics (1) including rupture nucleation (2),

termination (3, 4), dynamics (5 ,6), resistance to shear (7), fault gouge generation (8),

critical slip distance (9), and the near-fault stress field (10). Prior comparative studies of

natural fault roughness on multiple surfaces were based on contact profilometer data (11-

13). The method is labor-intensive so only a few profiles were reported for each surface.

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The contact profilometer results were interpreted to show that fault roughness is

proportional to the measured profile length, i.e., faults are self-similar (11, 12). This

interpretation is also supported by recent LiDAR measurements on a single fault (14) and

implies that roughness is not dependent on fault displacement. In contrast, laboratory

experiments and geological observations suggest that faults progressively evolve with

increasing slip (4, 15-18), as the slip surfaces localize and coalesce.

To resolve this apparent contradiction we scanned 15 fault surfaces in the western

U.S. using a ground-based LiDAR (Light Detection And Ranging) instrument with 3 mm

resolution. We also measured the roughness of hand samples from the surfaces using a

laboratory laser profilometer with 10 µm resolution. Fault-surface roughness in a given

direction was measured by averaging the power spectral densities of hundreds of parallel

profiles in a chosen direction on each fault. Here we focus on seven scanned fault

outcrops (Table 1) that are particularly well-preserved and are relatively simple with each

surface having a single, consistent striation orientation (Fig. 1a). The scanned targets

include three strike-slip and oblique-slip faults with displacements < 1 m as well as four

normal fault surfaces that accommodated slip in excess of 10's to 100's of meters (Table

1, Figs. 1a and 1b).

Our data clearly indicates that the net slip correlates with fault roughness. Small-slip

faults (<1 m slip) are rougher than large-slip faults (~10-100 m slip) when measured

parallel to the slip direction. For instance, for 1 m profiles parallel to the slip direction,

the average deviation from a planar surface (RMS roughness) of the small-slip faults is

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6.5±3.5 mm while that of the large-slip faults is 0.9±0.3 mm. For 2 m profiles the RMS

values are 11±1 mm and 1.2 ±0.1 mm, respectively. These values are calculated from

averaged, detrended sections. Thus, at scales of 1-2 m in the slip-parallel direction, the

roughness of the large-slip faults is about constant and about one order of magnitude

smoother than small-faults (See example in Fig. 2a inset).

Another, closely related measure of roughness is the power spectral density. For

example, for a self-affine surface (12, 19), the power spectral density p is related to the

wavelength λ by

p = Cλβ (1)

where C and β are constants. If 1<β<3, the RMS roughness H is

H= (C/(β-1))0.5 λ (β-1)/2 . (2)

If β ≤ 1, changes in H with scale are very weak and may be below the measurement

resolution.

Power spectral density curves from profiles parallel to slip reinforce and extend the

conclusions based on RMS roughness (Figs. 2a and 2b). Using the spectra, we observe

that large-slip faults are distinctively different from small-slip faults. At large

wavelengths (>1 m), large-slip faults spectra have consistently lower values (are

smoother) than the small-slip ones (Fig. 2a). The small-slip faults might be self-affine,

but the curving spectra of the large-slip faults show that their geometry is clearly

wavelength-dependent (Fig. 2b). At short wavelengths in the LiDAR measurements, the

slope β of the large-slip faults is nearly that of an artificial smooth surface that was

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scanned for reference (red dotted line in Figs. 2a and 2b). Thus, these faults with

displacements of more than tens of meters are so polished that at ~1 m wavelength the

amplitude can be as low as ~3 mm, which is the LiDAR resolution limit. Below ~1 m

wavelength, the true roughness of large-slip faults is seen in the laboratory profilometer

data, which overlap the LiDAR spectra on length scales where the latter is noise limited.

For two hand samples from a large-slip fault, β ≈ 1 from 0.1 mm to ~5 cm (The two

green lines in Fig. 2b), while for samples from two other large-slip faults (brown and blue

curves in Fig. 2b) β ≈ 1 from ~1 mm to ~2.5 cm. Below 1mm the slope (β) for these two

samples becomes steeper possibly indicating that the polished zone has a lower limit.

Interestingly, Power and Tullis (12) showed a similar corner in their profilometer spectral

density curves, with β≤ 2 on wavelengths of 1 mm to 5 cm. They inferred that this was an

artifact but our data suggest that the curvature is real. However, samples from small-slip

faults (pink and grey curves in Fig. 2b) are consistently rougher: faults with 1 cm of

displacement have roughness that is essentially the same in directions parallel and

perpendicular to slip. Taken together, the large-slip fault surfaces are best described as

polished on length scales ≤ 1m and smoothly curved on larger scales. The spectra show

that the large-slip faults are not self-affine. This behavior is in clear contrast to the former

interpretation (11-14) and demonstrates that faults evolve during slip.

In summary, our measurements suggest that slip-parallel roughness can be divided

into two or even three different regions. 1) At length scales > 1 m the roughness is wavy.

2) At length scales from ~1 mm to ~l m, large-slip fault surfaces are polished. 3) Below

~1 mm, there may be a third regime where roughness may be controlled by grain size or

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small-scale erosion. Previous measurements are also consistent with this division,

although the prior interpretations have differed (12).

In the slip-perpendicular direction, the power spectra of the large-slip and small-slip

faults are more closely related. Our new measurements support previous observations

(11-13) that faults are consistently rougher in the direction perpendicular to slip than in

the direction parallel to slip (Fig. 2b, 2c). We also show that the spectra of small-slip

faults can be fitted by a power law on scales of microns to ~2 meters and the spectra of

large-slip faults can be approximated by power law relation at least from ~0.5 m and up

to ~100 m. For example, for a small-slip fault the value of β is 2.97±0.013 (pink line in

2c) from 10 µm to >1 m, and for a large-slip fault the value of β is 2.89±0.005 from 1 m

to 60 m (Fig. 1b and the upper green curve in Fig. 2c). Thus, at these wavelengths fault

roughness perpendicular to slip (Fig. 2c) can be interpreted as self-affine or even self-

similar (linear dependence of the RMS values on the profile length). The dashed line in

Fig. 2c shows that these spectra are similar to the spectrum of a surface with H=0.01λ,

which is the relation inferred for other natural fractures (19). We also recover a similar

relation for an erosional surface (upper grey curve in Fig. 2c). We therefore conclude that

the slip-perpendicular profiles reflect a level of roughness typical of natural fractures but

contain relatively little information about the slip process.

Above ~1 m wavelength, the large-slip faults have undulating 3D surfaces as seen in

topographic maps of the surface (Fig. 3). At least three large-slip fault surfaces have

smooth ellipsoidal ridges and depressions with dimensions that are ~1-5 m wide, ~10-20

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m long, and ~0.5-2 m high. The long axes of these bumps, or asperities, are parallel to

the slip direction. Below ~1 m wavelength, the LiDAR data are limited by the

instrumental noise level (red dots in Figs. 2b and 2c). At longer wavelengths than can be

measured on the outcrops, these asperities could represent the smallest scale of a self-

affine geometrical network like that proposed by earthquake statistics and map-scale

studies (20, 21).

The data is surprisingly consistent despite variations in lithology, faulting sense and

the depth of slip (Table 1). In our dataset, the large-slip faults are all normal faults, thus

it could also be concluded from this data that the normal faults are systematically

smoother than the others. However, there is no obvious reason why the normal faults

should be smoother, while there are a number of physical reasons that slip should wear

down and abrade faults, so we deduce that displacement is the discriminating factor.

We have shown through the variations in RMS roughness, spectral shape and 3-D

geometry that faults evolve with slip. Our surface roughness data complement previous

map-scale observations of fault traces which suggested that the number of steps along

strike-slip faults is reduced with the increasing displacement (4). We now have evidence

that faults become geometrically simpler as they mature at the scale of earthquake slip.

Fracturing and abrasional wear are the most obvious mechanisms for smoothing fault

surfaces. Tensile fracture surfaces are typically self-affine (22, 23). Since the roughness

of the observed faults at large slips is distinctly not self-affine and the small protrusions

are preferentially eliminated with slip, wear may be the more likely mechanism.

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The accurate geometric data of fault surfaces has implications for fundamental

earthquake processes (2, 3, 24, 25). Our data show the existence of regular geometric

slip-parallel asperities for a given fault on mature faults (Fig. 3), which should cause

predictable stress concentrations on the bumps in preference to the smooth regions. On

this basis, we predict that the stress heterogeneity, and therefore the resulting rupture

properties (e.g., slip magnitude, critical slip distance, radiated energy spectrum, etc.),

should be different on mature as opposed to immature faults. The ~20-m wide

microseismicity streaks on the San Andreas fault (26) may reflect interactions of smooth

asperities such as we have imaged here. Perhaps most tantalizing, if geometric control on

stress concentrations turns out to be dynamically significant, then a degree of

predictability may exist for earthquakes on a given fault.

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References

1. C. H. Scholz, The Mechanics of Earthquakes and Faulting (Cambridge Univ.

Press, Cambridge, ed. 2, 2002).

2. T. Lay, H. Kanamori, L. Ruff, Earthquake Predict. Res. 1, 3 (1982).

3. K. Aki, J. Geophys. Res. 89, 5867 (1984).

4. S. G. Wesnousky, Nature 335, 340 (1988).

5. E. E. Brodsky, H. Kanamori, J. Geophys. Res. 106, 16357 (2001).

6. H. Aochi, R. Madariaga, Bull. Seismol. Soc. Am. 93, 1249 (2003).

7. R. L. Biegel, W. Wang, C. H. Scholz, G. N. Boitnott, N. Yoshioka, J. Geophys.

Res. 97, 8951 (1992).

8. W. L. Power, T. E. Tullis, J. D. Weeks, J. Geophys. Res. 93, 15268 (1988).

9. M. Ohnaka, Science 303, 1788 (2004).

10. F. M. Chester, J. S. Chester, J. Geophys. Res. 105, 23421(2000).

11. W. L. Power, T. E. Tullis, S. R. Brown, G. N. Boitnott, C. H. Scholz, Geophys.

Res. Lett. 14, 29 (1987).

12. W. L. Power, T. E. Tullis, J. Geophys. Res. 96, 415 (1991).

13. J. J. Lee, R. L. Bruhn, J. Struc. Geol. 18, 1043 (1996).

14. F. Renard, C. Voisin, D. Marsan, J. Schmittbuhl, Geophys. Res. Lett. 33, L04305

(2006).

15. R. H. Sibson, Annu. Rev. Earth Pl. Sci. 14, 149 (1986).

16. J. S. Tchalenko, Geol. Soc. Am. Bull. 81, 1625 (1970).

17. F. M. Chester, J. P. Evans, R. L. Biegel, J. Geophys. Res. 98, 771 (1993).

18. Y. Ben-Zion, C. G. Sammis, Pure Appl. Geophys. 160, 677 (2003).

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19. S. R. Brown, C. H. Scholz, J. Geophys. Res. 90, 2575 (1985).

20. Y. Y. Kagan, Geophys. J. R. Astr. Soc., 71, 659 (1982).

21. C. A. Aviles, C. H. Scholz, J. Boatwright, J. Geophys. Res. 92, 331 (1987).

22. A. Hansen, J. Schmittbuhl, Phys. Rev. Lett. 90, 045504 (2003).

23. E. Bouchbinder, I. Procaccia, S. Sela, Phys. Rev. Lett. 95, 255503 (2005).

24. S. J. Steacy, J. McCloskey, Geophys. J. Int. 133, 11 (1998).

25. M. T. Page, E. M. Dunham, J. M. Carlson, J. Geophys. Res. 110, B11302 (2005).

26. A. M. Rubin, D. Gillard, J. L. Got, Nature, 400, 635 (1999).

27. S. F. Personius, R. L. Dart, L. A. Bradley, K. M. Haller, “Map and data for

Quarternary faults and folds in Oregon” (Tech. Rep. 03-095 USGS, 2003).

28. C. R. Bacon, M. A. Lanphere, D. E. Champion, Geology 27, 43 (1999).

29. W. L. Power, T. E. Tullis, J. Geophys. Res. 97, 15425 (1992).

30. We thank J. Caskey, M. Doan, J. Fineberg, J. Gill, M. Jenks, R. McKenzie, Z.,

Reches, S. Skinner and A. Sylvester. Funding was in part provided by the

Southern California Earthquake Center.

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Table1: Scanned faults.

Fault Name Location

Displacement Lithology

Split M.1 33.014 o -116.112o 30±15 cma Sand stone

Split M.2 33.0145 o -116.112 o 15±5 cma Sand stone

Mecca Hills 33.605 o -115.918 o 20±10 cma Fanglomerate (Calcite)

Little Rock 34.566 o -118.140 o 1-3 cmde Quartz Diorite

Flower Pit1 42.077 o -121.856 o 50m-300 mb Andesite

Flower Pit2 42.077 o -121.852 o 50m-300 mb Andesite

KF1 42.1346 o -121.7955 o 50m-300 mb Basalt+Andesite

KF2 42.332 o -121.819 o 50m-300 mbe Basalt+Andesite

Dixie V. (Mirror) 39.7951 o -118.0747 o >10 mc Quartz

a Based on direct measurements of offset of sedimentary layers or displacement of

structural markers.

b Belong to the Klamath Graben Fault system and to the Sky Lakes fault zone, in the

northwestern Basin and Range (27). The scanned faults are exposed by recent quarrying,

so are relatively unweathered. Fault surfaces are on footwall Quaternary volcanic rocks

(Fig. 1c) which were faulted against hanging wall Holocene gravels (27, 28). Minimum

displacement along a single slip surface is more than 50 m. Assuming Middle Pleistocene

ages for the faulted volcanic rocks, and slip rates of 0.3 mm/year (28), the cumulative

displacement along them is probably no more than a few hundred meters. The

surrounding region is seismically active, including a 1993 sequence of earthquakes with

magnitude Mw =6.

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c The fault surface exposed in fine crystalline rocks (Fig. 1a). The fault zone includes

several other anastomosing slickensided and striated surfaces (see also ref. 29) in the

~10-20 m subjacent to the principal fault surface active in Quaternary time. The scanned

surfaces probably formed at an unknown depth. The cumulative displacement along the

fault zone may be 3 km or more, but individual slip surfaces probably accommodated

much smaller displacement (29).

d Small-slip faults from within the Little Rock fault zone (not the main fault surface).

e No large fresh outcrop exposures exist so only profilometer measurements were made.

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a b

c

0

0.6 m

X (4m)

Top

ogra

phy

X

Y

Y

100 m

Figure 1. Two of the large-slip fault surfaces analyzed in this paper. a) Section of partly eroded slip surface at the Mirrors locality on the Dixie Valley fault, Nevada (Table 1). LiDAR fault-surface topography is presented in the color-scale map (b) which was rotated so that the the X-Y plane is the best-fit plane to the surface and the mean striae are parallel to Y. c) One of three large, continuous fault segments exposed at the Flower Pit, S. Oregon (Table 1).

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-510

-610

-710

010-210 -110

a

3P

ow

er s

pect

ral

den

sity

(m

)

Wavelength (m)

2cm

1 m

c

3P

ower

spe

ctra

l de

nsit

y (m

)

Wavelength parallel to the slip (m)

210010-210-410

b 1=

b = 1

b=

3H

= .

1

00

l

210

-410

-610

-810

-1010

-1210

-1410

010

-210

b

3P

ower

spe

ctra

l de

nsit

y (m

)

-410

-210

010

210

210

-410

-610

-810

-1010

-1210

-1410

010

-210

b = 1

b = 1

b =

3H

0 =

.0

1l

Little Rock

Split M.1

Split M.2

Mecca Hills

Small faults Large faults

Erosional surface

Flower Pit1

Flower Pit2

KF1

KF2

Dixie V.

Wavelength prependicular to the slip (m)

Figure 2. Power spectral density curves calculated from sections of seven different fault surfaces that have been scanned using ground-based LiDAR, and from 8 hand samples scanned by a profilometer in the lab. a) Power spectral density values over the wavelength range of 0.01-1 meter which are calculated from sections of the same length on small and large faults that are measured parallel (thick curves) and normal (thin curves) to the slip. Each curve represents data from 250 individual 2.3-2.5 m profiles spaced 3 mm apart. The red dotted lines represent scans of smooth, planar reference surfaces. The inset shows the typical topography parallel to fault slip on four different example faults.

Panels (b) and (c) include both LiDAR data (upper curves) and profilometer data (lower curves) from profiles of a variety of lengths b) profiles parallel to the slip and c) profiles perpendicular to the slip. The LiDAR measurements cover wavelengths from 1cm to 100m. The profilometer measurements cover wavelengths of 10 mm to 5 cm and each curve was calculated from 600 parallel profiles. Colors are as in (a) and the red dotted lines again represent scans of smooth, planar reference surfaces for the LiDAR (above) and the profilometer (below). Dashed black lines are slopes of b = 1 and b = 3.

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05

1015

2025

30

Fault topography (m)

Len

gth

alon

g sl

ip (

m)

a

6 m0

1.3 m

I

II

II IV

0

16 m

35 m

2 m

III

III

4.2m

4.2 m 0

0.4 m

12 m

02.4 m

c

6.6 m

b

0.1 m

5 m

IV

0.9 m

0

21 mII

Figure 3. Color-scale fault-surface topography of the large scanned faults. a) Profiles (left) and map (right) of fault KF1. The map show elliptical bulges (red) and depressions (blue) identical in their dimensions aligned parallel to slip. The upper bulge (I) and the depression (II) are partly eroded. b) Negative and positive elliptical bumps (marked by roman letters) on large section of fault surface (Flower Pit1, See also fig 1b). c) Bumps on three different fault surfaces (Dixie V.-left, Flower Pit2-middle, and Flower Pit1-right). The middle image shows single elliptical asperity by contours.