Faults Smooth Gradually as a Function of Slip
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Emily E. Brodsky1, Jacquelyn J. Gilchrist1,4, Amir Sagy2 and Cristiano Collettini3
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1
Dept. of Earth & Planetary Sciences, University of California, Santa Cruz, USA
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2
Geological Survey of Israel, 30 Malkhe Israel St., Jerusalem, Israel
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3
Dipartimento di Scienze della Terra, Università degli Studi di Perugia, Italy
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4
Current Address: Dept. of Earth Sciences, University of California, Riverside, USA
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ABSTRACT
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Geometry and roughness of fault surfaces plays a central role in the dynamics and
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kinematics of faulting. Faults smooth with increasing slip, but the degree of the
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smoothing has not previously been well-constrained for natural faults. We measure
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the roughness as a function of displacement for a suite of 16 faults with cumulative
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offsets ranging from 0.1 m to approximately 500 m. We find that slip parallel
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roughness evolves gradually with slip. For instance, for segments of length 0.5 m, H
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≈ 2 x 10-3 D-0.1 where H is the RMS roughness and D is the displacement on the fault
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strand with both quantities measured in meters. The gradual nature of the
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smoothing is robust to varying lithology and erosion. The weak function implies a
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decrease in the rate of gouge formation for a model with increasing slip for a model
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in which gouge is generated by abrading an asperity tip. The relatively gradual
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evolution of roughness could be explained by lubrication by the accumulated gouge
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that mitigates the abrasional smoothing that occurs during slip and/or re-
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roughening processes.
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1. Introduction
Brittle fracture and wear are fundamental processes in earthquake mechanics and
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fault surface development (Scholz , 2002). Continuous faulting in the upper brittle crust
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is typically characterized by localization of slip on surfaces, which absorb the chief part
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of the displacement (Sibson, 1977; Cowan et al., 2003; Chester et al., 2004). As rocks
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grind past each other they wear down bumps and generate gouge. Such geometric
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evolution may be significant for mechanical aspects of faulting and earthquakes (Lay et
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al., 1982; Biegel et al., 1992; Rubin et al., 1999; Harrington and Brodsky, 2009). This
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abrasional process is part of the large-scale slip during earthquakes and yet is usually
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omitted from dynamic models in large part because it is poorly constrained.
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One strategy to quantify the influence of evolution processes on natural fault
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surfaces and on faulting processes is to measure its effects through fault roughness.
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Previous measurements of fault surfaces demonstrated that the roughness of these
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surfaces has well-defined statistical properties (Brown and Scholz, 1985; Power et al.,
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1987; Lee and Bruhn, 1996, Renard et al., 2006; Candela et al., 2009). Our previous work
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also indicated that fault roughness evolved and surfaces became smoother with the
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continuation of slip (Sagy et al., 2007). While our prior work recognized the fact that
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faults evolve with slip, the main aim of this paper is to quantify the exact relationship.
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Measurements of step-overs suggest that the widths of segments at the kilometer-scale
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decrease nearly linearly with total offset and the spread of splay orientations also
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decreases with offset (De Joussieau and Aydin, 2009; Wechsler et al., 2010), but little is
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known about the evolution of roughness at the scale of slip during observable
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earthquakes (centimeters-meters). Such a relationship would be useful for its mechanical
2
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implications. It could additionally be used as a tool to constrain displacement for faults
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where offset cannot be determined directly, as is often the case.
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In this paper, we will utilize ground-based LiDAR (Light Detection And Ranging)
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data from a set of faults that slipped 10 centimeters to a few hundred meters to map out
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the variation of roughness with displacement. After reviewing the methodology, we will
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present roughness measurements in the form of power spectra in the slip parallel
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direction. We will then focus on a restricted set of scales in the topography where the
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data is well resolved for the full set of faults and derive a displacement-roughness
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relationship for comparison with previous predictions. We will find that although faults
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smooth with increasing slip, the smoothing process is gradual, i.e., roughness depends on
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slip raised to a small exponent. We will then evaluate the robustness of this conclusion in
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light of the potential complications of lithology and erosion before proceeding to examine
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its implications for fault mechanics.
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2. Fault Localities and Displacement Controls
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We scanned a suite of faults in the Western U.S. and Italy for this study (Table 1).
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One of the major limiting factors in selecting faults for study is the presence (or absence)
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of displacement controls. For very favorable exposures, generally associated with small
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displacement faults, we have measured the offset of stratigraphic markers exposed
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directly in the outcrop. For some larger displacement faults where it is not possible to
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observe in the field the displaced lithology in the hanging wall and footwall blocks, we
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have constructed geological cross sections perpendicular to fault strike and we have
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evaluated the displacement on the ground of the juxtaposed lithologies. This method is
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particularly helpful in the Apennines, since the exposed carbonatic multilayer is made of
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different stratigraphic units with well-constrained thicknesses (Barchi et al., 2001). Other
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large faults require estimates of displacement by more circuitous means, such as
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topography or fault length. In the appendix we document the constraints as they exist for
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each fault, as this information is critical for further interpretation.
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The faults are separated into two categories by the degree of precision available
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for the displacement constraints. The first category includes the faults with displacements
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that were measured directly and the second includes the faults whose displacements were
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estimated from non-direct means.
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3. Fault Roughness Measurements
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3.1 Scanning and Processing
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Roughness for each fault was determined using three-dimensional LiDAR data. The
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laser scanning method collects a point cloud of data that records the topography of each
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exposed fault surface (Figure 1). All data used here was collected with a ground-based
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Leica HDS3000 which can scan with point spacing as close as 3 mm from a distance of
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25 m. The actual point spacing depends on the size of the exposure, but in most cases
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hundreds of profiles with 3 mm-5 mm spacing were available. Range error is 3-4 mm
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depending on scanning conditions. A planar reference board was placed in many scans to
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constrain the noise level and resolution.
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The faults included in the study were chosen for their large, clear exposures. Other
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faults were scanned but not used because they were eroded or too much of the surface
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was obscured by vegetation. The scans were combined with digital photographs to
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distinguish clear fault surface from non-fault features and eroded areas. This manual
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cleaning of the extremely large datasets (10-60 million points) was enabled by SlugView,
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a 3D point cloud editor and visualizer with RGB capabilities written by the UC Santa
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Cruz Seismology Group (http://www.pmc.ucsc.edu/~msteffec/SlugView).
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Once all non-fault features such as trees, grass or anthropogenic structures, are
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removed, the surfaces are then rotated so that the mean slip direction is horizontal
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allowing profiles to be taken along slip. The slip direction is taken to be the smoothest
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direction along a fault surface as determined by the smallest relative power spectra at a
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specified wavelength as shown by Sagy et al. (2007). This result is consistent with visual
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inspection of striations, tool marks, etc (Petit, 1987; Means, 1987).
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3.2 Roughness as Function of Segment Scale
Like many natural surfaces, roughness is a function of observation scale for faults
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(Wesnousky, 1988; Power et al., 1988, Sagy et al., 2007). The average deviation from a
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planar surface (RMS asperity height) increases with the size of the segment being
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measured. Therefore, in order to perform meaningful comparisons between fault surfaces,
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we need to compare the roughness measured at a range of scales as well as the roughness
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at a particular scale common to all observations.
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Power spectral density measures the strength of the sinusoidal components of the
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topography over a range of wavelengths by performing a Fourier decomposition (e.g.,
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Press et al., 2007). We average the 1-D spectra of hundreds of profiles in the slip parallel
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direction for each surface in order to arrive at a spectral estimate with minimal variance.
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Over a restricted range of wavelengths, the topographic data in spectral space can
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be fit by a power law of the form
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(1)
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where C and β are constants and k=1 /λ where λ is wavelength (Figure 2). We will use
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this functional fit to infer an RMS roughness amplitude as a function of scale so that we
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can easily interpret the relative roughness of a suite of faults. In using the power-law
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model, we imply that the fault is adequately modeled as self-affine over this range of
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wavelengths for the purpose of this comparison even though a finer attention to the
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detailed structure may reveal otherwise. We will evaluate this assumption by comparing
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the RMS height obtained through integrating the power law fit to the spectrum with a
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direct measure of the residuals from a planar fit.
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The RMS height H of a profile y(x) over a segment of length L is related to the
spectral power density by Parseval’s Theorem,
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(2)
If 1< β <3 for a section of length L (as will be observed), substituting in (1) to (2) yields
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(3)
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The parameter C can be estimated from the power at the wavelength corresponding to the
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segment length L, i.e., C=p(λ=L)/Lβ . Estimates of p(λ=L) are made from the power
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spectral density after first smoothing log p with a three-point running average. (The
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smoothing operation ensures stable estimation; the log allows an arithmetic mean to be
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used.) Substituting C into 3 and simplifying yields
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(4)
This model-dependent estimate of the roughness is evaluated by comparing H as
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calculated with Eq. 4 to an alternative estimate of the RMS. We break each profile up
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into segments of length L and directly measure the standard deviation of the residuals
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from a straight line fit for each segment. We then average the results for all segments of
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length L on all profiles in the study region and use this mean as an estimate for RMS
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height as a function of L that we will call
.
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4. Results
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4.1 Power Spectra
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Roughness was measured in the slip parallel and perpendicular direction for all of the
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faults. The largest available clean surface was used from each fault. A surface is
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considered rougher than another at a given wavelength if its power spectral density is
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higher at that wavelength. In this paper we primarily focus on the slip parallel roughness
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as it is most clearly related to the predictions of wear models.
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Slip parallel roughness of faults that were measured in Italy is intermediate between
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the large (>10-100 m or more) and small slip (<1 m) faults that were measured in western
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United States in Sagy et al. (2007). It also decreases with slip as seen by the spread of
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the spectra in Figure 2. This indicates that roughness does decrease with increasing slip
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through slip distances of a few centimeters to hundreds of meters.
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We now compare the two different estimation methods for roughness as a
function of scale: H from Eq. 4 and
. For our best-resolved data, the two methods
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generate nearly identical results (Figure 3a). In this comparison and what follows, β is
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estimated from a power law fit to the power spectral data over wavelengths of 0.1-2 m.
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For the full set of faults in Table 1, the mean value of the fit slopes for the spectra of
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sections taken parallel to slip is 2.1 with a standard deviation of 0.6.
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Less well-resolved data shows a discrepancy between H and
at short scales
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(Figure 3b). Noise overwhelms the signal for
limiting the zone of resolved data.
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However, the stacking inherent in the spectral estimation along with the extrapolation of
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the slope from larger wavelengths allows H to still be resolved. Therefore, the
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approximation of H from the power spectrum (Eq. 4) is a useful tool for extrapolating the
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data into the region of wavelengths that cannot be measured directly with noisy data.
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4.2 Roughness as a function of displacement
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We will now investigate the evolution of roughness with displacement. In order to
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make a comparison, we need to restrict ourselves to a small subset of the data. The power
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spectra in Figure 2 are only well resolved for the full set of faults for a very restrictive set
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of wavelengths. At extremely small wavelengths, the LiDAR measurement is limited by
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the range error of the laser beam. For example, for a smooth surfaces with H << λ, the
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value of H determines the minimum value of λ for which the power spectrum can be
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resolved. This limit is reached for the smoothest surfaces at a wavelength of 0.2 m. For
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large wavelengths, the data is limited by the exposure surface size. For our smallest
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surfaces, this limit is reached at 1 m. Therefore, we focus on the variation of RMS height
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H as inferred from power spectra measured only in this range. For comparison, we will
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also show
for the same range of scales while recognizing that it is more poorly
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resolved at short wavelengths.
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Using the full dataset from Table 1, we begin with L=0.5 m as this wavelength is
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available for all faults and is well above the noise level (Figure 4). We see that the power
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spectral density (Figure 4a), the spectrally estimated H (Figure 4b) and the RMS directly
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measured as
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discussed above, H is a better metric of roughness for the LiDAR data. Therefore, in
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round numbers, we infer a roughness evolution relationship of
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(Figure 4c) all decrease gently with displacement. For the reasons
H(L=0.5m) = 2x 10-3 D-0.1
(5)
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where D is displacement and all quantities are measured in meters. The small absolute
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value of the exponent in Eq. 5 indicates a gradual smoothing.
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The weak dependence on displacement in Eq. 5 remains the same for other
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segment lengths at the bounds of the resolved range (Figure 5). For both L=1 m and
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L=0.25 m, the decay of H with displacement again has an exponent that is identical to
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L=0.5 within error. As expected, the pre-factor for the L=1 m segments is higher than for
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the shorter segments indicating that surfaces asperity heights are generally higher for
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longer segments for a fixed displacement. For L=1,
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and recovers the same fit within error. For L=0.25, the trend is depressed as might be
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expected due to the interference of noise at short wavelengths.
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is consistent with the above result
In all of these cases, the scatter of the data is large, but the basic result holds: the
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absolute value of the exponent is much less than 1. The exponent must also be less than 0
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to be consistent with the spread of spectra in Fig. 2.
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5. Potential Complications
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We now proceed to investigate the robustness of the weakly decreasing trend of
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roughness with slip to several complications that may affect roughness values when
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measured in field. Below we test whether the regression remains discernibly different
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from a stronger linear decrease when considering three major factors that can affect the in
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situ measured roughness: poorly constrained displacement, erosion and lithology.
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We note that other parameters such as depth of burial, sense of motion, and tectonic
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regime may also affect roughness values in faults. However, data from other faults are
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needed to investigate the individual influence of these parameters. For the dataset here,
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the overwhelming majority of faults are normal faults which continue activity to shallow
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depths. Therefore, we would not expect these additional complicating factors to obscure a
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strong smoothing with displacement trend, should it exist.
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5.1 Displacement Errors
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First we limit the dataset to just those faults with well-constrained, directly measured
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displacement (see Table 1; Appendix A.1) and refit the data (Figure 6). Eq. 5 remains
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valid for the subset. Given that this fit is based on the highest quality data, we consider
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the result of Figure 6 to be the most robust result of this paper.
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5.2 Erosion
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Roughness is sensitive to time of exposure. A fortuitous example allowed us to
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quantify the effects of erosion at the scales we measured roughness. The Monte Maggio
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fault was originally exposed hundreds of years ago, but new roadwork just a few weeks
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prior to scanning revealed a new section of the fault (Figure 7). The comparison between
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the upper, eroded portion and the lower, pristine portion provides constraints on the
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influence of erosion on the interpretation.
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Figure 7b shows the power spectra for both the upper and lower sections. The
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more eroded section is rougher with higher spectral power density (The results in Figs. 4-
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5 only used the pristine lower section). Erosion generates pitting that roughens the
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surface. The difference between the eroded and non-eroded measurements can be
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appreciable. Although we tried to measure only well-preserved surfaces and to analyze
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only the most clearly striated sections along it, erosion naturally affects all of our values
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for all measured surfaces. However, Figure 7 demonstrates that both the eroded and non-
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eroded large-slip surfaces are clearly distinct from the rough small-slip faults. Therefore,
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the power spectra as measured are in fact capturing a variation in fault geometry that
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correlates with displacement.
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5.3 Lithology
A strong smoothing trend with increasing displacement could potentially be
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obscured by the large variety of lithologies studied. In order to evaluate this possibility,
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we limit the dataset to a single lithology and investigate whether a trend closer to that
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predicted by previous work becomes apparent.
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Figure 8 shows just the carbonate data, which is the most common lithology in
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our dataset. The slope in Figure 8 is the same within error as that in Figure 5. The data
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cannot accommodate a linear decrease in roughness with displacement, so we infer that
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the conclusion of a relatively weak smoothing with displacement stands.
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6. Implications for Fault Zone Processes
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The primary conclusion of this paper is that roughness evolves gradually with slip. The
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large scatter in the data results in larger error ranges in the fit exponents. However, a
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linear fit cannot be accommodated in this range. This result is robust despite the
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complicating factors of poor displacement controls, lithology, and erosion discussed
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above.
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Perhaps the most obvious explanation for surface smoothing in the slip parallel
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direction is that the surfaces are abrasionally polished during slip. If the evolution of
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surface roughness is dominated by wear, then we would expect the volume of wear
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products, i.e., gouge, to be related to the observed smoothing.
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Although the issue of gouge evolution in fault zones is controversial (Evans, 1990),
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some previous work indicates that the thickness of the finely comminuted abrasional
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gouge zone increases linearly with displacement in faults (Scholz 1987; Hull, 1988).
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These works interpret the linear increase in thickness as a natural consequence of the
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linear increase in wear products (gouge) expected from laboratory experiments.
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Engineering experiments find that the volume of wear powder produced is often linearly
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proportional to displacement (e.g., Archard, 1953; Wang and Scholz, 1994). Archard
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(1953) explained the relationship by specifically deriving a steady-state relationship for
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the case where the real contact area was determined by the deformation of asperities
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required to support an applied load. Several other theories based on alternative
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micromechanical models of asperity detachment produce similar linear relationships
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(Power and Tullis, 1988; Williams, 2005).
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We now proceed to compare the observed smoothing relationship to the predictions
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of a particular wear model. In order to perform this comparison, we first calculate the rate
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of gouge production that corresponds to the observed smoothing.
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6.1 Connecting Surface Smoothing and Wear Production
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We start by assuming that wear at any fixed scale progresses begins at the highest tips of
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asperities and bores down into the surface. This progressive smoothing of asperities is
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intrinsically a transient process. Following previous work on transient wear, we set the
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gouge volume generated equal to the volume removed from the surface (Queener, et al.
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1965; Power and Tullis, 1988),
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Vg=B(H0-H)AH
(6)
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where Vg is the volume of gouge, H0 is the original asperity height, H is the RMS height
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after some amount of slip, B is a geometric constant and AH is the area of the surface
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above that height H (Figure 9). Since H and H0 are mean (RMS) height values rather
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than peak values, we use the approximation in eq. 6 that the area removed is proportional
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to the rectangular area encompassed by the mean dimensions. The geometric constant
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accounts for the dimensionality of the original surface.
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As wear progresses, the highest asperity tips are eroded and the wear progresses
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into the thicker bases. Therefore, the area of the surface above height H increases with
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decreasing H (Figure 9). We can approximate the length of the section of the profile
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above height H using the average slope of the surface. Specifically,
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(7)
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297
where w is the width of the surface in the slip perpendicular direction. The approximation
298
used in Eq. 7 is that the length of the profile region about height H is equal to the height
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change divided by the average slope. The formulation in terms of slope useful because
300
the average gradient can be directly calculated from the power spectral information. From
301
Eq. 3,
302
(8)
303
where κ is a constant and Lmin is the minimum scale of the self-affine spectrum and β<3
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(Persson, 2005, Appendix C). Observationally, slip perpendicular roughness is
305
approximately independent of slip, so we infer that w is a constant (Sagy et al., 2007).
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Combining Eqs. 6,7 and 8 and differentiating by slip D, we find that
307
(9)
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We have observational constraints on the scaling of the three terms on the right-handside
309
of Eq. 9. The first term is constant with slip (Note that κ and β are for the initial fault
310
roughness as the initial gradient is used in Eq. 7). In the second term, H(D) is
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proportional to D-0.1 and therefore its derivative with slip is proportional to D-1.1. The
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third term requires some additional analysis. The initial asperity height for a fixed length
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can be approximated from the immature surface roughness. As shown in Figure 5 and
314
Sagy et al. (2007), faults with little slip have nearly the same roughness as the slip
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perpendicular profiles. This initial roughness state is approximately H~0.01L. We use this
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approximation for H0 for the 0.5 m length profiles used elsewhere and fit the resultant
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values to find that H0-H is proportional to D0.07+/-0.01 (Figure 10).
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Combining the observational constraints results in dVg/dD ~ D-1. In other words, the
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gradual smoothing of the faults with slip results in a prediction that wear production
320
should decrease with increasing slip. This prediction of decreasing gouge production is
321
at odds with the previous inferences of constant gouge production.
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6.2 Mechanisms to Generate Gradual Smoothing
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Our measurements and analysis above suggest, that while wear smooths the
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surface, it is not very efficient. Two specific possibilities for the gradual nature of this
326
process are that: (1) wear decreases with increasing slip and/or (2) the smoothing process
327
is mitigated by a re-roughening process.
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The first possibility is supported by some additional field evidence. Sagy and
329
Brodsky (2009) measured the thickness of the finely comminuted fault gouge for a small
330
set of secondary faults surrounding the Flowers Pit Fault (Table 1) and found that gouge
331
accumulated per unit offset decreased with increasing displacement (d2Vg/dD2<0). One
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difference between this natural situation and the laboratory experiments is that the faults
333
trap the wear products (gouge) in place while many experimental configurations
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continuously eject the gouge during slip. If the accumulated gouge has a different
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rheology than the intact rock, then the gouge can lubricate the surface and decrease wear.
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In fact, the decrease in wear might be evidence for such a lubrication process (Archard
337
and Hirth, 1956). Since wear generally depends on the real area of contact, a change in
338
wear behavior suggests a change in frictional behavior.
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The above discussion focuses on the wear products derived by sequentially
340
removing protrusions. If rock powder is generated by other processes, such as dynamic
15
341
pulverization (Wilson et al., 2005), the thickness of the gouge layer may still increase
342
linearly with displacement. However, the smoothing data rule out the possibility of the
343
gouge volume originating from removing asperity tips increasing linearly with
344
displacement unless new asperities are constantly generated through re-roughening.
345
Re-roughening of the surface provides another explanation for the gradual
346
evolution. For instance, Archard (1953) suggested that wear removed lumps from a
347
surface and therefore continually regenerated roughness while at the same time producing
348
gouge. In his formulation, wear can proceed as a steady-state process because the
349
statistics of roughness at the scale of asperities remains stationary (Kato and Adachi,
350
2000). In the natural situation, there are additional processes that can compete with the
351
abrasional smoothing in determining fault surface topography.
352
For instance, the formation of splays can roughen a fault. If a slip surface coheres
353
due to chemical precipitation or other healing processes, splays can be formed in
354
preference to continued slip on the surface (Karner et al., 1997; Muhuri et al., 2003).
355
Such splays are particularly likely to form as Riedel shears within the weak damage zone
356
(Tchalenko, 1970; Childs et al., 1995). The rheologically distinct layer can deform under
357
pure shear and generate new branches and rhombic structures (Shipton and Cowie, 2001).
358
In addition to facilitating splay formation, the gouge immediately abutting the
359
principal slip surface has another potentially important contribution to re-roughening. A
360
weak gouge layer can have distributed flow throughout its volume and therefore distort
361
the edge of the zone that makes up the principal slip surface. Previous observations of the
362
correlation of near-fault comminuted layer thickness and fault topography support this
363
interpretation (Sagy and Brodsky, 2009). In those measurements the thickest areas of the
16
364
near-fault granular layer corresponded to anomalously high areas of the fault surface and
365
thin layer regions corresponded to troughs. As the comminuted rock ponds into regions of
366
varying thickness with progressive slip, the fault surface can be re-roughened.
367
One candidate process for re-roughening can be ruled out as the controlling process
368
for this particular observation. The linkage between en echelon fault segments is likely an
369
important part of fault formation, but cannot explain the data presented here. As faults
370
grow, they can link together segments through overlap structures that may result in
371
corrugations (Segall and Pollard, 1983; Ferrill, 1999). These relict overlaps will result in
372
an increase roughness in the slip direction at a scale comparable to the length of the fault.
373
Total offsets generally are on the order of 1-10% of the length of a fault (e.g., Dawers et
374
al., 1993; Scholz, 2002). Therefore, re-roughening by linkage during fault formation
375
would be important at the scales considered in Figs. 4-6 (L=0.25-1 m) only if the suite of
376
offsets spanned 0.25-10 cm. This range just abuts the minimum offset of our dataset
377
(Table 1) and therefore linkage during fault formation is not likely to be the principle re-
378
roughening mechanism observed here.
379
380
7. Conclusions
381
Slip parallel roughness gradually decreases with increasing slip at scales of 0.25-1 m.
382
The weak trend e.g., H~ D-0.1 is inconsistent with gouge volume increasing linearly with
383
displacement for a model in which an asperity is progressively worn down. The
384
observations require a decrease in gouge production with slip and/or a re-roughening
385
process during slip. Either possibility depends on the rheologically distinct layer in the
386
fault zone affecting the evolution of the slip surface. The generation of gouge
17
387
fundamentally changes the constitutive law of the fault zone. Its subsequent deformation
388
affects slip surface geometry and should be taken into account in modeling the wear and
389
evolution of faults.
390
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Acknowledgements We are grateful to A. Billi and F. Agosta for generous help in
392
locating suitable faults for study and in providing geological context for interpretation.
393
We also thank N. Van der Elst for field assistance and M. Steffeck and T. Babb for
394
creating SlugView. We particularly thank C. Scholz for an insightful review that
395
significantly improved our data interpretation.
396
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551
Appendix: Fault Displacement Constraints
552
A.1: Faults with Direct Displacement Measurements
553
Certain faults had well-exposed offset markers that allowed direct measurement of the
554
displacement. The precise markers used for offset are documented below to illustrate the
555
clear constraints for these faults.
556
557
Vasquez
558
Small oblique fault in arkosic sandstone in the Vasquez Rocks Natural Area Park in Los
559
Angeles County with 10 cm of slip as measured directly from stratigraphic offset.
560
561
Mecca Hills
562
Small strike-slip fault in the Box Canyon Wash of Mecca Hills, Southern California in
563
the San Andreas system (Sylvester, 1999). The 20 cm of slip was measured directly from
564
stratigraphic offset.
565
566
Split Mountain
567
Small strike-slip fault in Southern California, near the Salton Sea, with 30 cm of slip as
568
measured directly from stratigraphic offset.
569
570
Venere Small
571
Second order fault in marble quarry in Venere, Italy, with 4 m of slip as determined by
572
offset of a fossil marker bed.
573
26
574
Chimney Rock
575
Normal fault cutting through limestone near Chimney Rock, Utah, with 8 m of slip as
576
determined by direct measurements of stratigraphic offset.
577
578
Monte Coscerno
579
Oblique normal fault exposed near a gully off the highway from Sant’ Anatolia, Italy. A
580
displacement of roughly 250 m was measured because the fault juxtaposed the lower part
581
of the Maiolica formation (200 m thick) in the footwall against the Scaglia Bianca
582
formation (50 m thick) in the hanging wall. The Marne a Fucoidi formation (50 m thick)
583
is elided by the fault activity.
584
585
586
Figure A1: Cross-section perpendicular to strike of the Monte Maggio fault.
587
Monte Maggio
588
Large surface with 3 m exposed less than a month before scanning. Slip is about 650 m
589
determined by comparing exposed rocks in the footwall block (middle part of the Calcare
590
Massiccio formation, ≈ 600 m thick) and hanging wall (middle portion of the Maiolica
27
591
formation, 200 m thick). The Calcari Diasprigni and Bugarone formations (total thickness
592
170 m) are elided by the activity of the normal fault.
593
594
Val Casana
595
Normal fault exposed by a road cut near Sant’ Anatolia, Italy. The displacement is about
596
150 m since the fault plane juxtaposes the lower and upper part of the Maiolica
597
formation (200 m thick) in the footwall and hangingwall blocks respectively.
598
599
Yeelim
600
Oblique normal fault in carbonate rocks (mostly Dolostone) located on the western
601
margins of the Dead Sea Basin. The relatively fresh surface was revealed by quarrying.
602
Displacement is 50-80 m measured from offset stratigraphy (Lower Shivta and upper
603
Tamar formations are placed against Netzer formation).
604
605
606
A.2 Faults with Estimated Displacements
607
Other faults required more circuitous reasoning to roughly constrain the displacement.
608
Scarp height and fault length were among the tools use for these faults.
609
610
Venere Large
611
Normal fault in a carbonate quarry near Gioia Di Marsi in the Abruzzo region of Italy.
612
The main trace has hundreds of meters of displacement and was likely involved in the
613
1915 M7.0 event (Agosta and Aydin, 2006). The total fault displacement on the system
28
614
is about 600 m calibrated on seismic reflection profiles. This fault surface is one of the
615
principal strands observed at the surface, with an individual offset of at least 20 m.
616
However a precise value cannot be evaluated because of the lack of markers in the
617
hanging-wall and footwall blocks. Therefore this strand is only shown in the power
618
spectral density plot of Figure 2 and not used in the displacement-roughness regressions.
619
620
Cascia
621
Overhanging normal fault with the hanging wall exposed. The fault surface is covered by
622
a wire mesh fence that was manually removed from the scan. Displacement is about 50
623
m since the fault separates the Scaglia Bianca formation (50 m thick) in the hanging wall
624
from the Marne a Fucoidi formation (50 m thick).
625
626
Gubbio Upper and Lower splays
627
Both fault planes are splays of a fault zone that has 3 kilometers of total displacement.
628
The topographically higher splay juxtaposes the upper and lower portion of the Scaglia
629
Rossa formation (about 200 m thick) in the hanging wall and footwall block respectively.
630
The resulting fault displacement is 50-100 m. The lower splay separates the Scaglia
631
Variegata formation (50 m thick) in the hanging wall block from the middle-lower
632
portion of the Scaglia Rossa in the footwall block. Fault displacement is about 200 m.
633
Along this fault the 1984, Mw = 5.6, Gubbio earthquake occurred (Collettini et al., 2003).
634
635
Lake Mead
636
Large normal fault exposed in a dacite breccia in the River Mountain area near Lake
29
637
Mead in Nevada. Striated polished surface is exposed with 5 m of exposure along the
638
striation orientation. The fault present low-angle dipping of the surface is probably
639
because of late areal rotation. Displacement is roughly 500 – 1000 m (E.I. Smith,
640
University of Nevada, Las Vegas, 2006, pers. comm.).
641
642
Flower Pit
643
Part of the Klamath graben fault system in the northwestern Basin and Range (Personius
644
et al., 2003). The faults are exposed by recent quarrying, so are relatively unweathered.
645
Minimum displacement along a single slip surface is >50 m. Assuming middle
646
Pleistocene ages for the faulted volcanic rocks, and slip rates of 0.3 mm/yr (Bacon et al.,
647
1999), the cumulative displacement is probably no more than a few hundred meters. The
648
region is seismically active as demonstrated by a 1993 sequence of earthquakes that
649
included two Mw=6 events.
650
651
West Fucino
652
Located in the central Apennines at the Western edge of the Fucino Basin. The maximum
653
throw on the fault constrained stratigraphically is 250 m (DeVoto, 1970 as interpreted by
654
A. Billi, pers. comm.). An alternative estimate of the displacement comes from assuming
655
a range of displacement to length ratios of 1-10%. The mapped trace is 830 m which
656
provides a lower bound of the actual fault extent (DeVoto, 1970). Combining the above
657
constraints results in a best estimate of ~80 m displacement.
658
30
658
Table 1: Faults used for roughness measurements.
Fault Name
Location
Displacement
Lithology
Sense
Cascia
42.719° N 13.002° E
50 m*
Carbonate
Normal
Gubbio Upper
43.344° N 12.597° E
50-100 m*
Carbonate
Normal
Gubbio Lower
43.344° N 12.597° E
200 m*
Carbonate
Normal
Monte Coscerno
42.692° N 12.887° E
250 m
Carbonate
Normal
Monte Maggio
42.762° N 12.941° E
650 m
Carbonate
Normal
Val Casana
42.718° N 12.857° E
150 m
Carbonate
Normal
Venere Large
41.971° N 13.664° E
>20 m*
Carbonate
Normal
Venere Small
41.971° N 13.664° E
4m
Carbonate
Normal
West Fucino
41.940° N 13.362° E
~80 m*
Carbonate
Normal
Vasquez Rocks
34.483° N 118.316° W
10±5 cm
Sandstone
Normal
Yeelim
31.223° N 35.354° E
50-80 m
Carbonate
Normal
Split Mountain 33.014° N 116.112° W
30±15 cm
Sandstone
Strike slip
Mecca Hills
33.605° N 115.918° W
20±10 cm
Carbonate**
Strike slip
Flower Pit
42.077° N 121.856° W
100-300 m*
Andesite
Normal
Chimney Rock
39.227° N 110.514° W
8m
Carbonate
Normal
Lake Mead
36.062° N 114.831° W
500-1000 m*
Dacite
Normal
659
* indicates displacement estimated from non-direct means (see Appendix A.2). The
660
general term “carbonate” is used for a range of lithologies including dolostone, limestone
661
and marly limestone that can be interbedded and therefore both present at a single
662
locality. **Mecca Hills fault surface is directly on a layer calcite that is separate from the
663
underlying fanglomerate sequence.
31
664
a
665
b
666
Figure 1. Example fault surface and digital LiDAR data. (a) Photograph of West
667
Fucino Fault. (b) Digital point cloud imaged in SlugView with RGB colors from
668
photograph mapped onto the point cloud. Only pristine, uneroded areas of the
669
fault like that in the yellow box are used for the subsequent power spectral analysis.
670
On this fault, the yellow box is approximately 10 m long.
671
32
672
673
Figure 2. Power spectral density profiles parallel to slip calculated from 16 different
674
fault surfaces that have been scanned using ground-based LiDAR. Each profile
675
includes 100-1000 continuous, individual profiles from the best part of the fault.
676
Black dashed lines indicate a slope of β=3 for reference. Warm colors are small
677
slip faults and cool colors indicate large slip faults. Faults are arranged in the legend
678
in order of increasing offset. Noise level corresponds to manufacturer’s reported
679
horizontal and range precision of 4 mm.
680
33
680
681
a
682
b
683
Figure 3: Comparison of the height H calculated from the power spectral density
684
(eq. 4) and
685
Gubbio Lower Fault and (b) Venere Small Fault. (See Table 1 for documentation of
686
faults).
measured directly using deviation from segments of length L for (a)
687
34
687
688
a
689
b
35
690
c
691
692
Figure 4. Roughness as a function of displacement using three different metrics for
693
the full suite of faults. (a) Power spectral density at a wavelength of 0.5 m. Error
694
bars throughout the paper are the standard deviation of 1000 bootstrap trials. (b)
695
Height H calculated from the power spectral density with L= 0.5 (See eq. 4). (c)
696
Height
697
0.5 m.
calculated directly from mean deviation (RMS) of segments of length L=
698
36
699
700
a
b
37
701
c
702
d
703
Figure 5. Roughness metrics for range of segments length L. (a) RMS Height H
704
calculated from the PSD with L= 1 m (See eq. 4), (b)
705
0.25 m, (d)
with L=1 m, (c) H with L=
with L=0.25 m.
706
38
706
707
Figure 6. Roughness measured by H as a function of fault displacement for only the
708
faults with the best displacement constraints (See Table 1). H is estimated from
709
power spectral density with L=0.5 m (See eq. 4).
710
39
710
711
712
a
713
714
b
715
Figure 7. Monte Maggio Fault with both eroded and newly exposed surfaces. (a)
716
Photograph of the study area. (b) Power spectral density for eroded surface and
717
newly exposed surface. For comparison, faults with less than a meter slip are shown
718
(Mecca Hills, Split Mountain and Vasquez rocks). The small-slip faults are all
719
measurably rougher than the erosive surface.
720
40
721
722
Figure 8. Roughness measured by H for the carbonate-bearing faults only. H is
723
estimated from power spectral density with L=0.5 m (See eq. 4). The trend for the
724
restricted subset of data is the same as that for the full set (Fig 4b) to within error.
725
41
725
726
Figure 9. Cartoon illustrating the removed volume for gouge generation. The shaded area
727
is the volume of gouge Vg generated after smoothing the surface from height H0 to height
728
H. The area of the base of the removed zone is AH = LH w where w is the width of the
729
proturberance in the slip perpendicular direction. Note that as wear progresses, H
730
decreases and LH increases. The base of the figure is the centerline of the fault plane.
731
42
731
732
733
Figure 10. The difference between initial asperity height and worn height at a fixed
734
reference scale of 0.5 m. The initial height H0 is approximated using the immature fault
735
relationship H=0.01L (Fig. 2). For L=0.5 m, H0 is therefore 5 mm.
736
43