Strain Localization in Sandstone‐Derived Fault Gouges Under Conditions Relevant to Earthquake Nucleation

Constraining strain localization and the growth of shear fabrics within brittle fault zones at sub‐seismic slip rates is important for understanding fault strength and frictional stability. We conducted direct shear experiments on simulated sandstone‐derived fault gouges at an effective normal stress of 40 MPa, a pore pressure of 15 MPa, and a temperature of 100°C. Using a passive strain marker and X‐ray Computed Tomography, we analyzed the spatial distribution of deformation in gouges deformed in the strain‐hardening, subsequent strain‐softening, and then steady‐state regimes at displacement rates of 1, 30, and 1,000 µm/s. We developed a machine‐learning‐based automatic boundary detection method to recognize the shear fabrics and quantify displacement partitioning between each fabric element. Our results show fabrics oriented along R1 and Y (including boundary) shears are the two major fabric elements. At rates of 1 and 30 µm/s, the relative amount of displacement on R1 shears is displacement dependent, increasing to ∼20% of the total displacement up to the strain‐softening stage, then decreasing to ∼10%–18% at the steady state. This trend is absent at the high rate where ∼18% of the displacement occurs on R1 shears throughout all investigated stages. At all rates, the relative amount of displacement on Y shears increases linearly with displacement to a total of larger than 50% at the steady state. Our study provides constraints on the development of the active slip zone, which is an important factor controlling heating and weakening associated with small‐magnitude earthquakes with limited displacement (mm‐dm), such as induced seismicity.


Introduction
Field and borehole observations conducted on brittle fault zones have provided evidence indicating that fault cores frequently consist of fine-grained wear products, referred to as fault gouge, which are incohesive or have negligible cohesion (Chester & Chester, 1998;Collettini et al., 2009;Sibson, 1977Sibson, , 1986)).In addition, fault gouges often exhibit structural fabrics characterized by distinct distributions of grain size and shape, which can be attributed to the processes of grain fragmentation and wear occurring during fault slip.These fabrics are generally interpreted as indicators of strain localization in near planar zones where fault slip has been accommodated.Gouge fabrics can also be used to infer faulting mechanisms (Boullier et al., 2009) and estimate stress states after earthquakes (Kuo et al., 2022).Comprehending the phenomenon of strain localization and the evolution of shear fabrics within brittle fault zones holds paramount importance, as these shear fabrics bear direct implications for evolution of shear zone fabrics within sandstone-derived fault gouges utilizing the X-ray CT technique • Our samples show similar evolution of shear fabrics, slip partitioning, and mechanical response with shear strain at all tested velocities • Up to 50% of the total imposed displacement can be accommodated within shear-parallel shear bands during earthquake nucleation Supporting Information: Supporting Information may be found in the online version of this article.
Laboratory friction experiments have shown that natural shear fabrics can be reproduced in experimental fault zones from subseismic (V < 100 μm/s; e.g.Beeler et al., 1996;Bedford & Faulkner, 2021;Haines et al., 2013;Logan, 1979;Mercuri et al., 2018;Moore & Byerlee, 1991, 1992;Noël et al., 2023;Volpe et al., 2022;Wojatschke et al., 2016) to seismic rates (V > 1 m/s; e.g.Kuo et al., 2014;S. A. F. Smith et al., 2013).At earthquake nucleation velocity (i.e., of order 1 μm/s), Logan et al. (1992) systematically reported on the evolution of experimental shear fabrics within simulated calcite gouges with variable gouge thicknesses, shear strains, and confining pressures.To identify the development of gouge fabrics and to quantify the amount of displacement that is accommodated on these fabric elements, as well as to elucidate any correlations to the mechanical behavior, they used a 1-mm thick layer of hydrocarbon-coated calcite gouge with a black color as a strain marker within regular white calcite gouges.They observed that the simulated fault gouges developed four major fabric elements, that is, R 1 , R 2 (e.g., Riedel, 1929), P, and Y shears (akin to boundary shear denoted as B) in a repeatable and predictable manner, evolving with increasing shear strain, without explicitly defining the B shear separately.A general observation is that the onset of localization (i.e., R 1 and R 2 shear) occurs during an initial strain-hardening phase and is accompanied by gouge dilation.As a result, the dilatancy of the sample and the development of R 1 shear planes accommodate most of the deformation (Logan, 2007;Logan et al., 1992).Strain softening or occasionally unstable sliding follows, during which the strain shifts to be accommodated within shear-parallel shear bands (i.e., Y or B shears), developed due to the presence of rigid boundary walls and rotation of the stress field (Bedford & Faulkner, 2021;Haines et al., 2013;Logan et al., 1992;Niemeijer et al., 2020;Scuderi et al., 2017).Haines et al. (2013) studied the evolution and development of gouge fabrics within clay-rich fault gouges at a similar range of shear strains but a larger range of normal stresses.They demonstrated that the fabric elements evolved in a systematic manner, from Riedel shear along R 1 orientations at low strain to shear-parallel Y (and B) shear bands at high strain, where clay particles could accommodate strain within multiple narrow Y or B surfaces without much grain size reduction.However, studies of gouge microstructure evolution with displacement remain relatively limited, not to mention the quantification of displacement partitioning between these fabric elements and the bulk gouge.This is primarily due to the time-consuming nature of conducting multiple experiments achieving different displacements, using identical starting materials and consistent conditions, followed by the analysis of resulting microstructures.Therefore, it remains poorly understood how the total fault slip is distributed over these fabric elements, particularly in quartz-rich gouges, during fault acceleration, that is, at varying slip velocities such as during earthquake nucleation.
In this study, we systematically investigate how strain localization evolves at different frictional stages (i.e., during an initial strain-hardening stage, subsequent strain-softening stage, and then steady-state stage) and at varying imposed displacement rates, using Slochteren sandstone gouges (SSG, i.e. simulated, quartz-rich gouges) retrieved from the Groningen gas field, located in the Northeast of the Netherlands.We chose Slochteren sandstone as starting materials because it is the main reservoir lithology and hosts most induced events in the Groningen field (e.g., Dost & Haak, 2007;Dost et al., 2020;J. D. Smith, 2019;Spetzler & Dost, 2017;Van Eijs et al., 2006).All friction experiments were performed at an effective normal stress of 40 MPa, a pore fluid pressure of 15 MPa, and a temperature of 100°C, which is comparable to the in situ reservoir conditions in Groningen.Three different shearing velocities of 1, 30, and 1,000 μm/s were employed to simulate different frictional stages during fault slip acceleration from subseismic slip rates leading to instability (i.e., an earthquake).The key aim is to understand how displacement partitioning between different shear fabrics depends on shear displacement and displacement rate, as well as how this affects the associated mechanical response.In addition, the results may provide important constraints on the development (thickness) of the active principal slip zone, and on the heat budget associated with small-magnitude earthquakes with limited displacement (mm-dm), such as induced seismic events in the Groningen field.

Starting Materials
We used crushed Slochteren sandstone obtained from the Groningen gas field, as the starting material (courtesy of the field operator, the Nederlandse Aardolie Maatschappij BV-NAM).The Slochteren sandstone, sourced from the core of the Stedum 1 (SDM-1) borehole, served as the material of interest.Sandstone cores, extracted both above and below the gas-water contact (GWC, at a depth of ∼2,980 m below the surface during drilling), were crushed into a powdered form using a jaw crusher.The resulting powder was employed as the starting material to simulate the fine-grained gouge product typically found within the principal slip zones of natural fault zones (Chester & Chester, 1998;Sibson, 1986), such as those hosting induced seismicity in the Groningen gas reservoir.Note that the resulting powder, derived from the core below the GWC, may contain some salts because the highsalinity brine present in the core upon recovery resulted in salt precipitation in the pore space during core storage.The grain size distribution of the crushed materials is characterized by a mean grain size of ∼25 μm with a maximum grain size up to ∼200 μm where approximately 80 wt% of grains are smaller than 50 μm (see Figure S1 in Supporting Information S1).The mineral composition of the Slochteren sandstone gouge (SSG) consists of ∼75 wt% quartz, ∼12 wt% feldspar, minor amounts of clay minerals (∼5 wt%, kaolinite, and phengite), carbonates (∼5 wt%), and other minerals (∼3%).The composition given here is the average value of the mineral composition of the SSG below and above the GWC as reported by Hunfeld et al. (2017).Around 2.86 g of the SSG materials were used to produce a roughly 1 mm thick gouge layer for direct shear testing (Figures 1a-1c).
To visualize strain distribution within simulated gouge layers after deformation, we added a ∼5 mm wide (∼0.34 g), 1 mm thick gouge strip of pure albite, with a grain size <106 μm, as a passive strain marker to the middle of the SSG layer (∼2.86 g) (Figures 1a-1c).The use of the albite can provide significant gray-scale intensity contrast versus quartz, in X-ray Computed Tomography (XCT) scans, to allow the identification of a visible boundary before and after the shearing experiment (Figure 1d).In addition, the use of a minor amount of albite has a negligible impact on the mechanical behavior of the material (see Figure S2 in Supporting Information S1).

Direct Shear Experiments
To conduct the experiments, we utilized a direct shear assembly (Figure 1e) incorporated within a conventional triaxial apparatus known as the Shuttle apparatus, located in an Instron 1362 loading frame (as described by Verberne et al. (2014)).The simulated fault gouge layers of approximately 1 mm thickness were sandwiched between two L-shaped pistons with individual dimensions of 35 mm in diameter by 70 mm total length, containing a 35 mm × 49 mm, grooved piston face (in contact with the sample), a 35 mm × 9 mm smooth surface, plus a cylindrical 35 mm × 12 mm end-piece.To minimize the rebound effect of the pistons during the unloading process, we use a heat-shrink FEP tube and a silicone polymer ("silly putty") as the outer confining jacket and the spacer material, respectively.A total of 15 experiments were performed, including 14 constant-velocity experiments and one velocity-stepping experiment, conducted at a confining pressure of 55 MPa, a pore fluid (De-Ionized water, DI water) pressure of 15 MPa (drained conditions), and a temperature of 100°C, to simulate the in situ reservoir conditions in Groningen (Hunfeld et al., 2017(Hunfeld et al., , 2020)).Due to the presence of salts in the SSG, any salts present in the SSG presumably would dissolve in the DI water in the experiments, which would lead to slightly salty water for all experiments.The piston set, including the simulated fault, was subjected to loading at a constant displacement rate, using the Instron 1362 electro-servo-controlled loading frame.Silicone oil was employed as the confining medium during the experiments, and the application of confining pressure was initially achieved using a compressed-air-driven diaphragm pump.The confining pressure and pore fluid pressure were controlled by an ISCO pump.Heating was facilitated through the utilization of a Thermocoax internal furnace.The temperature control was implemented using a three-term CAL2300 industrial controller, which allowed precise regulation within 0.1°C of the designated set-point temperature.The temperature of the sample was monitored using a thermocouple that penetrated the upper direct shear piston and reached a position within 24 mm of the sample layer.In our experimental setup, the application of shear stress to the gouge layer was accomplished by advancing the loading piston within the Shuttle vessel.Before shearing, all tested samples remained pressurized at the targeted conditions for at least 12 hr to ensure thermal and pressure equilibration as well as chemical equilibrium between soluble phases in the sample and the pore fluid.
Throughout each experiment, data on axial load, piston displacement in the axial direction, confining pressure, temperature, pore fluid pressure, and pore fluid volume were collected at a logging rate ranging from 10 to 100 Hz.Shear stress (τ) was calculated by dividing the internal axial load by the contact area of the shear surface, which was assumed to be equal to the initial contact area.The apparent coefficient of sliding friction (μ app ) was determined as the ratio of τ to the effective normal stress (σ n eff ), under the assumptions of zero cohesion as described by Byerlee (1978) and uniform pressure in the pore-fluid/sample system.The maximum error in the effective normal stress (σ n eff ) was within ±0.004 MPa.Since P c is always equal to σ n in the current testing assembly, the effective normal stress, defined as σ n eff = P c -P f , was equal to 40 MPa in all experiments.Measured displacement was corrected for machine stiffness yielding data with an error within 20 μm.
With the aim of investigating the partitioning of displacement at different stages of the shear stress τ versus displacement curve, and at different slip velocities, we analyzed deformed samples produced in experiments stopped after (a) 1.3 mm of displacement corresponding to the attainment of the peak stress, termed as the "strainhardening stage," (b) 2.1 mm of displacement after the peak stress (i.e., 3.4 mm total displacement), termed as "strain-softening stage," and (c) 5.5 mm of displacement corresponding to the steady-state stage, under slip velocities of 1, 30, and 1,000 μm/s.Figure 2 shows a schematic diagram of the evolution of the shear stress against displacement with the three corresponding frictional stages.The experiments performed are listed in Table 1, along with the conditions and key information.We additionally conducted a velocity-stepping experiment with velocity steps to 1-30-1,000-30 μm/s, each over a displacement interval of 1-2 mm (see Figure S2b in Supporting Information S1), for control purposes of the mechanical strength on the pure SSG.
After each experiment, the length of the sample assembly was measured, and the entire assembly was oven-dried for at least 7 hr.The length change of the sample assembly before and after each experiment is defined as the external shear δ for the gouge sample.Subsequently, the direct shear setup was disassembled, and intact fragments of the sheared gouge layers were retrieved for further microstructural analysis.We carefully collected the fragments of the deformed gouge sample containing the albite-SSG boundary.To make the sample more cohesive, we added a few drops of Paraloid B72 binder in 10% Acetone to the sample and let it air-dry for at least 10-15 min.The dried samples were then glued on the tip of pencil leads or toothpicks for X-ray computed tomography (XCT) analysis (Figure 1c).For clarity, we define the width, length, and thickness of the gouge sample as the x, y, and z directions, respectively (Figure 1c).

X-Ray Computed Tomography (XCT) Scan
A Zeiss Versa 610 XCT Versa high-resolution microscope system was used to investigate the microstructures of the samples.This provides mm-scale observations of the orientation of the shear band and fracture arrays within the deformed gouge sample.In addition, the scan provides 2-D projections and 3-D imaging of the sample without damaging the sample.For each XCT run, the sample with pencil lead (or toothpick) was mounted vertically on a sample holder and installed in the XCT machine between the X-ray source and detector.
We used a detector with an objective of 4X magnification and applied an Xray beam with a voltage of 60 kV and a power of 6.5 W to the sample with an exposure time of 20 s.These conditions, together with the distance between the sample and detector, provide a square field of view of dimension 5 mm and an image resolution of ∼2.5 μm per pixel.Based on the field of view and pixel resolution, we exported an average number of ∼2,000 2-D slice images for each sample.

Automatic Boundary Detection and Quantification of Slip Localization
We employed a custom-designed machine-learning (ML) trainable segmentation tool from "scikit-image," an open-source image processing library (available at https://scikit-image.org/; Van der Walt et al., 2014), to develop our automatic boundary detection method.This was used to identify the albite-quartz boundary for more than hundreds of XCT images for each sample.Trainable segmentation is a pixel-based segmentation method computed using local features and a "random forest" approach (Ho, 1995).We first pre-defined the albite and the SSG regions to train a random-forest classifier.Based on local intensity and textures at different scales, the pixels of the mask were trained to obtain a classifier (e.g., Kreshuk & Zhang, 2019;Pedregosa et al., 2011).The trained classifier can then automatically identify and predict the unlabeled pixel content in the remaining SSG region.This allows segmentation boundaries, inferred by the classifier between the albite gouge and the SSG, to be subsequently and automatically retrieved.With this ML-based segmentation approach, we can significantly displacement, alongside corresponding frictional stages from strainhardening to strain softening (for over-compacted samples), and to steadystate stages, as typically observed for (simulated) fault gouges deformed at a constant (nucleation-relevant) shearing velocity (e.g., Logan et al., 1992).
The blue curve represents an over-compacted gouge sample, that is, one which dilates as shear stress increases.The green curve represents an undercompacted gouge sample without a peak stress at the onset of shear deformation.Note that the second stage is still strain hardening for the under-compacted example, as observed in our mechanical data.Note.All the experiments were conducted at a confining pressure of 55 MPa, a pore fluid (DI water) pressure of 15 MPa (drained conditions), and a temperature of 100°C.We took the friction coefficient reached at the strain-hardening stage μ hardening as "peak" friction μ pk .V = the slip velocity.Disp.= the total imposed displacement.μ hardening = the apparent friction coefficient measured at the strain-hardening stage.μ softening = the apparent friction coefficient measured at the strain-softening stage.μ ss = the apparent friction coefficient measured at the steady-state stage.ΔP max = the maximum pore fluid pressure increase measured from the ISCO pump during shearing.Figure 3 shows the workflow of the automatic boundary detection and localization quantification method.The entire procedure is divided into six main steps: 1.For each analyzed sample, we first picked five images out of the total images that have equal intervals of image number in the space domain of the entire analyzed width of the sample, as the standard images for training the segmentation.For each of the five images, we labeled the albite gouge and the SSG regions by drawing masks (blue and green rectangles for albite gouge and SSG, respectively) to automatically find the main color boundary (yellow curve) (Figure 3b).One thing to note is that some samples show extremely thin B shears which are too thin to be identified with the current resolution.To circumvent this problem, we did not consider these B shears during the automatic detection procedure.The amount of displacement along B shears for each experiment was determined as the difference between the external shear δ and internal shear L, determined by the projected length of the albite-SSG boundary (without B shear) on the gouge-forcing block boundary.This relation is schematically illustrated in Figure S3 in Supporting Information S1 and will be further discussed in Section 4.3.1.The displacement along the B shear is added to the internal shear L and Y shear afterward when quantifying displacement partitioning between deformation features.2. To remove spurious boundaries, we used the Density-Based Spatial Clustering of Applications with Noise (DBSCAN; Ester et al., 1996) clustering method to retrieve the albite-SSG boundary with the highest density of clusters (Figure 3c) 3. We applied a moving average with a moving window of 4 (pixel) and a window step size of 1 (pixel) to the high-density cluster to perform the first step of smoothing (Figure 3d). 4. We applied the Ramer-Douglas-Peucker (RDP) algorithm (Douglas & Peucker, 1973;Ramer, 1972), a nonparametric line fitting and turning point (i.e., point of max curvature) detection method, to reduce the number of points in the boundary curve and performed a second smoothing and to subsequently identify the turning points (Figure 3e).The degree of simplification of the fitted curve is controlled by the "tolerance" parameter, which defines the maximum allowable deviation between the simplified path and the original path (i.e. the smoothed curve from step 3).As the tolerance value increases, the resulting simplified path becomes coarser or less refined in its representation.The determination of the turning points of the boundary curve is controlled by a minimum angle (between 0 to π in radians).If the angle between the direction vectors on the simplified curve is larger than the defined minimum angle, we consider the point where the direction vector changes as the turning point.We selected a tolerance level of 5 (maximum distance with five pixels) and a minimum angle coefficient of 0.05 (minimum angle = 0.05 × π) for the line fitting and the turning point detection.These selected values provide good consistency of the turning points between the manual identification and the automatic detection (Figures 3a and 3e). 5.After the boundary and turning points were identified, we adopted the same methods used by Logan et al. (1992) to assess strain partitioning between different deformation features (e.g., homogeneous deformation vs. R 1 , and Y shears) and to quantify the amount of displacement on each feature.We define R 1 shears as bands oriented in a range from 45 to 3°relative to the gouge-host block boundary (clockwise rotation from the shear direction to be positive), as previous experimental studies have shown that R 1 shears can be nearly parallel to the shear direction at the shear-zone boundary but become larger further away from the boundary (e.g., Verberne et al., 2014).For the definition of a Y shear, we selected the angle ranging from 3 to +3°relative to the shear direction.Figure 3f shows that the displacement accommodated by homogeneous/ distributed deformation, slip on R 1 , and slip on Y shears, obtained from both the automatic and manual methods have a good consistency.Manual identification of the marker boundary and localization quantification is a crucial process we applied to validate the training data.Here, we defined good consistency such that the displacement tolerance misfit for a specific deformation feature between the automatic and manual results is within a pre-defined value of 10%.Once the results of the first five images of the manual and automatic methods are consistent, we further applied identical trainable segmentation conditions to another five images as the validation data to examine whether the segmentation boundary produced by the segment classifier is acceptable and does not produce much overfitting.This is another validation process, which is further illustrated in Supporting Information S1 (see Text S1; Figures S4 and S5). 6.Finally, we fit the rest of the images with the segment classifier and run the same procedure (indicated by the pink arrows).Figure 3g shows the total displacement and the displacement partitioning between homogeneous, Y, R 1 , and R 2 shears as a function of slice number.The interval between slices is equivalent to 1 pixel resolution which is 2.54 μm in this case.Despite identical segmentation conditions, we still obtain a few discontinuous segmentation boundaries which can be easily identified in both the total displacement and the Journal of Geophysical Research: Solid Earth 10.1029/2024JB028889 HUNG ET AL. output images.For example, in some slices, the segmentation boundary was not detected to be a continuous cluster as compared to the good example.We used the Z-score to remove these outliers to obtain the final result, as shown in Figure 3h.

Frictional Behavior
All the experiments exhibit a similar evolution of apparent friction coefficient μ app with displacement, but for small variations with displacement rate, as exemplified in Figure 4.Note that the displacement shown here has been corrected for the elastic deformation of the apparatus.After initial loading (sample settling), μ app shows a rapid and near-linear increase, reaching an apparent yield point (departure from linearity) within the first ∼0.5 mm of displacement.This is followed by hardening toward a broad peak friction μ pk and subsequent softening toward a roughly linear softening stage then to a "steady-state" friction μ ss .At the displacement rate of 1,000 μm/s, we notice that the μ app at the strain-hardening stage (∼0.59) is lower than at the strainsoftening stage (∼0.62).For the purpose of comparison, we take μ pk as the μ app reached at the strain-hardening stage for all the experiments (Figure 4).In addition, since "steady-state" sliding was not attained in all the experiments, we take μ ss as the minimum μ app reached during or after the strain-softening stage (i.e., at around 5.5 mm displacement).Overall, μ pk at 1 and 30 μm/s lies at ∼0.63, which is slightly larger than that at 1,000 μm/s (∼0.59).Values of μ ss of ∼0.59-0.6 are achieved at all velocities.Our results show good reproducibility of the μ versus displacement curves obtained at 1 and 30 μm/s, while curves obtained at 1,000 μm/s generally show lower strength at any given displacement, especially at 0.5-3 mm displacement (Figure 3 and Figure S2 in Supporting Information S1).On the other hand, in this displacement range at 1,000 μm/s, we observed a sharp pore pressure increase by up to ∼0.5 MPa, peaking at a displacement of 0.8 mm followed by a steady decrease and ultimate approach to subbackground levels (i.e., ≤15 MPa).The observed maximum fluid pressure increase ΔP max for each experiment is summarized in Table 1.

Macroscopic Observations
After dismantling the L-shaped pistons, most of the gouge samples remained attached to one of the two forcing blocks (left pictures in Figures 5-7).In general, we found that the completeness (i.e., physical integrity) of the recovered sample depends on the imposed amount of shear strain.Most samples deformed into the strainhardening and strain-softening stages show a high degree of completeness (i.e., splitting occurred along one of the sample-forcing block boundaries).However, the gouge samples sheared to large displacement disintegrated into cohesive fragments within the central portion of the albite gouge layer, splitting along shear-induced fabrics aligned with the shear planes in R 1 type Riedel shears, and attaching to both forcing blocks (Figures 6f and 7a, 7c,  7f).In addition, most of the samples show an extremely thin layer of the albite gouge smeared on top of the SSG layer at the gouge-forcing block boundary, which indicates the development of a boundary shear (Figures 6f and 7a,7c,7f).The sampling location at the boundary of the gouge layer is nearly identical for each experiment, as indicated by the red rectangles in Figures 5-7.

X-Ray CT Microstructural Observations
The pictures on the right in Figures 5-7 show representative XCT images of the gouge microstructures.All samples show a clear gray-scale intensity boundary between the albite gouge (dark gray area) and the SSG (light gray area).The presence of groove imprints observed at the boundaries of the cross sections is attributed to the porous plates of the forcing blocks.This observation suggests complete (local) sample recovery at the gougeforcing block boundary, as shown in Figure 5b.In the shear zone, we observed that R 1 shear and Y shear (including B shear) are the two major shear fabrics at all frictional stages, while none of the samples exhibited a  shear band in the P orientation.The criteria used to define these two shear fabric elements were based on the following observations: (a) if a developed band (or fracture) is orientated as defined in the automatic localization quantification, and/or (b) if the albite-SSG boundary is offset by the corresponding shear sense.Note that most of the identified R 1 shears do not cause visible offset to the marker boundary (Criterion 2) because they often develop without accommodating much displacement.For a Y shear, both criteria must be satisfied because a shear-parallel fracture present in either the albite or SSG layers might result from opening during sample recovery.We did not consider grain size reduction as an essential criterion to determine the localization feature because in some cases we do not observe significant grain size reduction on R 1 or Y shear planes while they do offset the marker boundary; for example, the Y shear observed in Figure 6c (the toward center one).
In the strain-hardening stage, we see that the samples at all displacement rates do not show evident offsets of the marker boundary, but rather a fracture array orientated along R 1 shear with an angle of about 30 to 40°to the shear direction (Figure 5).Though virtually no displacement was visible along these R 1 shears, some grain size reduction can be observed (Figures 5e and 5f).Despite the absence of an offset of the albite-SSG boundary, we note that the angle of the marker boundary to the shear direction does not completely follow the expected simple shear angle (i.e.∼45°boundary rotation in this sample with shear strain around 1).At 1,000 μm/s only, we observed one B shear also occurred, accompanied by visible grain size reduction and smearing of an extremely narrow SSG layer (less than 50 μm thick) (Figures 5h and 5i).
In the strain-softening stage, samples deformed at all displacement rates exhibited offsets developed along the marker boundary with an angle of about 15°to 20°relative to the shear direction (Figure 6).R 1 and Y shears are easier to distinguish in this stage at all velocities.Displacement along the top and bottom boundaries of the shear zone is also visible together with zones of grain size reduction, which is particularly significant at velocities of 1 and 30 μm/s (Figures 6b, 6c, and 6e).The nearly vertical opening cracks observed at 1 μm/s result from sample recovery/handling (Figures 6b and 6c).
At the large-displacement or steady-state stage, more abundant Y and B shears developed at all velocities.In the B shears, the marker boundary was further smeared out, and an extremely thin (∼few microns) localized layer that can be clearly identified (Figure 7e).The R 1 shears remain observable, especially at the displacement rates of 1 and 30 μm/s (Figures 7b and 7d), while the angle of some R 1 shears becomes lower with an angle of less than 10°(Figure 7d).

Quantification of Displacement Partitioning
Figure 8 shows the image-inferred partitioning of displacement between different shear features across the analyzed sample length after removal of the outliers.Overall, the proportion of the outliers is less than 10% of the total number of images.The slice number from small to large indicates the analysis from the gouge boundary toward the center.The total displacement (blue dots) and Y (B) shear (green dots) shown here include the B shears (the difference between L and δ) which were not considered during the automatic boundary detection procedure.
Here, we should note that there is a clear increase in variability of displacement, particularly for the shear features, from the strain-hardening stage to the steady-state stage; in other words, the determined displacement becomes less horizontally stable (across slices, i.e. a larger variation in the amount of displacement).The reason for this will be further discussed in Section 4.2.In general, the amount of displacement, for all shear features, and the microstructurally resolved total displacement increase with increasing displacement at all velocities.An exception is the experiment at 1 μm/s at the steady-state stage, which shows a decrease in the total displacement from the softening to steady-state stages.This mainly results from the missing boundary shear which is difficult to identify with the automatic boundary detection method, as mentioned in Section 2.4.
Along the entire analyzed width of the sample, we do not observe significant variation in the displacement partitioning between the shear features, though the results seem in contrast with few observations of the XCT Figure 5. Macroscopic (left) and microstructural (right) observations of gouge samples deformed at displacement rates of (a-c) 1 μm/s, (d-f) 30 μm/s, and (g-i) 1,000 μm/s in the strain-hardening stage.The pictures on the left show the appearance of the deformed gouge after dismantling the L-shaped pistons.The sampling location for the XCT analysis is indicated by the red rectangle.The images on the right show representative XCT images of the deformed gray-scale color boundary between the albite gouge (dark gray) and Slochteren sandstone gouge (light gray).The groove imprint is indicated by the yellow dashed line in (b).In general, R 1 shear bands are the dominant localization feature without accommodating much displacement.Some Y (or B) shear also developed, as indicated, particularly at higher slip velocities (e, h).
microstructures (e.g., Figures 6b and 7g) which show more B shears developed at the sample boundary.In other words, the results do not reveal an observable increasing trend in the amount of displacement for Y shear with increasing slice number.Thus, we determined the spatial average and standard error of displacement for each deformation features.
The compiled data of the characteristics of the albite-SSG boundary and the displacement partitioning for the different deformation features for the nine experiments, are summarized in Table 2.We note that the external shear δ, in all experiments, is shorter than the elastically corrected imposed shear D. The amount of variation (D-δ) increases with D from 0.26 to 0.35 at the strain-hardening stage to 0.55-0.78at the steady-state stage.In addition, some experiments show L/δ larger than 1.These observed variations will be discussed in Section 4.3.
In Figure 9, we show the relative amount of displacement attributable to homogeneous deformation, R 1 shear, and Y shear (including B shear) at slip velocities of 1, 30, and 1,000 μm/s.Each deformation feature exhibits a similar evolution with increasing displacement regardless of the slip velocities.During the period of strain-hardening stage, over 80% of the total displacement is homogeneously distributed within the bulk gouge layer without Macroscopic observations show that all recovered samples split along R 1 shears, and a small portion of the albite gouge is attached to the gouge-forcing block boundary.The microstructures are similar to the ones in the strain-softening stage (Figure 6) while gouge smearing with only few microns thick at the gouge-forcing block boundary and grain size reduction becomes significant at all velocities.One thing to note is that only the sample deformed at 1,000 μm/s shows spatial variation with respect to the deformation where the cross section at the sample boundary (g) shows a better developed boundary shear than the one close to the center (h).much displacement on localized features (<10%), with the exception of the 1,000 μm/s experiment, which shows a slightly larger amount of localized displacement (∼16%-18%), occurring along both R 1 and Y shears.From the strain-hardening to the strain-softening stages, displacement attributable to homogeneous deformation continuously increases, while R 1 and Y shear bands start to accommodate a larger proportion of displacement (20%-30% and 16%-19%, respectively).From the strain-softening stage to the steadystate stages, the relative amount of displacement due to homogeneous deformation remains nearly constant without much variation.Instead, a large proportion of the displacement, up to 50% of the total displacement, is localized along the Y shears.

Comparison With Previous Mechanical Data
We compare our mechanical results with those reported by Hunfeld et al. (2017) who conducted experiments with nearly identical starting materials and experimental conditions.Few differences in terms of the experimental methods are that (a) we added a ∼10 weight % of albite gouge layer to the SSG layer obtained from cores from both above and below the GWC interface while they tested both separately; (b) we used SSG with 20 wt% of grains larger than 50 μm while they used a grain size overall less than 50 μm; (c) we performed experiments at a single velocity in contrast to velocitystepping experiments.Both our and their mechanical data display comparable frictional characteristics with a strain-hardening stage, a strain-softening stage, and a steady-state stage (linear softening stage).
At a displacement rate of 1,000 μm/s, our samples show a slight decrease in both μ pk and μ ss down to 0.59, suggesting a velocity weakening/neutral behavior between 30 and 1,000 μm/s, as also observed in a velocity-stepping experiment that we performed for control purposes on the pure SSG (Figure S2 in Supporting Information S1).We observed that the μ app in the strainhardening stage (∼0.58-0.60) is lower than in the strain-softening stage (∼0.60-0.61),indicating a delay in the generation of peak friction.The development of peak friction is associated with gouge dilatation at the onset of shearing (Bos & Spiers, 2001;Marone et al., 1991;Niemeijer et al., 2020).In all the experiments at V = 1,000 μm/s, the amount of final gouge compaction is similar (approximately 200 μm, see Table S1 in Supporting Information S1), with a minor dependence on the imposed shear strain and displacement rate.This suggests that the bulk of the gouge compaction occurred already during the initial slip (i.e., during strain hardening), regardless of the final imposed displacement.However, we observed an instantaneous pore fluid pressure increase up to ∼0.5 MPa, measured externally, at initial slip at a displacement rate of 1,000 μm/s (Figure 4).The minor observed fluid pressure increase is suggested to result from shear-induced compaction because the gouge layer was insufficiently drained under these relatively high-velocity conditions.Thus, the delay in the generation of peak friction might be explained by the observation of an increased pore pressure, which suggests compaction during initial sliding as opposed to dilatation.We also note that samples s015 and s053 exhibit relatively low peak values (0.53 and 0.5, respectively) as compared to samples s052, s055, and s057 (0.6, 0.59, and 0.58, respectively, Table 1), while the ΔP max does not exhibit strong variations between these experiments.Since the measured pore fluid pressure increase is a macroscopic measurement with quite a distance from the gouge layer, the local pore pressure changes might be much more variable from experiment to experiment.This could explain the variability in apparent peak friction.To sum up, the peak strength should depend on (a) initial porosity of the gouge layer and (b) possible local pore pressure increases due to sample compaction and the drainage of the environment.Variability in the peak strength due to the latter reason could be the result of variable drainage paths for the local pore pressure (affected by the presence of the albite marker).
On the other hand, we note that the delay in the generation of peak friction and fluid pressure increase are not observed in the pure SSG experiment (Figure S2 in Supporting Information S1).This suggests that the presence of the albite marker only seems to affect the initial slip behavior at the highest displacement rate investigated.The reason for the above observations could be that the albite marker allows for a higher initial porosity after the precompaction so that shear-enhanced compaction with fluid pressurization can occur.As mentioned before, this compaction behavior only influences the initial frictional behavior and occurred only at 1,000 μm/s.Also, the strain-hardening-stage gouge microstructure at this velocity is comparable to those at lower velocities (Figure 5).Thus, we argue that the added albite gouge had a minor influence on the gouge microstructure, if at all, despite the difference in the value of μ pk .Similar frictional behavior close to this velocity range (i.e., 1-1,000 μm/s) was also observed in previous room temperature studies on different materials (e.g., Mair et al., 2007).Overall, our mechanical results show good reproducibility and consistency compared to the published data (Hunfeld et al., 2017).

Reliability of the Automatic Boundary Detection Method
As far as we are aware, our study is the first to investigate the evolution of shear fabrics within quartz-rich fault gouges utilizing the X-ray CT technique.Unlike optical and SEM analysis, XCT scanning avoids artifacts resulting from epoxy-impregnation, cutting, and polishing of the sample, as well as providing the spatial strain distribution across the gouge layer (quasi-3D) (though a few papers have produced SEM without using epoxy resin- Haines et al., 2013;Wojatschke et al., 2016).To automatically identify the boundary between the albite gouge and the SSG for thousands of XCT images, we developed an automatic boundary detection method based on machine learning.This segmentation approach is shown to be effective and efficient in retrieving the boundary from most of the images, which is needed for the quantification of slip partitioning, that is, to identify localization (Section 2.4; Figure 4 and Figure S4 in Supporting Information S1).The relatively few proportions of the outliers with less than 10% (Figure 8) indicate that more than 90% of the boundary detections are reliable.The main reason for the outliers is due to the development of fractures, either during shearing, unloading, or sample recovery, that crosscut the interface which is then incorrectly registered as a discontinuous boundary by the trainable segmentation (see Figure S4f in Supporting Information S1 for example).In addition, sample recovery becomes more difficult when the sample has experienced more shear strain, as more fractures develop either during shear or upon unloading.Some parts of the gouge layers would stick to the piston, which likely results from the thinning of the gouge layer due to the shearing.This increases the likelihood of internal splitting, rather than splitting on the gouge-forcing block boundary, which may explain why we observe more outliers in experiments stopped in the steady-state stage (Figures 8c, 8f, and 8i).
Another possible factor that could affect the automated analysis is related to the variation in the intensity of grayscales across the analyzed regions.Local intensity has much higher importance than local textures and edges in the trainable segmentation method (van der Walt et al., 2014).For most of our recovered samples, their width (x-direction) is not uniform across the sample length (y-direction).Thus, even in an identical cross section, the average gray-scale intensity of the same material (i.e., quartz) within the cross section might be slightly different due to variations in the recovered gouge width or thickness.This variation is likely to be more significant when sample recovery is poor.Because we only applied one classifier trained from a few images to fit the rest of the images for each experiment, undesired segmentation outcomes can also result from variations in average intensity between cross sections.In summary, the present method offers a reliable method of boundary detection, with less than 10% of detections being rejected by the outlier filter.To further improve segmentation quality, future improvements in image pre-processing could be made within the framework of automatic boundary method; for example, by employing fracture suturing or intensity adjustment.This, in principle, can be done relatively easily, if only processing a few images, but becomes more challenging when dealing with more than hundreds or thousands of images-thus demanding further application of efficient machine learning tools for these purposes.

Localization Quantification
The results of the localization quantification are based on the fabric elements observed along the marker boundary rather than within the sandstone powder layer.One concern that might be raised is whether the microstructure produced from the marker boundary is representative of that produced within the sandstone domain due to the differences in the material and/or grain size (distribution) properties.This is difficult to examine because (a) the strain marker itself should be chosen as a material that has a contrast to the starting materials in imaging in order to be able to visualize the strain distribution, and (b) in the absence of a strain marker, localization of deformation can only be inferred from locations where grain size reduction occurred.To examine the effect of marker properties on shear zone development, we also experimented with white quartz powder as a strain marker with comparable grain sizes to SSG and observed the marker boundary deformation using reflective light microscopy.We showed that the mechanical behavior with white quartz is shown to be consistent with the experiments using albite gouges (Figure S6 in Supporting Information S1).Since the use of pure white quartz does not provide visible intensity differences against the SSG under XCT analysis, the quantification of slip distribution over fabric elements was only based on one to three thin section profiles of the gouge layer for each experiment (Figure S7 in Supporting Information S1).Despite this, similar occurrences of fabric elements can be observed using either albite or pure white quartz as a strain marker.Thus, we argue that albite can be effectively used as a strain marker against SSG and, in this case, the development of shear zone and strain localization does not depend strongly on mineralogy as long as the grain shapes and sizes are comparable.The major advantage and novelty of using albite is that the strains can visualized in 3-D using X-ray CT imaging.

Determination of Shear-Parallel B Shear Band
We first discuss the relationship between different terminologies that we reported in Table 2 because these parameters influence how we quantify the shear-parallel B shear band and the result of the displacement partitioning.Here, we ignore the effect of gouge compaction on the evolution of gouge microstructures because the amount of compaction for each experiment does not show much variation, even for experiments with different amounts of displacement (see Table S1 in Supporting Information S1), and, in addition, it is difficult to determine when the compaction occurred exactly.Mainly, we present three different length parameters D, L, and δ, which are defined as elastically corrected imposed shear, internal shear, and external shear.Considering pure homogeneous gouge deformation, if we imposed a load-point displacement of 1 mm to a 1 mm thick gouge layer, the D, δ, and L would be 1, 1, and 1, respectively.If shear displacement begins to localize along R 1 shear planes, D and δ would remain at 1 while L becomes less than 1 due to the offset of the marker boundary.The more R 1 shears develop (or other non-shear-parallel fabric elements), the shorter the L-value, while the development of shearparallel fabrics such as Y or B shears does not reduce L. The above description can be visualized in the schematic plots summarized in Figure S3 in Supporting Information S1.
As mentioned previously, we quantify the amount of displacement along the B shears as the difference between L and δ (instead of D).This choice is based on the following assumptions and observations: (a) the localization of slip on non-shear-parallel planes (or zones) does not cause much shortening in the L, otherwise, the amount of displacement on B shears would be overestimated; (b) we inferred that back shear of the pistons might occur and might cause reverse shear to the sample.Assumption (a) should be reasonable, as we barely observe any highangle offset along the marker boundary in all gouge microstructures (e.g., R 2 shear).Thus, if no B shear develops, the difference between L and δ should be negligible.In the case of assumption (b), the inference of the back shear is based on the observation that the δ is always shorter than the D in all experiments and this difference (D-δ) increases with D (Table 2).This discrepancy in displacement might be due to (a) compaction of the gouge sample and (b) the back shear of the pistons caused by elastic relaxation of the jacket during the unloading process as the confining pressure and/or fluid pressure are removed.Since the gouge compaction does not show much variation between the experiments, we infer that the back shear of the pistons is the main factor causing such differences.We argue that the back shear influences the microstructure to some extent because the gouge layer remains under shear stress when we depressurize the vessel and the sample.However, it is difficult to quantitatively examine how significantly the back shear affects the gouge microstructure.Here, we consider the effect of back shear and adopt δ rather than D to determine the amount of displacement on B shears where Y shears were quantified by the automatic detection method.

Displacement Partitioning Between Deformation Features
To obtain the displacement partitioning between the deformation features for each experiment, we averaged the displacement of identical deformation features (i.e., homogeneous vs. R 1 , Y (including B) shears) across all profiles.This is based on the observation of an absence of any clear spatial trend in the strain distribution within the analyzed regions after removing the outliers.It is noted that the error bars (absolute value) become larger with increasing shear displacement for all deformation features (Figures 9a-9c).The largest error bars suggest that the localization of slip varies largely perpendicular to the shear plane within only a few microns (equivalent to the pixel resolution).We argue that the increasing trend is likely attributable to an artifact of our automatic detection method due to the combined effect of poor sample recovery as well as the transformation of R 1 to Y shear in highstrain experiments.With increasing shear strain, gouge samples become thinner and more difficult to recover due to the increased development of slip localization and shear features within the gouge layer.This would result in an increasing number of turning points identified on the intensity boundary and, thus, likely increase the errors of the amount of localized slip quantified between slices.On the other hand, a general observation for the evolution of shear zone fabrics, which almost all previous studies agree on, is that R 1 shears initially form at high angles (∼30-40°) to the shear plane, in response to Mohr-Coulomb failure, and adopt lower angles during the rotation of the stress field.Figure 10 schematically illustrates the progression of gouge deformation from distributed shear to localization of slip on the principal R 1 , R 2 , and Y shear bands.During the initial slip, homogeneous shearing plays a significant role in accommodating the initial displacement within the zone (Figure 10a).However, once the major fabric elements such as R 1 and Y shears are formed, homogeneous shearing becomes comparatively passive and less influential in accommodating further displacement (Figures 10b and 10c).With increasing shear strain, low-angle R 1 shears rotate to become parallel to the gouge-forcing block boundary due to the rigid boundaries of the shear zone (Figure 10c; Logan et al., 1992;Logan, 2007).Thus, at low shear strain (i.e., strain-hardening stage), fewer turning points would be identified as only high-angle R 1 shears and homogeneous deformation were observed within the gouge layer (Figure 5).In contrast, at high shear strain (after the strain-softening stage), more turning points would be detected due to the ongoing development and transformation of the R 1 shears.Once more turning points are identified, the variability in the proportion of localization attributed to each shear feature, from one slice to another, is prone to become significant due to the spatial distribution of shears and the variation in gray-scale intensity within images.For example, for a pure Y shear (defined as 3°< θ < +3°) identified in successive slices, we might obtain different amounts of slip due to differences in the position of the turning points defining the Y shear.

Spatial Variation in Gouge Deformation
In general, the pattern of gouge deformation is consistent (i.e., uniform) throughout the analyzed gouge width, for most experiments.However, the deformation of the marker boundaries in two experiments, one at 1 μm/s in the strain-softening stage and the other at 1,000 μm/s in the steady-state stage (experiment s043 and s015 in Table 1, respectively), show a clear variation from one end (i.e., top) toward the center of the gouge layer segment analyzed (Figures 6b and 6c, 7g and 7h).In both cases, more deformation appears to be accommodated by a B shear, and less by R 1 shears, at one end of the analyzed gouge segment width, whereas the deformation looks more "distributed" for sections closer to the center.However, we do not see a clear trend in the amount of slip computed on either the R 1 shears or Y shears (Figures 8b and 7i).Despite the insignificant difference in displacement partitioning obtained from our automated analyses, we argue that this change in deformation pattern is real and could be related to the difference in the initial stress field at the sample end versus center likely due to (a) the radial effect of the cylindrical shape of the direct shear setup and/or (b) the proximity to the free surface of the gouge sample in the shear direction.It is impossible to link the change of the gouge deformation to the effect of the normal stress or rotation of the principal stress axes without detailed FEM modeling (e.g., Logan et al., 1992), including realistic boundary conditions, which is beyond the scope of this study.

Shear Fabric Evolution, Displacement Partitioning, and Mechanical Response
Overall, we observe that the evolution of the shear fabrics, displacement partitioning between these fabrics, and the mechanical response are highly consistent at all tested velocities.Slip localization in our samples has a minor dependency on displacement rate within the observed velocity range.One of the important findings is that the shear fabrics evolve with increasing shear strain in a repeatable and hence predictable manner.R 1 shears were first initiated during the attainment of the peak stress followed by the development of Y shears from the strainsoftening stage to the steady-state stage.This geometric evolution is fully consistent with the results of Logan et al. (1992) for calcite gouges, using Tennessee Sandstone as forcing blocks, a similar normal stress of 30-35 MPa and an initial gouge thickness of ∼1 mm, -despite the pore fluid pressure of 15 MPa and the temperature of 100°C applied in this study.While the presence of similar fabric elements has been observed across a diverse range of lithologies, including pure quartz and calcite (Bedford & Faulkner, 2021;Friedman & Higgs, 1981;Noël et al., 2023;Scuderi et al., 2017Scuderi et al., , 2020;;Wang, 1989), as well as mixtures containing clays (Haines et al., 2013;Logan & Rauenzahn, 1987;Moore et al., 1989;Wojatschke et al., 2016), the extent of strain required for the development of these fabric elements varies depending on the composition of the simulated gouge.Softer materials like halite (e.g., Buijze et al., 2017;Chester & Logan, 1990) and calcite (e.g., Verberne et al., 2014) generally have lower mechanical strength and tend to exhibit steady-state fabrics at lower shear strains compared to harder minerals (e.g., quartz or feldspar; Masuda et al., 2019), because the fracturing and compaction processes are easier.
To conclude, our quartz-rich samples show similar evolution of shear fabrics, displacement partitioning, and mechanical response to previous work on calcite gouges, despite differences in experimental conditions.This suggests that the mechanics of localization should also be comparable to that previously suggested, based on ringshear experiments on granular materials (Mandl et al., 1977) and finite-element studies of gouge zones (Logan et al., 1992).These studies demonstrated that the initial high-angle R 1 shears form in response to Mohr-Coulomb failure as the stress level increases to a critical level.Due to the rotation of the stress field, the angle of the R 1 shears becomes progressively lower and ultimately (sub)parallel to the gouge-forcing block boundary.Our microstructural observations also support this observation.In previous work, Y and B shears are then suggested to occur, owing to kinematic constraints, whereby the most displacement becomes localized along these shearparallel features due to the limited displacement that can be accommodated within R and P shears.Although P shears are not identified in our sample, we also showed that multiple Y and B shears develop, crosscut by a few R 1 shears within the simulated gouge zone at the steady-state stage.While this geometric change is consistent with previous studies on gouges that are clay free or clay poor (e.g., Higgs, 1981;Logan et al., 1992), we note that the importance/presence of P shears and the stage (imposed displacement) at Y and B shears develop do show some dependency on gouge composition, that is, on whether the fault zone is clay-rich (e.g., Haines et al., 2013), quartz-rich (e.g., Bedford & Faulkner, 2021;Noël et al., 2023) or polymineralic (e.g., Logan & Rauenzahn, 1987;Moore et al., 1989).

Implications for Small-Displacement Earthquakes
Localization of strain has broad influences on the aseismic and seismic nature of tectonic faulting.For instance, the development of shears along Y orientations may increase the permeability parallel as opposed to normal to the fault zone, due to an increase in porosity or anisotropy.This could enhance the fluid flow within the fault zone during aseismic creep, as observed in some natural fault zones (e.g., Caine et al., 1996).For seismic events with large displacement (> few meters), localization of slip is reported to play a critical role in facilitating dynamic weakening as generated frictional heat would be localized within a narrow shear band facilitating thermal softening of the fault materials (e.g., S. A. Smith et al., 2015).However, whether the same mechanism operates in small-displacement earthquakes (i.e., cm-or mm-scale, equivalent to M 2.0-4.0)remains uncertain.
Our results show that about 60% of displacement is localized along the developed fabric elements in the quasisteady state simulated gouge zone, of which up to 50% (i.e., 5/6% of 60%) is localized on the shear-parallel Y (including B) shear bands, in a fault with only ∼5.5 mm displacement.We further show that the localization process has only minor dependence on displacement rates in the range from 1 μm/s to 1,000 μm/s, similar to the velocity range expected during fault acceleration during the nucleation stage of rupture development.If the dependence of strain partitioning on velocity remains small, and the fault slip is localized along one Y shear (i.e., principal slip zone, PSZ), when a fault subsequently accelerates to seismic slip rates (i.e., >0.1 m/s), our study provides constraints on the development (thickness) of the active slip zone.This is a crucial input parameter for the heat budget of mm-scale seismic slip events, and hence for constraining effects such as thermal pressurization or flash heating effects that may control dynamic slip weakening during seismic slip (cf.Hunfeld et al., 2021;Chen et al., 2023).
Based on numerical simulations, Platt et al. (2015) showed that the thickness of the PSZ has a major influence on various earthquake parameters.For a fault-zone gouge in which thermal decomposition and thermal pressurization are active, these authors showed that a decrease in PSZ thickness leads to faster rupture velocity and shorter total slip of an earthquake.Our microstructural observations show that the B shears were the most well-developed fabric elements at the steady-state stage, typically dominating at one side of the gouge layer, with an overall thickness of less than 150 μm (Figure 7e).In addition, the results of the localization quantification indicate that over half of the displacement was accommodated in these shear-parallel features (Figure 9).If ongoing fault slip is accumulated within such a thin deforming zone, the rupture velocity of the fault could therefore increase at least 3-4 times faster than a 1 mm thick layer of a homogeneously deforming fault gouge.However, the PSZ thickness within a natural fault gouge becomes difficult to estimate when considering the evolution of slip localization and natural earthquake conditions.For example, our gouges spend a short time at PT conditions before slip starts, whereas natural faults will have a long slip history, including previous earthquakes which will affect the initial microstructural state.The above implications can be better constrained if the characteristics of the PSZ (i.e., thickness and grain size) in natural pre-existing fault (both faults that have slipped in an induced event or experienced fault slip or as-yet silent faults) are better understood from borehole core observations or other exhumed analog faults with a similar lithology.

Conclusions
In this study, we conducted direct shear experiments on simulated sandstone-derived quartz-rich fault gouges, retrieved from the Groningen gas field, the Netherlands, at an effective normal stress of 40 MPa, a pore water pressure of 15 MPa, and a temperature of 100°C.We presented a quantitative 3-D analysis of the evolution of gouge microstructures in quartz-rich gouges combined with a stripe of albite gouge layer as a strain marker, using X-ray CT (XCT) scanning.To identify the fabric elements along the albite-quartz boundary and quantify the displacement partitioning between these features, we developed a machine-learning-based boundary detection method based on a trainable segmentation technique.The main findings of this study are summarized as follows: 1.The mechanical results of this study show good reproducibility and consistency compared to the published data despite the use of albite gouges as a strain marker.In addition, albite gouge segments are shown to be a useful strain marker owing to the significant intensity contrast versus quartz gouges in XCT scanning.2. The automatic boundary detection method based on machine learning developed in this study is an efficient and reliable tool to identify the albite marker gouge boundary, to detect shear bands, and to quantify the displacement partitioning along R 1 , Y, and B shears versus that accommodated by homogeneous shear of the gouge body.3. Our quartz-rich gouges show similar evolution of the shear fabrics, partitioning of displacement, and mechanical response with increasing shear strain at all tested velocities.The results also agree with previous studies but for the first time provide quantitative data on the displacement partitioning on the evolving shear band structures.4. At all velocities, a total of up to 50% displacement has accumulated on shear-parallel shear bands (Y and B shears) within a shear strain of 5.5 measured with respect to the initial gouge thickness.With the total imposed displacement of 5.5 mm, our results suggest that about 2 mm of fault slip will be accommodated through homogeneous shearing during rupture nucleation, at least up to slip velocities of 1 mm/s.This provides constraints on the development of the active (principal) slip zone, which is an important factor in controlling heating and weakening associated with small-magnitude earthquakes with limited displacement (mm-dm), such as induced seismic events.

Figure 1 .
Figure 1.Direct shear set-up with a starting Slochteren sandstone gouge (SSG) layer with a 5 mm wide albite marker layer.(a) Photograph of the starting layer.(b) The assembled set-up with the shear sample sandwiched by the set-up, jacketed by FEP heat shrink tube.(c) A section of the sample containing albite-SSG boundary prepared for analysis with the Zeiss Versa 510 X-ray microscope.(d) Example of X-ray CT reconstruction showing the initial sample with the albite marker layer after compaction.The boundary between the albite and the SSG is indicated by the yellow dashed line and can clearly be identified on the basis of contrast in the gray-scales.(e) Schematic plot of the direct shear setup.

Figure 2 .
Figure2.Schematic diagram showing the evolution of shear stress against displacement, alongside corresponding frictional stages from strainhardening to strain softening (for over-compacted samples), and to steadystate stages, as typically observed for (simulated) fault gouges deformed at a constant (nucleation-relevant) shearing velocity (e.g.,Logan et al., 1992).The blue curve represents an over-compacted gouge sample, that is, one which dilates as shear stress increases.The green curve represents an undercompacted gouge sample without a peak stress at the onset of shear deformation.Note that the second stage is still strain hardening for the under-compacted example, as observed in our mechanical data.
reduce the time required to analyze hundreds to thousands of images.Detailed information on the ML training (e.g., training parameterization) and validation (e.g., training data) are summarized in Supporting Information S1 (see Text S2.1).

Figure 3 .
Figure 3.The workflow of image processing and quantification applied to our stacks of XCT slice images (a) An example of the XCT image slice of the gouge layer deformed at 30 μm/s at steady-state stage, which shows different deformation features along the SSG-albite boundary.(b) Step 1: Trainable segmentation by masking the SSG and albite gouge regions based on the different features such as local intensity, textures, and edges at different scales to train a random-forest classifier.(c) Step 2: Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering to retrieve the boundary with the highest density of clusters.(d) Step 3: Moving average with a moving window of 4 (pixel) and a window step of 1 (pixel) to perform first smoothing.(e) Step 4: Ramer-Douglas-Peucker (RDP) algorithm to perform a second smoothing and to subsequently identify the turning points along the boundary.(f) Absolute amount of localized displacement against homogeneous, R 1 , and Y shears obtained from the automatic and manual methods.(g) Displacement partitioning between homogeneous, Y, R 1 , and R 2 shears as a function of slice number.Two examples of good and bad segmentation boundaries are shown where good represents a continuous cluster along the boundary while bad represents discontinuous clusters of the boundary.(h) Final result of the displacement partitioning between different deformation features after applying Z-score to remove the outliers.See main text for more detailed descriptions.Black and pink arrows indicate the first and second rounds of segmentation, respectively.

Figure 4 .
Figure 4. Representative frictional behavior of the Slochteren sandstone gouges for ∼5.5 mm displacement at three different displacement rates of 1, 30, and 1,000 μm/s.Experiments were stopped at the strain-hardening, strain-softening, and steady-state stages, which are equivalent to ∼1.3, ∼3.4, and ∼5.5 mm displacement, respectively, as indicated.The solid curve indicates apparent friction while the dashed curve indicates pore fluid pressure measured at the ISCO pump.

Figure 6 .
Figure6.At strain-softening stage.Macroscopic observations show that all recovered samples split along the gouge-forcing block boundary (a and d) except the sample at 1,000 μm/s, which split along the R 1 shears (f).The XCT images show that displacement starts to localize along the fabric elements, mostly on the R 1 shears, indicated by the offset of the marker boundary.In addition, a significant contrast in grain size between the localized zone and the remainder of the gouge layer is visible.The sample deformed at 1 μm/s shows a clear spatial variation in terms of the pattern of deformation where the cross section at the sample boundary developed more boundary shears than the one closer to the center.

Figure 7 .
Figure7.At steady-state stage.Macroscopic observations show that all recovered samples split along R 1 shears, and a small portion of the albite gouge is attached to the gouge-forcing block boundary.The microstructures are similar to the ones in the strain-softening stage (Figure6) while gouge smearing with only few microns thick at the gouge-forcing block boundary and grain size reduction becomes significant at all velocities.One thing to note is that only the sample deformed at 1,000 μm/s shows spatial variation with respect to the deformation where the cross section at the sample boundary (g) shows a better developed boundary shear than the one close to the center (h).

Figure 8 .
Figure 8. Displacement against individual XCT slice number for different deformation features after removing the outliers for each experiment.The slice number from small to large indicates the analysis from the gouge boundary toward the center.Note that the amount of the slip along R 2 shear is almost zero and no P shear was identified.Some experiments have less than a thousand slices due to the removal of substandard-quality images.Px represents pixel.
Note.SH = Strain hardening, SS = Strain softening.W = The gouge thickness after shearing, D = The imposed displacement, L = The internal shear, δ = The external shear, Homo.= Homogeneous.The uncertainties for the thickness W and the external shear δ are the resolution of the caliper we used (0.01 mm).The uncertainties for the internal shear L represent the spatial standard error of the total displacement data obtained from Figure8with a 95% confidence interval.

Figure 9 .
Figure 9. Relative amounts of slip as a function of external shear δ (mm) at slip velocities of 1, 30, and 1,000 μm/s for different shear features.(a) Homogeneous shearing; (b) R 1 shear; (c) Y shear (including B shear).The error bars represent the standard errors, indicating the variability in the measurements, with a 95% confidence interval.

Figure 10 .
Figure 10.Schematic plot of the evolution of fabric elements within the gouge shear zone at different frictional stages with progressive shear strain, modified from Logan et al. (1992), with representative microstructures obtained from the experiments.The gray color indicates the zones in which displacement is mostly accommodated.(a) Initial state of the gouge zone before shearing.(b) Strain-hardening stage with the formation of high-angle R 1 shears.(c) Strain-softening stage with the transformation of high-angle R 1 shears to low-angle R 1 shears, and to shear-parallel Y (and boundary) shear bands.(d) Steady-state stage with a further development of boundary shears.Note that P and X shears are difficult to distinguish from the homogeneous deformation in our low phyllosilicate content samples and does not seem to accommodate much displacement.

Table 2
Data Compiled From the Albite-SSG Boundary and the Strain Partitioning Between Different Shear Features