Tracking the evolution of the deformational energy budget within accretionary systems provides insight into the driving mechanisms that control fault development. To quantify the impact of these mechanisms on overall system efficiency, we estimate energy budget components as the first thrust fault pair develops in dry-sand accretion experiments. We track energy budget components in experiments that include and exclude a basal layer of glass beads in order to investigate the influence of detachment strength on work partitioning. We use the measurements of normal force exerted on the backwall to estimate external work, and measurements of strain observed on the sides of the sand packs to estimate the internal work, frictional work and work against gravity done within increments of each experiment. Thrust fault development reduces the incremental external work and incremental internal work, and increases the incremental frictional work and incremental gravitational work. The faults that develop within higher-friction detachment experiments produce greater frictional work than the faults in experiments with glass bead detachments because the slip distribution along the detachments remains the same, while the effective friction coefficient of the detachment differs between the experiments. The imbalance of the cumulative work budget suggests that additional deformational processes that are not fully captured in our measurements of the energy budget, such as acoustic energy, consume work within the deforming wedge.
In accretionary prisms, margin-perpendicular convergence produces distributed layer-parallel compaction ahead of the wedge until strain localizes as slip along discrete frontal thrust faults (e.g., Koyi, 1995; Burberry, 2015; Ghisetti et al., 2016; Lathrop and Burberry, 2017). The frictional strength of the basal detachment and rheology of the wedge control the internal deformation throughout the wedge prior to thrust fault development. Consequently, the timing and geometry of new fault development may vary with varying basal detachment strength.
Understanding the energetic trade-offs between pervasive internal strain and fault development can help predict the timing and geometry of new frontal accretion thrust faults (e.g., Del Castello and Cooke, 2007; McBeck et al., 2017). Investigations of the energy available for creating new fault surfaces show that new frontal accretion faults may only develop when the system has stored sufficient energy that can be expended in the development of new faults, which consume both acoustic and propagation energy (Del Castello and Cooke, 2007; Herbert et al., 2015). Numerical simulations of physical accretion experiments demonstrate that optimizing the total external work done on the wedge can successfully predict the position and dip of new frontal accretion thrusts (McBeck et al., 2017). These and other numerical efforts demonstrate the ability of energy criteria to successfully predict and understand fault development (e.g., Masek and Duncan, 1988; Hardy et al., 1998; Burbidge and Braun, 2002; Cubas et al., 2008; Marshall et al., 2010; Dempsey et al., 2012; Mary et al., 2013; Yagupsky et al., 2014; Cooke and Madden, 2014; McBeck et al., 2016, 2017). However, few studies have used energy criteria to assess fault development within scaled physical analog experiments (e.g., Ritter et al., 2018a). In particular, investigations of the energy budget of physical accretion experiments have thus far focused on two components: the external work and work of fault propagation (Herbert et al., 2015). The complete deformational energy budget has not been calculated for deforming physical analog accretionary wedges. Calculating the components of the complete energy budget – including the energy consumed in frictional slip, uplift against gravity and internal diffuse deformation – provides a more complete picture of evolving energy partitioning throughout the system and the trade-offs between deformational processes associated with each work budget component.
We tracked the complete work budget from the onset of deformation through the formation of the first thrust pair within four scaled dry-sand accretion experiments performed at the University of Cergy-Pontoise (UCP). Half of the experiments employed a basal layer of glass beads in order to provide a low-friction basal detachment. Digital image correlation (DIC) and force measurements enabled estimation of the energy expended in uplift against gravity, work done against frictional slip, energy stored as pervasive off-fault deformation and total external work done on the physical accretion experiments. We compare the evolution of work budget partitioning for experiments with high- and low-friction detachments in order to reveal the sensitivity of different processes captured in the work budget to detachment strength.
Field observations, physical analog experiments and numerical simulations inform the energy budget associated with the spatiotemporal evolution of faults within accretionary systems.
The material properties that control strain localization and thrust fault
development in accretionary prisms include the evolving frictional strength
of the detachment, the internal frictional coefficient and cohesion of the
relatively intact material within the wedge, the evolving cohesion and
frictional strength of the thrust faults, and the effective stiffness of the
wedge (e.g., Davis et al., 1984; Dahlen et al., 1984; Lohrmann et al.,
2003; Le Pourhiet, 2013). An energy budget framework can quantify the
impact of each of these evolving properties, and the resulting stresses and
strains within the wedge, on system deformation (e.g., Dahlen, 1988;
Burbidge and Braun, 2002). In particular, recent investigations of fracture
propagation and interaction indicate that tracking the evolution of various
components of the work budget of a deforming fault system sheds insight into
mechanical processes that control fault system development (e.g., Del
Castello and Cooke, 2007; Dempsey et al., 2012; Cooke and Madden, 2014;
Herbert et al., 2015; McBeck et al., 2017; Newman and Griffith, 2014).
The energy budget of a deforming fault system includes the internal work of
deformation,
The evolving energy budget of accretionary systems can help predict the
spatiotemporal development of accretion faults (Burbidge and Braun, 2002;
Del Castello and Cooke, 2007; McBeck et al., 2017). Del Castello and
Cooke (2007) show that accretionary faults evolve to optimize the total work
done in the system, even as individual components of the work budget
increase. In these numerical accretion simulations, the development of the
new forethrust increases
In this study, we track the evolving energy budget in wedges with detachments of differing strengths in order to assess how detachment strength influences the overall efficiency of the wedge (external work), as well as the magnitude of fault slip (frictional work), uplift against gravity (gravitational work) and pervasive internal strain (internal work). We expect that higher detachment strength may (1) increase external work by providing greater resistance to contraction, (2) increase the frictional work if the magnitude and distribution of slip along the detachments remain the same and (3) increase the internal work prior to thrust faulting due to greater shear tractions on the detachment that produce higher stresses within the wedge.
Field observations suggest that off-fault deformation within accretionary prisms, such as distributed microcracking and ductile deformation, produce diffuse thickening of strata that accommodates a significant proportion (30 %–40 %) of total shortening (e.g., Lundberg and Moore, 1986; Morgan et al., 1994; Morgan and Karig, 1995; Moore et al., 2011). Recent retro-deformations of seismic profiles from the central Hikurangi Margin suggest that macroscopic thrust faults and folds accommodate < 50 % of the margin-perpendicular shortening due to plate convergence (Ghisetti et al., 2016). The protothrust zone identified in seismic transects of the Nankai wedge between the trench and a zone of imbricate thrust faults (e.g., Moore et al., 2011) indicates that diffuse compaction within crustal wedges may be concentrated into particular zones, and not homogeneously distributed throughout the wedge.
The thousand- to million-year intervals between faulting events within crustal accretionary wedges amplify the need of scaled and quantitatively monitored physical experiments to directly document the transition from diffuse deformation (i.e., greater internal work) to localized faulting (i.e., greater frictional work). Recent analytical analyses indicate that the solutions governing the stability and critical taper of non-cohesive accretionary wedges do not differ in subaerial (dry) and submarine (normally pressured) conditions (Lehner and Schöpfer, 2018), suggesting that insights from dry physical accretion experiments are applicable to submarine, crustal accretionary prisms. Physical accretion experiments reveal distributed layer-parallel shortening associated with detachment slip prior to the localization of slip along thrust faults (e.g., Mulugeta and Koyi, 1992; Koyi, 1995; Burberry, 2015; Lathrop and Burberry, 2017; McBeck et al., 2017). In dry-sand accretionary wedges, inclusion of a ductile detachment greatly increases the overall distributed internal strain associated with folding and thrusting (Lathrop and Burberry, 2017). Incremental displacement fields of the sides of wedges indicate that short-lived shear bands episodically develop until strain localizes onto a single frontal forethrust (e.g., Bernard et al., 2007; Dotare et al., 2016). The short-lived shear bands contribute to distributed internal deformation prior to localized slip.
Previous experiments observed transient increases and decreases in external
force associated with fault development, indicative of varying magnitudes of
external work (Nieuwland et al., 2010; Cruz et al., 2010; Souloumiac et
al., 2012; Herbert et al., 2015; Ritter et al., 2018b). Similarly, the
partitioning of the energy budget is expected to differ before and after
thrust fault development. Prior to faulting, distributed internal strain
(
To gain insight into the partitioning of energy components during fault development, we use four accretion experiments performed at UCP. Here, we describe the setup and quantitative post-processing of the physical experiments. Then, we describe the method of constraining the effective stiffness of the wedges and the calculation of the work budget components using observations from the experiments.
In these experiments, an electric screw motor translated one wall of the experimental apparatus toward the other in order to contract the dry-sand wedge. Throughout the duration of each experiment, three cameras captured photos of different views of the sand pack at 1 s intervals (Fig. 1). One camera took photos of the top of the sand pack, while the other two cameras took photos of the sand pack cross sections through both of the glass sidewalls. In addition, 16 uniaxial strain gauges mounted on the backwall of the experimental apparatus recorded changes in normal force exerted on the backwall throughout the experiment. Previous physical experiments performed at UCP indicate that variations in normal force on the backwall coincide with fault development (e.g., Souloumiac et al., 2012; Herbert et al., 2015).
Schematics of experimental setup, force and faulting evolution.
The sand deposition method strongly controls the density and frictional properties of the system, and thus how the sand pack accommodates strain (e.g., Krantz, 1991; Lohrmann et al., 2003; Maillot, 2013). To construct homogeneous and isotropic sand packs, a sedimentation device, designed and built at UCP, sieves the sand two or three times before deposition (Maillot, 2013). We used this sedimentation device to construct the sand packs.
To investigate the impact of a weaker basal detachment on the energy budget,
two of the experiments included a 0.5 cm thick layer of glass beads (median
grain size of 160
For each set of two experiments that either include or exclude a glass bead layer, we modified the configuration of the experimental apparatus in order to remove bias arising from sidewall friction following the methods of Souloumiac et al. (2012). Frictional sliding of the sand pack along the glass sidewalls produces a net force vector that has a different direction depending on whether the base is fixed or moving. The drag of the sidewall produces curvature in the strike of thrusts that is expected to develop concave to the motor direction. We changed the direction of the sidewall friction drag by switching the position of the backwall with respect to the motor (Fig. 1). We aim to eliminate the bias in the experimental observations that arises from sidewall friction by synthesizing observations from the two experiments.
In two experiments (E373, E374), the base of the apparatus slid under the
fixed backwall (Fig. 1c). In the other experiments (E375, E376), the base was
fixed and the screw motor pushed the backwall so that the sand slid over the
stable glass base (Fig. 1d). In the remaining text, we refer to these
different configurations as the moving-base (E373, E374) and
moving-backwall (E375, E376) experiments. The opposing apparatus configurations
used here were expected to produce only minimal differences in the position
of the thrusts at the sand pack sides because the ratio of the area of the
sand pack in contact with the sidewalls to the area in contact with the base
was low (
Incremental displacement fields of top and side views of experiment
E374 (glass detachment and moving base) throughout the development of the
first thrust pair at 0.5 mm increments of applied backwall displacement,
To constrain the active-fault geometry and calculate the energy budget components throughout each experiment, we used digital image correlation (DIC) to calculate the incremental displacement fields of the top and sides of the sand pack (Fig. 2). For each sequential pair of photos, DIC analysis determines the incremental displacement field at a grid of points via DIC of pixel constellations (e.g., Adam et al., 2005). The incremental displacement fields revealed active thrusts where slip produces sharp gradients in the displacement field (i.e., localized shear and normal strain) (Fig. 2). We calculated the incremental shear strain fields of each of the views of the sand pack using the curl of the incremental displacement field, which indicates the incremental rotational angle. In our analysis, the tangent of the incremental rotation angle approximately equals the angle (in radians) because we investigate small changes in displacement. Thus, the curl of the incremental displacement field approximately equals the incremental shear strain under these conditions. This calculation of shear strain is independent of coordinate system, so that shear along all orientations has equal representation.
To perform DIC, we employed several techniques to produce accurate incremental displacements from the photos. During the experiment, we acquired 10 MB, 24 bit color JPEG photographs. We orthorectified the photos to remove distortion near the edges, converted the color photos to gray scale and increased the contrast in order to aid the DIC calculation. We performed these steps, and performed DIC with a triple pass filter, using the PIVlab MATLAB™ plug-in (Thielicke, 2018). The analysis produced incremental displacements with a spatial resolution of 0.01 cm and temporal resolution of 2 s, or 0.2 mm of applied backwall displacement.
To capture fluctuations in normal force exerted on the backwall throughout
each experiment arising from strain hardening and softening of the sand pack,
we used 16 uniaxial strain gauges mounted on plaques in contact with the
backwall (blue in Fig. 1c–d). Four plaques each containing four uniaxial
strain gauges were connected in series, so that the mean strain of the
16 sensors are reported (Fig. S1 in the Supplement). Throughout each
experiment, uniaxial strain was recorded at 0.1 s intervals. Calibration of
the strain gauges to known weights produced a linear relationship of machine
strain units to applied weights with
Each of the components of the work budget arises from integrating the product of force and displacement over the corresponding deforming region (e.g., Cooke and Madden, 2014). We estimated the incremental gravitational, frictional, internal and external work at stages of the experiments using the incremental displacement fields of the sides of the wedge and the normal force exerted on the physical backwall. Previous work presents the equations for each component of the energy budget (i.e., Cooke and Madden, 2014). Here, we describe how we used the experimental measurements to estimate the values used in those equations.
At the slow stepper motor rate prescribed here (0.1 mm s
The motor supplies work to the wedge by applying a force to the moving wall
as it displaces at the prescribed velocity. The cumulative external work done
from the start of deformation to the stage of interest is the area under the
force-displacement curve (e.g., Cooke and Murphy, 2004). Thus, the external
work done in an increment of an experiment may be considered to be the area
under the force-displacement curve for that increment of backwall
displacement measured from the DIC fields of the top view. To calculate the
external work,
The work against gravity,
The frictional work,
Internal work measures the energy consumed in internal strain of the material
as quantified by strain energy density, which is a product of the components
of the stress and strain tensors. Here, we use this quantity to capture the
elastic contribution to deformation outside the fault zones. Whereas
localized faults within the sand pack deform inelastically, the sand pack
around the faults stores and releases strain in concert with fault slip. The
overall elastic response of the sand pack produces the observed reduction in
external force associated with the growth of new thrusts (Fig. 3a). To
estimate the internal work,
Backwall normal force curves with faulting events.
Throughout each experiment, the gravitational, frictional and internal work calculated from the displacement field of one side of the sand pack may differ from the work calculated from the opposite side of the sand pack. These differences arise from changes in the fault geometry along strike, as well as in the quality of the incremental displacements calculated through DIC. Consequently, we present the components calculated from the incremental displacement fields of both sides of each experiment. This demonstrates the variability that can be expected in different accretion experiments (e.g., Cubas et al., 2010).
The calculation of internal work within the accretion experiment depends on the stress state within the wedge, which is not measured in these experiments. To constrain the internal stress state from the observed strain fields using Hooke's laws and the effective stiffness of the material, we must estimate the effective stiffness of the sand wedges. To do this estimation, we used measurements of the normal force exerted on the backwall and contraction along the sides of the sand pack (Text S1). The slope of the resulting stress–strain curve at 50 % of the peak stress reveals the effective stiffness of the sand (e.g., Barber, 2002). Like other geotechnical materials with overall nonlinear rheology, sand aggregates show linear behavior around 50 % of peak stress (e.g., Klinkmüller et al., 2016). Consequently, the slope of the normal stress–normal strain curve preceding thrust fault development provides an acceptable estimate of the stiffness of the wedge to use in the approximations of internal work.
We calculated the tangent of the horizontal longitudinal strain,
The accuracy of the incremental displacement field calculated through DIC
varied due to slight differences in illumination, focal depth and camera
positioning between each experiment, and between each side of one experiment.
To assess the robustness of each incremental displacement field, we
calculated the 2-D kinematic compatibility of each field. We solved the 2-D
kinematic compatibility equation at all specified points from the strain,
First, we describe the relationship between thrust fault development and the overall efficiency of the wedges. Then, we use the experimental data to estimate the changes to the energy budget associated with the development of new accretionary faults. Finally, we link specific deformational processes to the evolution of the work budget components.
In the four experiments, the sequence of faulting followed that observed by Herbert et al. (2015). The DIC strain fields reveal that, first, a backthrust–forethrust pair developed near the leading edge of the protowedge (Figs. 2, 3). Then, a new backthrust propagated in front of the pre-existing backthrust, further from the backwall. Next, a new forethrust propagated in front of the pre-existing forethrust. Finally, a new backthrust–forethrust pair developed in front of the latest forethrust.
The evolution of the normal force exerted on the backwall highlights these
faulting events (Fig. 3). The measured backwall force tracks the evolution of
external work because the external work is a function of the normal force
exerted on the backwall and the applied backwall displacement. For each
experiment, the normal force rose to a local maximum (peak) and fell to a
local minimum (trough) coincident with new fault development (Fig. 3). Prior
to thrust faulting, the backwall force steadily increased as the wedge
compacted and thickened, and greater work was required to maintain the
backwall velocity. The three different camera views of the physical
experiment enabled identification of thrust faulting events at the top of the
sand pack and at both sides of the experiment (Fig. 2). The faults, identified
as localized shear strain in the side views and normal contraction in the top
view, emerged at the top of the sand pack 0.5–1 mm before the force peak as
the force curve transitions from linear to the strain-softening behavior
(Fig. 3b–e). The force trough occurred after we observed the first evidence
of faulting on either side of the experiment, confirming the findings of
laboratory rheometric tests that faults within sand continue to weaken with
decreasing friction coefficient as they accrue several millimeters of slip
(e.g., Vermeer, 1990; Lohrmann et al., 2003; Ritter et al., 2016).
Consistent with findings of Herbert et al. (2015), the experiments with
glass bead detachments had lower force drops (24–28
To determine the contribution of each deformational process to the increase in overall efficiency associated with fault development, we estimated the energy consumed or stored in increments of applied displacement throughout each experiment. First, we calculated each incremental work budget component over successive increments of backwall displacement (Fig. 4). This incremental work corresponds to the rate of work.
Incremental work budget components throughout the development of
the first thrust pair for experiments with the sand detachment (left column) and
glass detachment (right column).
Thrust faulting decreased the incremental
The incremental internal work,
Prior to thrust fault development, work against frictional slip occurred
along the basal detachment fault. For each experiment, thrust fault
development increased
Thrust faulting increased
Prior to faulting, the increasing external work applied to the wedge was
accommodated with increasing internal work, increasing uplift against
gravity and increasing work against frictional sliding along the detachment.
The maximum rate of increase in frictional and gravitational work budget
components correlates with the minimum incremental external work, minimum
rate of increasing internal work and peak in backwall normal force. After
this peak force, the system fails; more work was expended as work against
frictional slip and stored as work of uplift against gravity than was stored as
internal work. Of the calculated components of the work budget, thrust
faulting produced the smallest changes in
The positive values in the incremental energy budgets suggest that the
cumulative work components monotonically increase throughout thrust fault
development, but at varying rates. The incremental energy budget of the
physical experiments indicates that thrust fault development increased
Vertical displacement fields of moving-backwall experiment excluding
glass bead layer (E375) preceding
The vertical displacement fields of the sides of the physical sand packs
demonstrate that diffuse uplift preceded the development of discrete thrusts
(Fig. 5). The evolution of
Shear strain of incremental displacement fields of experiments
excluding
The increase in
Evolution of strain as the thrust faults develop in experiment E375.
Gray regions in sketches in right column indicate portion of strain field
that contributes to
Tracking the evolution of the strain tensor components provides insight into internal deformation prior to thrust fault development, which contributes to the internal work of the system (Fig. 7). Preceding faulting in experiment E375, the wedge contracted horizontally and thickened vertically, producing high normal strains dispersed through the wedge and localized shear strain along the detachment (Fig. 7a–b). With continued backwall displacement, horizontal contraction and vertical extension shifted toward the distal tip of the detachment, where the thrusts ultimately developed, and the zone of high shear strain surrounding the detachment extended further from the backwall. In the incipient stages of thrust development, horizontal contraction and vertical extension concentrated along the incipient thrusts, forming broad bands of high strain a few centimeters thick (Fig. 7c). As the thrust faults slipped, the zones of high horizontal contraction and vertical thickening localized, and shear strain along the forethrust increased, while shear strain along the backthrust remained low (Fig. 7d).
Synthesizing quantitative observations from physical experiments reveals energy partitioning associated with thrust fault development. Here, we discuss how the energy budget balanced in these experiments and the impact of the apparatus design on strain localization.
Total accumulation of work done throughout experiment E376. Upper
black line shows total
Evolving diffuse deformation, uplift and localizing strain change the overall
work done in the system (Fig. 8). Following the conservation of energy, the
total
However, in each experiment, the sum of
To constrain the potential range in error in
To constrain the potential range in error in
In our calculations of
Noise in the displacement fields may also have introduced errors into the work budget calculations. However, variations between the true displacement field and calculated displacement field are likely smaller than differences in the displacement fields on different sides of each experiment, where differences in fault geometry influence the displacement fields. Although we do not know the displacements within the center of the sand pack, the record of displacement at the two side windows provides two viable expressions of the experiment's overall deformation. Consequently, we consider the difference in the work budget values calculated for either side as estimates of uncertainty in the calculations. The shaded regions in Fig. 8 show the difference in the values calculated for each side and function as uncertainty estimates.
The imbalance of the work budget suggests that other processes besides
diffuse internal deformation, frictional slip and uplift against gravity
consume work. Processes not directly considered in this study include the
creation of new fault surfaces and the generation of seismic energy or
acoustic emissions (e.g., Madden et al., 2017; Herbert et al., 2015).
Previous investigations of physical experiments indicate that the total work
of creating new fault surfaces and released in seismic energy during fault
propagation (
Normal strain perpendicular to the backwall from top views of
experiments
In these experiments, we find that
Recent advances in field techniques provide insights into the magnitude of
We expected the opposing apparatus setup to exert only a minimal impact on deformation within the wedge, and the resulting energy budget components, because the ratio of sand pack area in contact with the sidewalls and in contact with the base is < 0.1 (Souloumiac et al., 2012). However, this ratio was determined from experiments in which the materials in contact with the base and sidewalls were the same, and so it may not be valid for the experiments with glass beads. If the frictional sliding of the sand pack against the sidewalls had an appreciable influence on thrust fault geometry, then the trace of the thrust faults would curve near the sidewalls. In the top view displacement field, we observe mature thrust fault traces sub-perpendicular to the applied contraction direction across the full width of the sand pack (Figs. 2, S6). However, when the thrust faults just began to initiate within the center of the sand pack and propagate towards the sidewalls (Fig. 2a), the curvature in the traces of the developing faults was more pronounced than the later mature fault traces (Fig. S6). The resulting difference between the displacement fields viewed through the sidewalls and the displacements that occur within the center of the sand pack suggest that the energy budget components calculated from the side view displacement fields may differ from those within the center of the sand pack most significantly before the thrust faults develop across the full sand pack width.
The distribution of internal compaction differs in the sets of experiments
with differing apparatus configurations. The moving base compacted a larger
volume of the sand pack than the moving backwall prior to thrust fault
development (Fig. 9). When only the backwall is displaced, the horizontal
contraction of the top of the wedge only reveals significant contraction
within 10–15 mm of the backwall (Fig. 9b), preceding thrust fault
development (0.19 mm backwall displacement). When the base is
displaced, the strain field reveals compaction at further distances from the
fixed backwall (> 20 mm) (Fig. 9a). The experiment setups differ
in the area of sidewall where sand grains move relative to the sidewall. A
smaller area of the sand pack slides past the
sidewalls in the moving-wall experiment than within the moving-base
experiment. While the influence of sidewall friction on thrust fault
curvature is low, nonzero sidewall friction might produce more diffuse
compaction prior to fault formation. These differences in the actively
compacting volume influenced the strain done within the compacting volumes
visible through the glass sidewalls preceding thrust fault development
(Fig. S2). These differences lead to slightly higher estimates of
This study compared the energetic trade-offs of frictional slip, uplift and distributed off-fault deformation within physical accretion experiments in order to shed insight on the impact of fault development and detachment strength on deformational processes within accretionary environments. We demonstrate that the new experimental setup used here minimizes the effects of sidewall friction on deformation and the subsequent energy budget estimates. This study is the first effort to quantify four components of the deformational energy budget in accretion physical experiments using force and strain measurements. We use these data to calculate external work, internal work of distributed deformation, work against frictional slip and work of uplift against gravity. Constraining the evolving energy budgets of scaled accretion experiments revealed that thrust fault development increased the overall system efficiency, decreasing the incremental external work. Thrust fault development decreased the incremental external work and incremental internal work, and increased the incremental frictional work and incremental work against gravity. The evolution of gravitational work highlighted the broad uplift of the sand pack that begins prior to slip on localized thrust faults. Variations in the frictional work reveal that lower friction coefficients, as well as lower slip on the backthrust and detachment in the wedges with lower strength detachments, suppressed the increase in frictional work arising from thrust fault development in these experiments relative to the higher-strength detachment experiments. The imbalance of the cumulative energy budget indicates that additional processes besides those captured here, such as the work of propagation and acoustic energy, may consume a significant portion of the energy budget.
The experimental data, including incremental displacement fields and force measurements, are available on the GFZ repository (McBeck et al., 2018).
The supplement related to this article is available online at:
JM, PS, BeM and BaM ran the experiments. JM and MC processed the results and did the work budget analysis. All authors contributed to the writing of the manuscript.
The authors declare that they have no conflict of interest.
This work was supported in part by a Geological Society of America Student Research Grant and an International Association of Mathematical Geologists Student Research Grant to Jessica McBeck, and NSF grant EAR-1650368 to Michele Cooke. The experimental data, including incremental displacement fields and force measurements, are available on the GFZ repository (McBeck et al., 2018). The authors thank topical editor Ylona van Dinther and reviewers Matthias Rosenau and Arthur Bauville for constructive suggestions that improved the paper. Edited by: Ylona van Dinther Reviewed by: Matthias Rosenau and Arthur Bauville