Predicting fault slip via transfer learning

Data-driven machine-learning for predicting instantaneous and future fault-slip in laboratory experiments has recently progressed markedly, primarily due to large training data sets. In Earth however, earthquake interevent times range from 10’s-100’s of years and geophysical data typically exist for only a portion of an earthquake cycle. Sparse data presents a serious challenge to training machine learning models for predicting fault slip in Earth. Here we describe a transfer learning approach using numerical simulations to train a convolutional encoder-decoder that predicts fault-slip behavior in laboratory experiments. The model learns a mapping between acoustic emission and fault friction histories from numerical simulations, and generalizes to produce accurate predictions of laboratory fault friction. Notably, the predictions improve by further training the model latent space using only a portion of data from a single laboratory earthquake-cycle. The transfer learning results elucidate the potential of using models trained on numerical simulations and fine-tuned with small geophysical data sets for potential applications to faults in Earth.

Using Structural Geology and Cosmogenic Nuclide Dating to Infer the Slip Rate and Frictional Strength of the Active Mai’iu Low-Angle Normal Fault, Eastern Papua New Guinea

<p>Low-angle normal faults (LANFs) have induced debate due to their apparent non -Andersonian behaviour and lack of significant seismicity associated with slip. Dipping 21°/N, the Mai’iu Fault, located in the Woodlark Rift, Eastern Papua New Guinea is an active LANF that occupies a position at the transition between continental extension and seafloor spreading. Surface geomorphology indicates that the Mai’iu Fault scarp is not significantly eroded despite high rainfall and ~2900 m of relief. Based on modelling of regional campaign GPS data (Wallace et al., 2014) the Mai’iu Fault is thought to accommodate rapid (7–9 mm/yr) horizontal extension; however the slip rate of the Mai’iu Fault has not been directly validated. I use a range of methodologies, including field mapping, cosmogenic exposure dating, cosmogenic burial dating, and Mohr-Coulomb modelling, in order to provide new constraints on LANF strength and slip behaviour. I analyse the structure of conglomeratic strata within a back -rotated rider block atop the Mai’iu Fault surface. The Gwoira rider block is a large fault-bounded sedimentary rock slice comprising the Gwoira Conglomerate, located within a large synformal megamullion in the Mai’iu Fault surface. The Gwoira Conglomerate was originally deposited on the Mai’iu Fault hanging wall concurrent with extension, and has since been buried to a maximum depth of ~2 km (evidenced by modelling of vitrinite reflectance data, and structural analysis), back-tilted, and synformally folded. The Mai’iu Fault is also overlain by a large fault slice (the Gwoira rider block), that has been transferred from the previous LANF hanging wall to the current footwall by the initiation of the younger Gwoira Fault. Both the Gwoira Conglomerate (former hanging wall) and mylonitic foliation (footwall) of the Mai’iu Fault have been shortened ~E-W, perpendicular to the extension direction. I show that N-S trending synformal folding of the Gwoira Conglomerate was concurrent with on-going sedimentation and extension on the Mai’iu Fault. Structurally shallower Gwoira Conglomerate strata are folded less than deeper strata, indicating that folding was progressively accrued concurrent with ~N -S extension. I also show that abandonment of the inactive strand of the Mai’iu Fault in favour of the Gwoira Fault, which resulted in formation of the Gwoira rider block, occurred in response to progressive megamullion amplification and resultant misorientation of the inactive strand of the Mai’iu Fault. I attribute N-S trending synformal folding to extension-perpendicular constriction. This is consistent with numerous observations of outcrop-scale conjugate strike-slip faults that deform the footwall and hanging wall of the Mai’iu Fault (Little et al., 2015), and accommodate E-W shortening. Constrictional folding remains active in the near-surface as evidenced by synformal tilting of inferred Late Quaternary fluvial terraces atop the Gwoira rider block. In order to date this sequence of progressive constrictional folding, I have processed ten ²⁶Al/¹⁰Be terrestrial cosmogenic nuclide burial samples obtained from the Gwoira Conglomerate; unfortunately these data were not yet available at the time of printing, due to reasons outside of my control. I also present terrestrial cosmogenic nuclide (TCN) exposure ages for ten rock samples obtained from the lowermost Mai’iu Fault scarp at Biniguni Falls, in order to determine the Holocene slip-rate and style using cosmogenic ¹⁰Be in quartz. I model exposure age data after the approach of Schlagenhauf et al. (2011), using a Monte-Carlo simulation in which fault slip rate, the period of last slip on the fault, and local erosion rate are allowed to vary. Modelling evidences that the Mai’iu Fault at Biniguni Falls is active and slipping at 13.9±4.0 mm/yr (1σ), resolved over the last 13.2±2.7 ka (1σ). Modelling constrains the time of last slip to 2.9±1.4 ka (1σ); this is consistent with a seismic event at that time, followed by non-slip on the Mai’iu Fault until the present day. Finally, because rider block formation records abandonment of the uppermost part of a LANF, Coulomb fault mechanical analysis can be applied to field observations to provide an upper limit on LANF frictional strength (µf). Calculations are made in terms of Mohr-Coulomb mechanics, after the framework of Choi and Buck (2012). The lock-up (abandonment) orientation at any particular position on the Mai’iu Fault is principally a function of fault friction (µf), crustal friction (µc), fault cohesion (Cf), crustal cohesion (Cc), depth, fault orientation, fluid pressure, and the orientation of the greatest principle stress. Model results suggest that fault friction for the active Gwoira-Mai’iu Fault surface is 0.128≤μf≤0.265 for Cf<1.8 MPa, and 0.2≤μf≤0.265 for Cf≤0.5 MPa. Modelling of abandonment of the inactive Mai’iu Fault suggests that 0.26≤μf≤0.309 for Cf<1.8 MPa. This suggests that past slip on the inactive Mai’iu Fault, and continued slip on the active Gwoira-Mai’iu Fault, were enabled by low fault frictional strength. I also model the strength of the active Mai’iu Fault at Biniguni Falls; results suggest greater LANF friction (μf≥0.32) than the Gwoira-Mai’iu Fault surface, and inactive Mai’iu Fault. In order to explain active slip on the LANF at Biniguni Falls concurrent with widespread field observations of outcrop-scale faulting of the LANF footwall, I suggest a process whereby overall the LANF remains viable and active, but locally stress conditions exceed the LANF abandonment criteria; this results in highly localised and temporary ‘footwall damage’ where the LANF footwall is locally dissected by outcrop-scale faulting.</p>

Using Structural Geology and Cosmogenic Nuclide Dating to Infer the Slip Rate and Frictional Strength of the Active Mai’iu Low-Angle Normal Fault, Eastern Papua New Guinea

<p>Low-angle normal faults (LANFs) have induced debate due to their apparent non -Andersonian behaviour and lack of significant seismicity associated with slip. Dipping 21°/N, the Mai’iu Fault, located in the Woodlark Rift, Eastern Papua New Guinea is an active LANF that occupies a position at the transition between continental extension and seafloor spreading. Surface geomorphology indicates that the Mai’iu Fault scarp is not significantly eroded despite high rainfall and ~2900 m of relief. Based on modelling of regional campaign GPS data (Wallace et al., 2014) the Mai’iu Fault is thought to accommodate rapid (7–9 mm/yr) horizontal extension; however the slip rate of the Mai’iu Fault has not been directly validated. I use a range of methodologies, including field mapping, cosmogenic exposure dating, cosmogenic burial dating, and Mohr-Coulomb modelling, in order to provide new constraints on LANF strength and slip behaviour. I analyse the structure of conglomeratic strata within a back -rotated rider block atop the Mai’iu Fault surface. The Gwoira rider block is a large fault-bounded sedimentary rock slice comprising the Gwoira Conglomerate, located within a large synformal megamullion in the Mai’iu Fault surface. The Gwoira Conglomerate was originally deposited on the Mai’iu Fault hanging wall concurrent with extension, and has since been buried to a maximum depth of ~2 km (evidenced by modelling of vitrinite reflectance data, and structural analysis), back-tilted, and synformally folded. The Mai’iu Fault is also overlain by a large fault slice (the Gwoira rider block), that has been transferred from the previous LANF hanging wall to the current footwall by the initiation of the younger Gwoira Fault. Both the Gwoira Conglomerate (former hanging wall) and mylonitic foliation (footwall) of the Mai’iu Fault have been shortened ~E-W, perpendicular to the extension direction. I show that N-S trending synformal folding of the Gwoira Conglomerate was concurrent with on-going sedimentation and extension on the Mai’iu Fault. Structurally shallower Gwoira Conglomerate strata are folded less than deeper strata, indicating that folding was progressively accrued concurrent with ~N -S extension. I also show that abandonment of the inactive strand of the Mai’iu Fault in favour of the Gwoira Fault, which resulted in formation of the Gwoira rider block, occurred in response to progressive megamullion amplification and resultant misorientation of the inactive strand of the Mai’iu Fault. I attribute N-S trending synformal folding to extension-perpendicular constriction. This is consistent with numerous observations of outcrop-scale conjugate strike-slip faults that deform the footwall and hanging wall of the Mai’iu Fault (Little et al., 2015), and accommodate E-W shortening. Constrictional folding remains active in the near-surface as evidenced by synformal tilting of inferred Late Quaternary fluvial terraces atop the Gwoira rider block. In order to date this sequence of progressive constrictional folding, I have processed ten ²⁶Al/¹⁰Be terrestrial cosmogenic nuclide burial samples obtained from the Gwoira Conglomerate; unfortunately these data were not yet available at the time of printing, due to reasons outside of my control. I also present terrestrial cosmogenic nuclide (TCN) exposure ages for ten rock samples obtained from the lowermost Mai’iu Fault scarp at Biniguni Falls, in order to determine the Holocene slip-rate and style using cosmogenic ¹⁰Be in quartz. I model exposure age data after the approach of Schlagenhauf et al. (2011), using a Monte-Carlo simulation in which fault slip rate, the period of last slip on the fault, and local erosion rate are allowed to vary. Modelling evidences that the Mai’iu Fault at Biniguni Falls is active and slipping at 13.9±4.0 mm/yr (1σ), resolved over the last 13.2±2.7 ka (1σ). Modelling constrains the time of last slip to 2.9±1.4 ka (1σ); this is consistent with a seismic event at that time, followed by non-slip on the Mai’iu Fault until the present day. Finally, because rider block formation records abandonment of the uppermost part of a LANF, Coulomb fault mechanical analysis can be applied to field observations to provide an upper limit on LANF frictional strength (µf). Calculations are made in terms of Mohr-Coulomb mechanics, after the framework of Choi and Buck (2012). The lock-up (abandonment) orientation at any particular position on the Mai’iu Fault is principally a function of fault friction (µf), crustal friction (µc), fault cohesion (Cf), crustal cohesion (Cc), depth, fault orientation, fluid pressure, and the orientation of the greatest principle stress. Model results suggest that fault friction for the active Gwoira-Mai’iu Fault surface is 0.128≤μf≤0.265 for Cf<1.8 MPa, and 0.2≤μf≤0.265 for Cf≤0.5 MPa. Modelling of abandonment of the inactive Mai’iu Fault suggests that 0.26≤μf≤0.309 for Cf<1.8 MPa. This suggests that past slip on the inactive Mai’iu Fault, and continued slip on the active Gwoira-Mai’iu Fault, were enabled by low fault frictional strength. I also model the strength of the active Mai’iu Fault at Biniguni Falls; results suggest greater LANF friction (μf≥0.32) than the Gwoira-Mai’iu Fault surface, and inactive Mai’iu Fault. In order to explain active slip on the LANF at Biniguni Falls concurrent with widespread field observations of outcrop-scale faulting of the LANF footwall, I suggest a process whereby overall the LANF remains viable and active, but locally stress conditions exceed the LANF abandonment criteria; this results in highly localised and temporary ‘footwall damage’ where the LANF footwall is locally dissected by outcrop-scale faulting.</p>

Bayesian inference and Markov chain Monte Carlo based estimation of critical slip distance parameter in rate and state model for fault friction

We present an algorithmic framework to solve an inverse problem using Bayesian inference and Markov chain Monte Carlo sampling. The input of the inverse problem is the acceleration of the slipping seismogenic fault and the output is the probability distribution of the critical slip distance parameter of the rate and state model for fault friction.

Repeating caldera collapse events constrain fault friction at the kilometer scale

Fault friction is central to understanding earthquakes, yet laboratory rock mechanics experiments are restricted to, at most, meter scale. Questions thus remain as to the applicability of measured frictional properties to faulting in situ. In particular, the slip-weakening distance dc strongly influences precursory slip during earthquake nucleation, but scales with fault roughness and is challenging to extrapolate to nature. The 2018 eruption of K̄ılauea volcano, Hawaii, caused 62 repeatable collapse events in which the summit caldera dropped several meters, accompanied by MW 4.7 to 5.4 very long period (VLP) earthquakes. Collapses were exceptionally well recorded by global positioning system (GPS) and tilt instruments and represent unique natural kilometer-scale friction experiments. We model a piston collapsing into a magma reservoir. Pressure at the piston base and shear stress on its margin, governed by rate and state friction, balance its weight. Downward motion of the piston compresses the underlying magma, driving flow to the eruption. Monte Carlo estimation of unknowns validates laboratory friction parameters at the kilometer scale, including the magnitude of steady-state velocity weakening. The absence of accelerating precollapse deformation constrains dc to be ≤10 mm, potentially much less. These results support the use of laboratory friction laws and parameters for modeling earthquakes. We identify initial conditions and material and magma-system parameters that lead to episodic caldera collapse, revealing that small differences in eruptive vent elevation can lead to major differences in eruption volume and duration. Most historical basaltic caldera collapses were, at least partly, episodic, implying that the conditions for stick–slip derived here are commonly met in nature.