The future Community-Driven SCEC SEAS Code Comparisons for [1] Three-Dimensional fluid injection and [2] a Two-Dimensional dipping fault with variable normal traction.

Numerical simulations of Sequences of Earthquakes and Aseismic Slip (SEAS) have rapidly progressed to address fundamental problems in fault mechanics and provide self-consistent, physics-based frameworks to interpret and predict geophysical observations across spatial and temporal scales. Challenges in SEAS modeling include resolving the multiscale interactions between slow slip, earthquake nucleation, and dynamic rupture; and understanding the physical factors controlling observables such as seismicity and deformation. To advance SEAS simulations with rigor and reproducibility, we pursue community efforts to verify numerical codes in an expanding suite of benchmarks, including problems considering earthquake sequences on 2D and 3D fault models obeying rate-and-state friction with different treatments of inertial effects and fault dip under slow tectonic loading (Erickson et al., 2020; Jiang et al., 2022; Erickson et al., 2023).Here we present code comparison results from a new set of benchmark problems that focus on aseismic processes and earthquake nucleation, including the influence of (1) changes in effective normal stress and pore fluid pressure due to fluid injection and diffusion and (2) different formulations of fault friction evolution. Benchmark problem BP6-QD-A/S/C is a 2D problem that considers a single aseismic slip transient induced by changes in pore fluid pressure consistent with fluid injection and diffusion in fault models with different treatments of fault friction, including rate-and-state fault models using the aging (-A) and slip (-S) law formulations for frictional state evolution, respectively, as well as a constant friction coefficient (-C). BP7-QD/FD-A/S is a 3D problem with a 2D rate-and-state fault considering a circular velocity-weakening asperity that can produce sequences of repeating earthquakes or alternating seismic and aseismic ruptures, under different considerations of fault friction evolution and inertial effects. Comparisons of problems using the aging versus slip law illustrate how models of seismic and aseismic slip can differ in the timing and amount of slip achieved with different treatments of fault friction, including for individual aseismic slip events induced by the same perturbations in pore fluid pressure for BP6. We utilize simulations from different groups to explore how various numerical factors affect the simulated evolution of pore pressure and interaction between aseismic and seismic processes. We achieve excellent quantitative agreement across participating codes that utilize distinct numerical methods, by ensuring sufficiently fine time-stepping, large enough domain size for volumetric methods and consistent treatment of boundary conditions. Through these comparative studies, we seek to determine best practices for improving the accuracy and efficiency of SEAS simulations and develop quantitative metrics for benchmarking modeling results. These community-led exercises will foster the development of more realistic multi-physics SEAS models and their integration with geophysical observations, contributing to an improved understanding of fault dynamics.

SUMMARYWe present a 2-D thermomechanical computational framework for simulating earthquake sequences in a non-linear visco-elasto-plastic compressible medium. The method is developed for a plane-strain problem and incorporates an invariant formulation of the classical rate- and state-dependent friction law and an adaptive time-stepping, which allows the time step to vary by many orders of magnitude during a simulation. Long-term tectonic convergence is imposed by displacing a boundary at a constant rate, whereas temperature-dependent viscosity is solved using a rapidly converging Newton–Raphson scheme. The 2-D volume is discretized using finite differences on a fully staggered grid and marker-in-cell techniques. An adaptive free-surface approximation is used to modulate the air viscosity with the time step, which allows stresses to vanish on the free surface during the propagation of fast slipping events. We present a set of increasingly complex models in which we investigate how inertia, radiation damping, thermally activated non-linear rheology and off-megathrust splay-fault events affect sequences of seismic and aseismic slip on a simplified subduction megathrust. The new method provides a unique computational framework to analyse earthquake sequences and to connect forearc deformation with the dynamic properties of the megathrust, thus providing a physical link between observations spanning from slow interseismic strain accumulation to localized coseismic slip of individual earthquakes and post-seismic viscoelastic relaxation.

Internal and surface wave production in a stratified fluid

Effects of free surface on development of turbulent boundary layer and wake fields were investigated. By measuring flow field around a surface piercing cylinder in various advance speed conditions in a towing tank, free surface effects were identified. A towed underwater Stereoscopic Particle Image Velocimetry (SPIV) system was used to measure the flow field under free surface. The cross section of the test model was water plane shape of the Wigley hull, of which longitudinal length and width were 1.0 m and 100 mm, respectively. With sharp bow shape and slender cross section, flow separation was not expected in two-dimensional flow. Flow fields near the free-surface and in deep location that two-dimensional flow field was expected were measured and compared to identify free-surface effects. Some planes perpendicular to longitudinal direction near the model surface and behind the model were selected to track development of turbulent boundary layer. Froude numbers of the test conditions were from 0.126 to 0.40 and corresponding Reynolds numbers were from 395,000 to 1,250,000. In the lowest Froude number condition, free-surface wave was hardly observed and only free surface effects without surface wave could be identified while violent free-surface behavior due to wave-induced separation dominated the flow fields in the highest Froude number condition. From the instantaneous velocity fields, Time-mean velocity, turbulence kinetic energy, and flow structure derived by proper orthogonal decomposition (POD) were analyzed. As the free-surface effect, development of retarded wake, free-surface waves, and wave-induced separation were mainly observed.

This paper presents the minimum submergence depth of an underwater vehicle that can remove the effect of free surface on the resistance of the underwater vehicle. The total resistance of the underwater vehicle in fully submerged modes comprises only viscous pressure and friction resistances, and no wave resistance should be present, based on the free surface effect. In a model test performed in this study, the resistance is measured in the range of 2 to 10 kn (1.03–5.14 m/s) under depth conditions of 850 mm (2.6D) and 1250 mm (3.8D), respectively, and the residual resistance coefficients are compared. Subsequently, resistance analysis is performed via computational fluid dynamics (CFD) simulation to investigate the free surface effect based on various submergence depths. First, the numerical analysis results in the absence of free surface conditions and the model test results are compared to show the tendency of the resistance coefficients and the reliability of the CFD simulation results. Subsequently, numerical analysis results of submergence depth presented in a reference paper are compared with the model test results. These two sets of results confirm that the resistance increased due to the free surface effect as the high speed and depth approach the free surface. Therefore, to identify a fully submerged depth that is not affected by the free surface effect, case studies for various depths are conducted via numerical analysis, and a correlation for the fully submerged depth based on the Froude number of an underwater vehicle is derived.

Free surface effects on the thermodynamics and glass formation in simple monatomic supercooled liquids with the Lennard-Jones--Gauss interaction potential were studied by the molecular dynamics simulations. Glass with two free surfaces was obtained by cooling from the melt. We found the following important new results: Free surfaces significantly enhance atomic mobility in the system compared to that of the bulk and induce the formation of so-called layer structure of the interior of both liquid and glassy states. A mobile surface layer in the system exists for a wide temperature range; i.e., the thickness of the mobile surface layer and the discrepancy between atomic mobility in the surface and that in the interior have a tendency to increase with temperature. The atomic mechanism of glass formation in supercooled liquids with free surfaces exhibits ``heterogeneouslike'' behavior, unlike the ``homogeneous'' behavior observed in the bulk; i.e., the solidlike ``domain'' initiates/enhances in the interior and simultaneously grows outward to the surface to form a glassy solid phase. The interior of glass with free surfaces exhibits a stronger local icosahedral order compared to that of the bulk, and it may lead to higher stability of the glassy state compared to that of the latter. In contrast, the surface shell has a more porous structure and contains a large number of undercoordinated sites.

Repeating earthquakes most often occur as frequent small magnitude events, with repeating time increasing with magnitude. The Bárðarbunga caldera however is a rare example where moderate magnitudes (Mw ≥ 5) repeat frequently. During the 6 months caldera collapse event (2014-2015), 77 Mw ≥ 5 earthquakes were recorded and, in the years following the collapse, observations show quasi-periodic Mw ≥ 5 events. Recent seismological field campaigns have provided further constraints on the caldera’s geometry, mapping out a ring fault structure and offering excellent depth constraints. The repetitive nature of the earthquake sequences and good structural controls, make this case especially suitable to investigate using Sequences of Earthquakes and Aseismic Slip (SEAS) models. Furthermore, the periodicity of the ring fault is well captured to the first order by adopting a Spectral Boundary Integral approach. To mimic the observed data, we project relatively relocated seismic events to a mesh representation of the ring fault; we then convert the projected point clusters into frictional parameter maps that define the distribution of the rate weakening and rate strengthening asperities in the simulation. Finally, we quantify the differences between the simulated results and the observed seismic data by comparing for example reoccurrence time, magnitudes and partial rupture characteristics. We use the JAX Python library to achieve well resolved simulations, realistic frictional parameters and domain size. This library provides tools such as Just-In-Time (JIT) and Ahead-Of-Time (AOT) compilation, automatic differentiation and vectorization, all of which significantly speed up runtime. Moreover, JAX provides a flexible framework for running code on different accelerators such as GPUs, drastically reducing code runtime for parallelizable operations such as FFT computations. 

The effect of free surfaces on the glass transition temperature (T(g)) of thin polystyrene films was studied. Measurements were performed on films (8 nm<h<290 nm) with one free surface and on films capped with a 5 nm thick metal layer (no free surfaces). Potential problems with evaporative deposition were eliminated by studying samples made of two supported films placed with their free surfaces in contact and annealed. Uncapped films displayed reduced T(g) values for h less, similar 40 nm while all "properly" capped films exhibited a T(g) value the same as that of the bulk polymer (370+/-1 K). When the free surface was restored, the measured T(g) values the same as those of uncapped films of the same thickness. These results show that free surfaces are crucial for observing T(g) reductions in thin polymer films and address the role of the sample preparation history.

Unsteady characteristics of cloud cavitating flow near the free surface around an axisymmetric projectile

Recent advances in both experimental and numerical research have led to a better understanding of the phenomenon of cavitation. However, in most marine applications of lifting surfaces, operating near the free surface, cavitation is often unavoidable and should be considered in the early design stages. Even in the era of multiphase flow simulations, only a few works treat the problem of cavitating hydrofoils with free surface effects, mainly due to the high computational cost and complexity. On the contrary, lower-fidelity models based on ideal flow can be used to predict sheet cavitation at significantly lower computational cost with acceptable accuracy, by treating the attached cavity as a free boundary and using cavity termination models that bring simulated results closer to experimental data. In this work an adjoint-based prediction model for partially cavitating hydrofoils that move steadily beneath the free surface is proposed. Following an inverse problem formulation, at each optimization cycle the shape of the attached cavity and the corresponding cavitation number are approximated under the given cavity length assumption using sensitivities derived analytically via the continuous adjoint method. The objective function is evaluated using a source-vorticity BEM solver and the cavity boundary is parametrized using B-splines. The proposed numerical scheme compared against other potential-based methods is found to predict well the effects of free-surface on cavity shape and cavitation number at various submergence depths and Froude numbers. To conclude, the proposed lower-fidelity numerical scheme could facilitate the preliminary design of lifting surfaces with, or without, free-surface effects.

In this article, we analyzed the recent seismic activity in the northern Montney Play of British Columbia in 2015 and its connection with fluid injection (hydraulic fracturing and long‐term injection of gas and wastewater disposal) in the region. The earthquake sequence used in this study includes 676 events from 3 October 2014 to 31 December 2015 from the Progress Energy earthquake catalog with moment magnitude as small as 1. Spatial and temporal correlation of seismic activity with the fluid injection in the region revealed that these events are better correlated with hydraulic fracturing (correlation coefficient of ∼0.17 at confidence level close to 99.7%, with a lag time between 0 and 2 days) than other types of injection. Using the double‐difference relocation technique, we obtained depth constraints for some of the events for which supplementary, industry‐provided waveforms were available. The depths of these events range from 0.5 to 2.5 km and are mostly constrained above the target zone where hydraulic fracturing was taking place. The best‐fit moment tensor solution for the event on 17 August 2015 gives a moment magnitude of 4.6 and a predominantly thrust mechanism in the northwest–southeast direction with a shallow focal depth of 4 km. This is consistent with that obtained through double‐difference relocation for this event (1.3 km), given the depth uncertainty of the moment tensor inversion. [Electronic Supplement:][1] Tables of injection volumes and seismicity parameters, and figure of monthly distribution of seismic events and location of fluid injection sites in the vicinity of the 17 August 2015 M w 4.6 event. [1]: http://www.bssaonline.org/lookup/suppl/doi:10.1785/0120160175/-/DC1

The Bedretto Underground Laboratory for Geosciences and Geoenergies (BedrettoLab) is a deep underground laboratory in the southern Swiss alps that allows to induce and study rock deformation processes in situ, from exceptionally short distances, at 1 km depth. In the context of the Fault Activation and Earthquake Rupture (FEAR) project, we have conducted a series of fluid injection experiments, with the goal of inducing an ML~0.0 earthquake. In this 'M-zero' experiment series, we have used a custom-built remote control system to implement fluid injection protocols that were informed by 2D continuum hydro-mechanical earthquake cycle models, with the target of increasing the likelihood of inducing a larger event. In the first of two major experiments, after 16 hours of high pressure (20 MPa) fluid injection, we have induced a Mw~ -0.4 "main shock", which triggered an aftershock sequence with &gt;100 events in the first 3 seconds alone. The fluid injection was stopped 10 minutes after this main shock.The experiment and earthquake sequence was recorded on an extensive multi-domain and multi-scale 3D monitoring array, which combines various types of seismic sensors with distributed acoustic, strain and temperature sensing, Fibre Bragg Grating strain sensors, as well as pressure and flow monitoring. Although the main shock magnitude is smaller than the target magnitude (which was unclear at the time of its occurrence), the wide range of observations made, including high-resolution micro-seismicity catalogues covering 5 units of magnitude, offer a detailed look at seismological and rock mechanic processes before, during and after the main shock. In this talk we summarize some of the key observations and insights including i) the foreshock sequence, which shows signatures of a triggering cascade but which did not accelerate before the main shock; ii) a distinct Gutenberg-Richter b-value anomaly where the main shock occurred, and which may reflect the structural inventory and stress state of the activated fracture network; iii) the first-order consistency between early aftershock distributions and kinematic rupture models from spectral fitting, and a pronounced aftershock gap across a 2-by-2 metre patch where the main shock occurred, iv) static deformation patterns resolved on the strain sensor network, and their consistency with the focal mechanisms inferred from seismic data. We also discuss the implications for the planned fault activation experiments in the coming three years at the BedrettoLab.

In this study, two dimensional unsteady flows of cylinder and cylinder with additional fairing close to a free surface were numerically investigated. The governing momentum equations were solved by using the Semi Implicit Method for Pressure Linked Equations(SIMPLE). The Volume of Fluid(VOF) method applied to simulate a free surface. Non- uniform grid structures were used in the simulation with denser grids near the cylinder. Under the conditions of Reynolds number 150624, 271123, 210874 and 331373, the cylinders were simulated with different depths of invasion. It was shown that the flow characteristics were influenced by submergence depth and Reynolds numbers. When the cylinder close to the free surface, the drag coefficient, lift coefficient and Strouhal numbers will increase due to the effect of free liquid surface on vortex shedding. With additional fairing, can effectively reduce the influence of the free surface on the drag coefficient. Fairing will reduce lift coefficient at high Reynolds numbers, but increase lift coefficient when Reynolds numbers are small. Fairing can effectively reduce Strouhal numbers, thus can well suppress the vortex induced vibration

The 2012 Brawley swarm triggered by injection-induced aseismic slip

The flow structure in the cross-sectional and spanwise planes of a turbulent round jet interacting with a free surface has been studied using planar particle image velocimetry. The submerged jet was positioned at an offset height of 5d below the free surface, where d is the nozzle diameter. Measurements were conducted in both streamwise-surface-normal (x-y) and nine streamwise-spanwise (x-z) planes (−4 ≤ y/d ≤ 4) located in the far-field (x/d = 42–62) at an exit Reynolds number of 28 000. To highlight the effects of the free surface, measurements were also performed to evaluate the characteristics of a reference free jet at similar initial conditions. For each jet, the spanwise planes were used to reconstruct the three-dimensional (3D) averaged velocity field to reveal the salient flow features in the cross section of the jet. The reconstruction shows the presence of the well-known surface current, which is usually prominent in the far-field of surface jets. The spanwise development of the surface current is found to reduce the streamwise and spanwise Reynolds normal stresses in the upper shear layer of the surface jet, but the Reynolds shear stress and its associated dominant quadrant motions in the spanwise plane are enhanced near the free surface. As the free surface is approached, the spanwise spread rate increases, but the local vorticity thickness decreases due to the enhancement of the mean shear in the spanwise direction. Two-point spatial correlations are used to show that the large-scale structures near the free surface undergo oblique stretching in the spanwise plane to augment the wider spanwise growth of the surface current. The spatial distributions of the energetic modes based on proper orthogonal decomposition also reveal interesting features near the free surface that are consistent with the inclination of the turbulent structures relative to the flow direction.