Fault volume digital twin to reproduce the full slip spectrum, scaling and statistical laws

Abstract

Seismological and geodetic observations of fault zones reveal diverse slip dynamics, scaling, and statistical laws. Existing mechanisms explain some but not all of these behaviors. We show that incorporating an off-fault damage zone-characterized by distributed fractures surrounding a main fault-can reproduce many key features observed in seismic and geodetic data. We model a 2D shear fault zone in which off-fault cracks follow power-law size and density distributions, and are oriented either optimally or parallel to the main fault. All fractures follow rate-and-state friction with parameters enabling slip instabilities. We do not introduce spatial heterogeneities in frictional properties. Using quasi-dynamic boundary integral simulations accelerated by hierarchical matrices, we simulate slip dynamics and analyze events produced both on and off the main fault. Despite spatially uniform frictional properties, we observe a natural continuum from slow to fast ruptures, as seen in nature. Our simulations reproduce the Omori law, inverse Omori law, Gutenberg-Richter scaling, and moment-duration scaling. We observe seismicity localizing toward the main fault before nucleation of main-fault events. During slow slip events, off-fault seismicity migrates in patterns resembling fluid diffusion fronts, despite the absence of fluids. We show that tremors, Very Low Frequency Earthquakes, Low Frequency Earthquakes, Slow Slip Events, and earthquakes can all emerge naturally within this fault volume framework, making it an ideal digital twin for testing hypotheses, performing ground-truth inversions, and probing mechanical properties inaccessible with natural observations.

Figures (16)

• Figure 1: Fault volume geometry of a case study: a) sketch of fault volume geometry (not to scale): the main fault in black and the off-fault fractures in red b) off-fault fracture density perpendicular to the main fault (linear scale) c) Frequency of length distribution of the faults, including the main fault d) rose diagram of off-fault fracture orientations and principal stress direction e) critical slip distance of all fractures with respect to their length. RL and LL stands for right and left lateral slip respectively.
• Figure 2: Time series of the moment rate $\dot{M}_0$. The black curve represents the contribution coming from the main rough fault, and the red curve represents the summation of the moment rate released by all the fractures. Panel a) The entire seismic cycle. Top x-axis is absolute time in years, and bottom x-axis is time normalized by recurrence time of earthquakes when considering only the main rough fault, without a damage zone ($\sim 62$ years). Panel b), c) and d) show time snapshots of the seismic cycle to highlight certain events. Here x-axis is relative time for the corresponding time snapshot. The spatiotemporal description of these events are shown in Figure \ref{['slip-rate-profile']}. Panel e) shows the catalog built from the above continuous moment-rate results using slip velocity threholds as described in section \ref{['catalog']}.
• Figure 3: Sequences of slip rate profiles on the main fault. Top x-axis is average slip accumulated during the specific time sequence. Left y-axis represents the along-strike distance on the main fault. Horizontal colored lines show the specific durations for different phases of the rupture sequence, with blue lines indicating slow phases and red lines indicating fast phases. Nucleation and afterslip phases are indicated by two blue lines at the beginning and end of fast events. The colormap represents slip rate. Black circles represent events detected on the fractures, and projected onto the main fault strike. Yellow stars represent the epicenters of the different events. Panel a) shows complex partial ruptures on the main fault. Panel b) shows one slow slip event. Panel c) shows a full rupture on the main fault. Panel d) shows an event, nucleated from one end of the fault and accelerated in a cascading process.
• Figure 4: Moment-rate functions (MRFs) (left panels), and their spectra (right panels), across different $M_w$ ranges for both off-fault and main fault events. (a) Selected MRFs from slow and fast events in the off-fault region within a narrow range of $-0.9 \leq M_w \leq -0.8$. (b) Same as (a), but for $-0.3 \leq M_w \leq -0.2$. (c) MRFs from main fault events, and their spectra, with fast ruptures in the range $2.2 \leq M_w \leq 3.8$ and slow slip events in the range $2.4 \leq M_w \leq 4.8$.
• Figure 5: MRF shapes for slow and fast events after normalization by centroid time with colors indicating moment magnitude. Panels (a) and (b) correspond to slow events in the off-fault region for the same magnitude ranges as in Figures \ref{['MRF_spectra']}a and \ref{['MRF_spectra']}b. (c) shows slow events on the main fault. Panels (d) and (e) correspond to fast off-fault events with the same $M_w$ ranges as in (a) and (b). (f) Fast events on the main fault.