Differentiating frictionally locked asperities from kinematically coupled zones

TL;DR

The paper tackles differentiating frictionally locked asperities from kinematically coupled zones on plate-boundary faults by unifying locking physics under the yield criterion and deriving a friction-law–independent constraint for interseismic periods. It develops a transdimensional locking inversion that represents locked regions as circular asperities and estimates their configuration from GNSS data, revealing a belt-like locking pattern with a distinct eastern–western gap along the Nankai zone. Applied to onshore/offshore GNSS data, the method identifies five major asperities that align with offshore basins and correspond to historical megathrust rupture zones, while noting that slow earthquakes largely occur in coupled but unlocked regions. The study also discusses limitations of a binary locking description, the influence of Green's-function errors, and the need for higher-resolution rheology-informed models, offering a framework that links mechanical locking to slip deficit and stress loading with practical implications for seismic potential assessment.

Abstract

Seismogenic areas on plate-boundary faults resist slipping until earthquakes begin. The delay in slip relative to plate motion, termed slip deficit, represents plate coupling as an interseismic proxy of seismic potential. However, when a part of a frictional interface sticks together (locked), the unlocked sliding surroundings are braked and slowed (coupled), causing coupled zones always wider than the locked zones that rupture during earthquakes. This study investigates the frictional physics that locked and unlocked zones should observe, laying the foundation for inferring frictionally locked segments, known as asperities in fault mechanics. Various friction laws are shown to have a unified representation of locking. (I) Locking means the pre-yield phase, where the fault interface does not slip, and unlocking means the post-yield phase, where stress on the interface equals strength. (II) For intersesismic periods, while locking still denotes constant slip, unlocking signifies quasi-steady creeping of constant stress. Locking inversion, a variant of conventional coupling inversion that incorporates this unified frictional physics, estimates the distribution of locking, determining slip and stress distributions consequently. We solve the locking inversion by a method that distributes circular asperities on unlocked interfaces. By applying this method to on-/off-shore GNSS data in southwestern Japan, we detect five primary locked segments along the Nankai subduction zone. Those segments accord with slip zones of historical megathrust earthquakes correlated with seafloor basins. Estimated locked zones avoid the occurrence zones of deep slow earthquakes, reproducing the hypothesis that the areas hosting slow earthquakes are normally, in interseismic timescales, coupled but unlocked.

Figures (11)

• Figure 1: Relationship among the slip deficit rate $\dot s_{\rm d}$, slip rate $\dot s$, and long-term subduction rate $V_{\rm pl}$, shown in the inertial coordinate of the hangingwall. The slip is decomposed into long-term part $V_{\rm pl}$ and the residual $\dot s_{\rm d}$. Assuming that crustal deformation from $V_{\rm pl}$ (dotted lines in the figure) is negligible, the slip deficit inversion ascribes observed surface deformation to $\dot s_{\rm d}$. This approximation corresponds to identifying the subduction at $V_{\rm pl}$ as an approximately traction-free solution.
• Figure 2: Frictional behaviors under the yield criterion (eq. \ref{['eq:yieldinglaw']}) and the complementarity between the rates of slip $s$ and stress loading $T$ (eq. \ref{['eq:complementarity_stressingsliprates']}), exemplified by a biaxial test. Until the stress reaches its threshold $\Phi$, the stress increases in proportion to the strain $\epsilon$ without sliding (pre-yield: locked). After the stress reaches the strength, the interface slips so that the stress matches the strength (post-yield: unlocked). Different friction laws give different unlocked behaviors depending on the time evolution laws of the strength (eq. \ref{['eq:complementarity_strengthexcess']}). Meanwhile, for the quasi-stationary behaviors outside the moment of faulting (gray in the figure), all friction laws give either zero slip rate or zero stress rate (eq. \ref{['eq:complementarity_stressingsliprates']}), and the former is locked, and the latter is unlocked.
• Figure 3: Spatial patterns of coupling, locking, and stressing, expected from the slip-rate-stressing-rate complementarity (eq. \ref{['eq:locking_constraint']}). A typical two-dimensional solution is visualized with a schematic, especially around the boundary of a locked zone and an unlocked zone. The gray region masked in Fig. \ref{['fig:lcs_rel']} corresponds to the gray region in Fig. \ref{['fig:yielding_strength']} and represents the very vicinity of the locked zone tip, to which eq. (\ref{['eq:locking_constraint']}) does not apply due to the artifact of divergent stress above the strength.
• Figure 4: Transdimensional parametrization of locked zones. Locked zones are decomposed into $n_{\rm p}$ segments, denoted by $A_n$, parametrized by center locations ${\bf x}_n^{\rm (C)}$ and radii $r_n$. While transdimensional schemes of slip deficit inversions (here called coupling inversion) superpose constant slip-deficit-rate zones on a slip-deficit-free boundary, transdimensional locking inversions superpose locked segments, where $\dot s_{\rm d}=V_{\rm pl}$, on a traction-free boundary, where $\dot T=0$.
• Figure 5: The optimal estimate of our locking inversion. Maximum likelihood estimation is employed for the configuration optimization of circular asperities. The number of asperities is optimized by the BIC. (a) The optimal locking-parameter field $\Psi$. (b) The coupling field $\dot s_{\rm d}/V_{\rm pl}$ computed from the optimal locking-parameter field. Observed and modeled surface displacements are indicated by arrows. (c) The stressing field $\dot T$ computed from the optimal locking-parameter field. Stressing rates greater than 15 kPa/year are rounded, given the unresolvable stress concentration at the crack tip. Artificial stress concentration right beneath the trough is masked for visibility.